Evolution of the DeNOC-based dynamic modelling for multibody systems

Directory of Open Access Journals (Sweden)

S. K. Saha

2013-01-01

Full Text Available Dynamic modelling of a multibody system plays very essential role in its analyses. As a result, several methods for dynamic modelling have evolved over the years that allow one to analyse multibody systems in a very efficient manner. One such method of dynamic modelling is based on the concept of the Decoupled Natural Orthogonal Complement (DeNOC matrices. The DeNOC-based methodology for dynamics modelling, since its introduction in 1995, has been applied to a variety of multibody systems such as serial, parallel, general closed-loop, flexible, legged, cam-follower, and space robots. The methodology has also proven useful for modelling of proteins and hyper-degree-of-freedom systems like ropes, chains, etc. This paper captures the evolution of the DeNOC-based dynamic modelling applied to different type of systems, and its benefits over other existing methodologies. It is shown that the DeNOC-based modelling provides deeper understanding of the dynamics of a multibody system. The power of the DeNOC-based modelling has been illustrated using several numerical examples.

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact

International Nuclear Information System (INIS)

Li Qing; Wang Tianshu; Ma Xingrui

2009-01-01

Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted flexible beam is investigated. The Hertzian contact law is used to describe the impact process, and the dynamic equations are formulated in the floating frame of reference using the assumed mode method. The two important geometric nonlinear effects of the flexible beam are taken into account, i.e., the longitudinal foreshortening effect due to the transverse deformation, and the stress stiffness effect due to the axial force. The simulation results show that good consistency can be obtained with the nonlinear finite element program ABAQUS/Explicit if proper geometric nonlinearities are included in the floating frame formulation. Specifically, only the foreshortening effect should be considered in a pure transverse impact for efficiency, while the stress stiffness effect should be further considered in an oblique case with much more computational effort. It also implies that the geometric nonlinear effects should be considered properly in the impact dynamic analysis of more general flexible multibody systems

Constraint Embedding Technique for Multibody System Dynamics

Science.gov (United States)

Woo, Simon S.; Cheng, Michael K.

2011-01-01

Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with

Substructured multibody molecular dynamics.

Energy Technology Data Exchange (ETDEWEB)

Grest, Gary Stephen; Stevens, Mark Jackson; Plimpton, Steven James; Woolf, Thomas B. (Johns Hopkins University, Baltimore, MD); Lehoucq, Richard B.; Crozier, Paul Stewart; Ismail, Ahmed E.; Mukherjee, Rudranarayan M. (Rensselaer Polytechnic Institute, Troy, NY); Draganescu, Andrei I.

2006-11-01

We have enhanced our parallel molecular dynamics (MD) simulation software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator, lammps.sandia.gov) to include many new features for accelerated simulation including articulated rigid body dynamics via coupling to the Rensselaer Polytechnic Institute code POEMS (Parallelizable Open-source Efficient Multibody Software). We use new features of the LAMMPS software package to investigate rhodopsin photoisomerization, and water model surface tension and capillary waves at the vapor-liquid interface. Finally, we motivate the recipes of MD for practitioners and researchers in numerical analysis and computational mechanics.

Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach

Energy Technology Data Exchange (ETDEWEB)

Wu, Long, E-mail: L.Wu-1@tudelft.nl [Delft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering (Netherlands); Tiso, Paolo, E-mail: ptiso@ethz.ch [ETH Zürich, Institute for Mechanical Systems (Switzerland)

2016-04-15

An effective reduction technique is presented for flexible multibody systems, for which the elastic deflection could not be considered small. We consider here the planar beam systems undergoing large elastic rotations, in the floating frame description. The proposed method enriches the classical linear reduction basis with modal derivatives stemming from the derivative of the eigenvalue problem. Furthermore, the Craig–Bampton method is applied to couple the different reduced components. Based on the linear projection, the configuration-dependent internal force can be expressed as cubic polynomials in the reduced coordinates. Coefficients of these polynomials can be precomputed for efficient runtime evaluation. The numerical results show that the modal derivatives are essential for the correct approximation of the nonlinear elastic deflection with respect to the body reference. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.

Modeling multibody systems with uncertainties. Part II: Numerical applications

Energy Technology Data Exchange (ETDEWEB)

Sandu, Corina, E-mail: csandu@vt.edu; Sandu, Adrian; Ahmadian, Mehdi [Virginia Polytechnic Institute and State University, Mechanical Engineering Department (United States)

2006-04-15

This study applies generalized polynomial chaos theory to model complex nonlinear multibody dynamic systems operating in the presence of parametric and external uncertainty. Theoretical and computational aspects of this methodology are discussed in the companion paper 'Modeling Multibody Dynamic Systems With Uncertainties. Part I: Theoretical and Computational Aspects .In this paper we illustrate the methodology on selected test cases. The combined effects of parametric and forcing uncertainties are studied for a quarter car model. The uncertainty distributions in the system response in both time and frequency domains are validated against Monte-Carlo simulations. Results indicate that polynomial chaos is more efficient than Monte Carlo and more accurate than statistical linearization. The results of the direct collocation approach are similar to the ones obtained with the Galerkin approach. A stochastic terrain model is constructed using a truncated Karhunen-Loeve expansion. The application of polynomial chaos to differential-algebraic systems is illustrated using the constrained pendulum problem. Limitations of the polynomial chaos approach are studied on two different test problems, one with multiple attractor points, and the second with a chaotic evolution and a nonlinear attractor set. The overall conclusion is that, despite its limitations, generalized polynomial chaos is a powerful approach for the simulation of multibody dynamic systems with uncertainties.

Modeling multibody systems with uncertainties. Part II: Numerical applications

International Nuclear Information System (INIS)

Sandu, Corina; Sandu, Adrian; Ahmadian, Mehdi

2006-01-01

This study applies generalized polynomial chaos theory to model complex nonlinear multibody dynamic systems operating in the presence of parametric and external uncertainty. Theoretical and computational aspects of this methodology are discussed in the companion paper 'Modeling Multibody Dynamic Systems With Uncertainties. Part I: Theoretical and Computational Aspects .In this paper we illustrate the methodology on selected test cases. The combined effects of parametric and forcing uncertainties are studied for a quarter car model. The uncertainty distributions in the system response in both time and frequency domains are validated against Monte-Carlo simulations. Results indicate that polynomial chaos is more efficient than Monte Carlo and more accurate than statistical linearization. The results of the direct collocation approach are similar to the ones obtained with the Galerkin approach. A stochastic terrain model is constructed using a truncated Karhunen-Loeve expansion. The application of polynomial chaos to differential-algebraic systems is illustrated using the constrained pendulum problem. Limitations of the polynomial chaos approach are studied on two different test problems, one with multiple attractor points, and the second with a chaotic evolution and a nonlinear attractor set. The overall conclusion is that, despite its limitations, generalized polynomial chaos is a powerful approach for the simulation of multibody dynamic systems with uncertainties

Rigid multibody system dynamics with uncertain rigid bodies

Energy Technology Data Exchange (ETDEWEB)

Batou, A., E-mail: anas.batou@univ-paris-est.fr; Soize, C., E-mail: christian.soize@univ-paris-est.fr [Universite Paris-Est, Laboratoire Modelisation et Simulation Multi Echelle, MSME UMR 8208 CNRS (France)

2012-03-15

This paper is devoted to the construction of a probabilistic model of uncertain rigid bodies for multibody system dynamics. We first construct a stochastic model of an uncertain rigid body by replacing the mass, the center of mass, and the tensor of inertia by random variables. The prior probability distributions of the stochastic model are constructed using the maximum entropy principle under the constraints defined by the available information. The generators of independent realizations corresponding to the prior probability distribution of these random quantities are further developed. Then several uncertain rigid bodies can be linked to each other in order to calculate the random response of a multibody dynamical system. An application is proposed to illustrate the theoretical development.

Linking rigid multibody systems via controllable thin fluid films

DEFF Research Database (Denmark)

Estupinan, Edgar Alberto; Santos, Ilmar

2009-01-01

, this paper gives a theoretical contribution to the combined fields of fluid–structure interaction and vibration control. The methodology is applied to a reciprocating linear compressor, where the dynamics of the mechanical components are described with help of multibody dynamics. The crank is linked......This work deals with the mathematical modelling of multibody systems interconnected via thin fluid films. The dynamics of the fluid films can be actively controlled by means of different types of actuators, allowing significant vibration reduction of the system components. In this framework...... to the rotor via a thin fluid film, where the hydrodynamic pressure is described by the Reynolds equation, which is modified to accommodate the controllable lubrication conditions. The fluid film forces are coupled to the set of nonlinear equations that describes the dynamics of the reciprocating linear...

Unconditionally Energy Stable Implicit Time Integration: Application to Multibody System Analysis and Design

DEFF Research Database (Denmark)

Chen, Shanshin; Tortorelli, Daniel A.; Hansen, John Michael

1999-01-01

of ordinary diffferential equations is employed to avoid the instabilities associated with the direct integrations of differential-algebraic equations. To extend the unconditional stability of the implicit Newmark method to nonlinear dynamic systems, a discrete energy balance is enforced. This constraint......Advances in computer hardware and improved algorithms for multibody dynamics over the past decade have generated widespread interest in real-time simulations of multibody mechanics systems. At the heart of the widely used algorithms for multibody dynamics are a choice of coordinates which define...... the kinmatics of the system, and a choice of time integrations algorithms. The current approach uses a non-dissipative implict Newmark method to integrate the equations of motion defined in terms of the independent joint coordinates of the system. The reduction of the equations of motion to a minimal set...

Planar multibody dynamics formulation, programming and applications

CERN Document Server

Nikravesh, Parviz E

2007-01-01

Introduction Multibody Mechanical Systems Types of Analyses Methods of Formulation Computer Programming Application Examples Unit System Remarks Preliminaries Reference Axes Scalars and Vectors Matrices Vector, Array, and Matrix Differentiation Equations and Expressions Remarks Problems Fundamentals of Kinematics A Particle Kinematics of a Rigid Body Definitions Remarks Problems Fundamentals of Dynamics Newton's Laws of Motion Dynamics of a Body Force Elements Applied Forces Reaction Force Remarks Problems Point-Coordinates: Kinematics Multipoint

System Theory Aspects of Multi-Body Dynamics.

Science.gov (United States)

1978-08-18

systems are described from a system theory point of view. Various system theory concepts and research topics which have applicability to this class of...systems are identified and briefly described. The subject of multi-body dynamics is presented in a vector space setting and is related to system theory concepts. (Author)

Static analysis of large-scale multibody system using joint coordinates and spatial algebra operator.

Science.gov (United States)

Omar, Mohamed A

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

First order sensitivity analysis of flexible multibody systems using absolute nodal coordinate formulation

International Nuclear Information System (INIS)

Pi Ting; Zhang Yunqing; Chen Liping

2012-01-01

Design sensitivity analysis of flexible multibody systems is important in optimizing the performance of mechanical systems. The choice of coordinates to describe the motion of multibody systems has a great influence on the efficiency and accuracy of both the dynamic and sensitivity analysis. In the flexible multibody system dynamics, both the floating frame of reference formulation (FFRF) and absolute nodal coordinate formulation (ANCF) are frequently utilized to describe flexibility, however, only the former has been used in design sensitivity analysis. In this article, ANCF, which has been recently developed and focuses on modeling of beams and plates in large deformation problems, is extended into design sensitivity analysis of flexible multibody systems. The Motion equations of a constrained flexible multibody system are expressed as a set of index-3 differential algebraic equations (DAEs), in which the element elastic forces are defined using nonlinear strain-displacement relations. Both the direct differentiation method and adjoint variable method are performed to do sensitivity analysis and the related dynamic and sensitivity equations are integrated with HHT-I3 algorithm. In this paper, a new method to deduce system sensitivity equations is proposed. With this approach, the system sensitivity equations are constructed by assembling the element sensitivity equations with the help of invariant matrices, which results in the advantage that the complex symbolic differentiation of the dynamic equations is avoided when the flexible multibody system model is changed. Besides that, the dynamic and sensitivity equations formed with the proposed method can be efficiently integrated using HHT-I3 method, which makes the efficiency of the direct differentiation method comparable to that of the adjoint variable method when the number of design variables is not extremely large. All these improvements greatly enhance the application value of the direct differentiation

Simbody: multibody dynamics for biomedical research.

Science.gov (United States)

Sherman, Michael A; Seth, Ajay; Delp, Scott L

Multibody software designed for mechanical engineering has been successfully employed in biomedical research for many years. For real time operation some biomedical researchers have also adapted game physics engines. However, these tools were built for other purposes and do not fully address the needs of biomedical researchers using them to analyze the dynamics of biological structures and make clinically meaningful recommendations. We are addressing this problem through the development of an open source, extensible, high performance toolkit including a multibody mechanics library aimed at the needs of biomedical researchers. The resulting code, Simbody, supports research in a variety of fields including neuromuscular, prosthetic, and biomolecular simulation, and related research such as biologically-inspired design and control of humanoid robots and avatars. Simbody is the dynamics engine behind OpenSim, a widely used biomechanics simulation application. This article reviews issues that arise uniquely in biomedical research, and reports on the architecture, theory, and computational methods Simbody uses to address them. By addressing these needs explicitly Simbody provides a better match to the needs of researchers than can be obtained by adaptation of mechanical engineering or gaming codes. Simbody is a community resource, free for any purpose. We encourage wide adoption and invite contributions to the code base at https://simtk.org/home/simbody.

The study about planetary gearbox virtual prototyping with nonlinear gear contact characteristics

International Nuclear Information System (INIS)

Yin Huabing; Zhou Guangming

2010-01-01

The virtual prototypes of gear transmission system built in most multi-body dynamic software have difficulties in describing the gear mesh characteristics. The gear mesh contact is modelled as rigid contact and this is not accurate for the gear mesh contact, which is elastic or flexible. The gear contact formula used in the multi-body dynamic software does not reveal the gear contact nonlinear stiffness characteristic. The model built with gear meshing contact is difficult to solve because of its time-consuming algorithm. In the paper a new method is put forward to build the virtual prototype of planetary gearbox system according to the nonlinear mesh stiffness and mesh phase obtained through FEM models. This new FEM method of gear mesh stiffness calculation is much more accurate than the common formulas. The gear mesh nonlinear stiffness of sun gear- pinion and pinion-ring gear of all the planetary gear sets in gearbox are obtained through MATALB code, which is used to read and plot the analyzing result data. The gear mesh phase differences between different pinions with suns or rings of different planetary gear set can be also obtained. With all these data modelled in simulink (or other software) and integrated with the multi-body dynamic planetary gearbox model and the gear meshing contact problem in multi-body gear models is solved easily and accurately. The interfaces for gear mesh stiffness and mesh phases are designed for multi-body dynamic model and simulink. The nonlinear planetary gear set prototyping models are integrated to become the whole planetary gear box model and the whole vehicle system model built in multi-body dynamic software can be integrated to simulate different duty conditions. At last high speed input is put into the nonlinear planetary transmission model and the different duty cases are simulated. The dynamic characteristics of different parts are obtained. The dynamic characteristic comparison between nonlinear and linear models is made

Masticatory biomechanics in the rabbit: a multi-body dynamics analysis.

Science.gov (United States)

Watson, Peter J; Gröning, Flora; Curtis, Neil; Fitton, Laura C; Herrel, Anthony; McCormack, Steven W; Fagan, Michael J

2014-10-06

Multi-body dynamics is a powerful engineering tool which is becoming increasingly popular for the simulation and analysis of skull biomechanics. This paper presents the first application of multi-body dynamics to analyse the biomechanics of the rabbit skull. A model has been constructed through the combination of manual dissection and three-dimensional imaging techniques (magnetic resonance imaging and micro-computed tomography). Individual muscles are represented with multiple layers, thus more accurately modelling muscle fibres with complex lines of action. Model validity was sought through comparing experimentally measured maximum incisor bite forces with those predicted by the model. Simulations of molar biting highlighted the ability of the masticatory system to alter recruitment of two muscle groups, in order to generate shearing or crushing movements. Molar shearing is capable of processing a food bolus in all three orthogonal directions, whereas molar crushing and incisor biting are predominately directed vertically. Simulations also show that the masticatory system is adapted to process foods through several cycles with low muscle activations, presumably in order to prevent rapidly fatiguing fast fibres during repeated chewing cycles. Our study demonstrates the usefulness of a validated multi-body dynamics model for investigating feeding biomechanics in the rabbit, and shows the potential for complementing and eventually reducing in vivo experiments.

Constraint Embedding for Multibody System Dynamics

Science.gov (United States)

Jain, Abhinandan

2009-01-01

This paper describes a constraint embedding approach for the handling of local closure constraints in multibody system dynamics. The approach uses spatial operator techniques to eliminate local-loop constraints from the system and effectively convert the system into tree-topology systems. This approach allows the direct derivation of recursive O(N) techniques for solving the system dynamics and avoiding the expensive steps that would otherwise be required for handling the closedchain dynamics. The approach is very effective for systems where the constraints are confined to small-subgraphs within the system topology. The paper provides background on the spatial operator O(N) algorithms, the extensions for handling embedded constraints, and concludes with some examples of such constraints.

Elastic Multibody Dynamics A Direct Ritz Approach

CERN Document Server

Bremer, H

2008-01-01

This textbook is an introduction to and exploration of a number of core topics in the field of applied mechanics: On the basis of Lagrange's Principle, a Central Equation of Dynamics is presented which yields a unified view on existing methods. From these, the Projection Equation is selected for the derivation of the motion equations of holonomic and of non-holonomic systems. The method is applied to rigid multibody systems where the rigid body is defined such that, by relaxation of the rigidity constraints, one can directly proceed to elastic bodies. A decomposition into subsystems leads to a minimal representation and to a recursive representation, respectively, of the equations of motion. Applied to elastic multibody systems one obtains, along with the use of spatial operators, a straight-on procedure for the interconnected partial and ordinary differential equations and the corresponding boundary conditions. The spatial operators are eventually applied to a RITZ series for approximation. The resulting equ...

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

Science.gov (United States)

Hu, Wei; Tian, Qiang; Hu, HaiYan

2018-04-01

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.

Dynamic analysis of multibody system immersed in a fluid medium

International Nuclear Information System (INIS)

Wu, R.W.; Liu, L.K.; Levy, S.

1977-01-01

This paper is concerned primarily with the development and evaluation of an analysis method for the reponse prediction of immersed systems to seismic and other dynamic excitations. For immersed multibody systems, the hydrodynamic interaction causes coupled motion among the solid bodies. Also, under intense external excitations, impact between bodies may occur. The complex character of such systems inhibit the use of conventional analytical solutions in closed form. Therefore, approximate numerical schemes have been devised. For an incompressible, inviscid fluid, the hydrodynamic forces exerted by the fluid on solid bodies are determined to be linearly proportional to the acceleration of the vibrating solid bodies; i.e., the presence of the fluid only affects the inertia of the solid body system. A finite element computer program has been developed for computing this hydrodynamic (or added) mass effect. This program can be used to determine the hydrodynamic mass of a two-dimensional fluid field with solid bodies of arbitrary geometry. Triangular elements and linear pressure interpolation function are used to discretize the fluid region. The component element method is used to determine the dynamic response of the multibody system to externally applied mechanical loading or support excitation. The present analysis method for predicting the dynamic response of submerged multibody system is quite general and pertains to any number of solid bodies. However in this paper, its application is demonstrated only for 4 and 25 body systems. (Auth.)

Roller-chain Drives Mechanics using Multibody Dynamics Tools

DEFF Research Database (Denmark)

Ambrosio, Jorge A. C.; Hansen, John Michael

1999-01-01

An integrated model for the simulation of roller-chain drives based on a multibody dynamics methodology is presented here in order to describeits complex dynamic behavior. The chain is modeled by masses lumped at the roller locations and connected by translational spring-damper elements in order ...... engagement on the sprockets responsible for the polygonal effect is thoroughly analyzed and the induced impulsive forces developed during that action are treated by a strategy where kinematic constraints between sprockets and rollers are added and deleted....

Event-based scenario manager for multibody dynamics simulation of heavy load lifting operations in shipyards

Directory of Open Access Journals (Sweden)

Sol Ha

2016-01-01

Full Text Available This paper suggests an event-based scenario manager capable of creating and editing a scenario for shipbuilding process simulation based on multibody dynamics. To configure various situation in shipyards and easily connect with multibody dynamics, the proposed method has two main concepts: an Actor and an Action List. The Actor represents the anatomic unit of action in the multibody dynamics and can be connected to a specific component of the dynamics kernel such as the body and joint. The user can make a scenario up by combining the actors. The Action List contains information for arranging and executing the actors. Since the shipbuilding process is a kind of event-based sequence, all simulation models were configured using Discrete EVent System Specification (DEVS formalism. The proposed method was applied to simulations of various operations in shipyards such as lifting and erection of a block and heavy load lifting operation using multiple cranes.

Validation of flexible multibody dynamics beam formulations using benchmark problems

NARCIS (Netherlands)

Bauchau, O.A.; Wu, Genyong; Betsch, P.; Cardona, A.; Gerstmayr, J.; Jonker, Jan B.; Masarati, P.; Sonneville, V.

2016-01-01

As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the

On the constraints violation in forward dynamics of multibody systems

Energy Technology Data Exchange (ETDEWEB)

Marques, Filipe [University of Minho, Department of Mechanical Engineering (Portugal); Souto, António P. [University of Minho, Department of Textile Engineering (Portugal); Flores, Paulo, E-mail: pflores@dem.uminho.pt [University of Minho, Department of Mechanical Engineering (Portugal)

2017-04-15

It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method.

Evolution of Flexible Multibody Dynamics for Simulation Applications Supporting Human Spaceflight

Science.gov (United States)

Huynh, An; Brain, Thomas A.; MacLean, John R.; Quiocho, Leslie J.

2016-01-01

During the course of transition from the Space Shuttle and International Space Station programs to the Orion and Journey to Mars exploration programs, a generic flexible multibody dynamics formulation and associated software implementation has evolved to meet an ever changing set of requirements at the NASA Johnson Space Center (JSC). Challenging problems related to large transitional topologies and robotic free-flyer vehicle capture/ release, contact dynamics, and exploration missions concept evaluation through simulation (e.g., asteroid surface operations) have driven this continued development. Coupled with this need is the requirement to oftentimes support human spaceflight operations in real-time. Moreover, it has been desirable to allow even more rapid prototyping of on-orbit manipulator and spacecraft systems, to support less complex infrastructure software for massively integrated simulations, to yield further computational efficiencies, and to take advantage of recent advances and availability of multi-core computing platforms. Since engineering analysis, procedures development, and crew familiarity/training for human spaceflight is fundamental to JSC's charter, there is also a strong desire to share and reuse models in both the non-realtime and real-time domains, with the goal of retaining as much multibody dynamics fidelity as possible. Three specific enhancements are reviewed here: (1) linked list organization to address large transitional topologies, (2) body level model order reduction, and (3) parallel formulation/implementation. This paper provides a detailed overview of these primary updates to JSC's flexible multibody dynamics algorithms as well as a comparison of numerical results to previous formulations and associated software.

Online Kinematic and Dynamic-State Estimation for Constrained Multibody Systems Based on IMUs

Science.gov (United States)

Torres-Moreno, José Luis; Blanco-Claraco, José Luis; Giménez-Fernández, Antonio; Sanjurjo, Emilio; Naya, Miguel Ángel

2016-01-01

This article addresses the problems of online estimations of kinematic and dynamic states of a mechanism from a sequence of noisy measurements. In particular, we focus on a planar four-bar linkage equipped with inertial measurement units (IMUs). Firstly, we describe how the position, velocity, and acceleration of all parts of the mechanism can be derived from IMU signals by means of multibody kinematics. Next, we propose the novel idea of integrating the generic multibody dynamic equations into two variants of Kalman filtering, i.e., the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), in a way that enables us to handle closed-loop, constrained mechanisms, whose state space variables are not independent and would normally prevent the direct use of such estimators. The proposal in this work is to apply those estimators over the manifolds of allowed positions and velocities, by means of estimating a subset of independent coordinates only. The proposed techniques are experimentally validated on a testbed equipped with encoders as a means of establishing the ground-truth. Estimators are run online in real-time, a feature not matched by any previous procedure of those reported in the literature on multibody dynamics. PMID:26959027

A Component Mode Synthesis Algorithm for Multibody Dynamics of Wind Turbines

DEFF Research Database (Denmark)

Holm-Jørgensen, Kristian; Nielsen, Søren R.K.

2009-01-01

A system reduction scheme related to a multibody formulation of wind turbine dynamics is devised. Each substructure is described in its own frame of reference, which is moving freely in the vicinity of the moving substructure, in principle without any constraints to the rigid body part of the mot......A system reduction scheme related to a multibody formulation of wind turbine dynamics is devised. Each substructure is described in its own frame of reference, which is moving freely in the vicinity of the moving substructure, in principle without any constraints to the rigid body part...... of the motion of the substructure. The system reduction is based on a component mode synthesis method, where the response of the internal degrees of freedom of the substructure is described as the quasi-static response induced by the boundary degrees of freedom via the constraint modes superimposed...

Dynamics and Embedded Internet of Things Input Shaping Control for Overhead Cranes Transporting Multibody Payloads

Directory of Open Access Journals (Sweden)

Gerardo Peláez

2018-06-01

Full Text Available Input shaping is an Optimal Control feedforward strategy whose ability to define how and when a flexible dynamical system defined by Ordinary Differential Equations (ODEs and computer controlled would move into its operative space, without command induced unwanted dynamics, has been exhaustively demonstrated. This work examines the issue of Embedded Internet of Things (IoT Input Shaping with regard to real time control of multibody oscillatory systems whose dynamics are better described by differential algebraic equations (DAEs. An overhead crane hanging a double link multibody payload has been appointed as a benchmark case; it is a multibody, multimode system. This might be worst scenario to implement Input Shaping. The reasons can be found in the wide array of constraints that arise. Firstly, the reliability of the multibody model was tested on a Functional Mock-Up Interface (FMI with the two link payload suspended from the trolley by comparing the experimental video tapping signals in time domain faced with the signals extracted from the multibody model. The FFTs of the simulated and the experimental signal contain the same frequency harmonics only with somewhat different power due to the real world light damping in the joints. The application of this approach may be extended to other cases i.e., the usefulness of mobile hydraulic cranes is limited because the payload is supported by an overhead cable under tension that allows oscillation to occur during crane motion. If the payload size is not negligible small when compared with the cable length may introduce an additional oscillatory mode that creates a multibody double pendulum. To give the insight into the double pendulum dynamics by Lagrangian methods two slender rods as payloads are analyzed dealing with the overhead crane and a composite revolute-revolute joint is proposed to model the cable of the hydraulic crane, both assumptions facilitates an affordable analysis. This allows

Dynamics and Embedded Internet of Things Input Shaping Control for Overhead Cranes Transporting Multibody Payloads.

Science.gov (United States)

Peláez, Gerardo; Vaugan, Joshua; Izquierdo, Pablo; Rubio, Higinio; García-Prada, Juan Carlos

2018-06-04

Input shaping is an Optimal Control feedforward strategy whose ability to define how and when a flexible dynamical system defined by Ordinary Differential Equations (ODEs) and computer controlled would move into its operative space, without command induced unwanted dynamics, has been exhaustively demonstrated. This work examines the issue of Embedded Internet of Things (IoT) Input Shaping with regard to real time control of multibody oscillatory systems whose dynamics are better described by differential algebraic equations (DAEs). An overhead crane hanging a double link multibody payload has been appointed as a benchmark case; it is a multibody, multimode system. This might be worst scenario to implement Input Shaping. The reasons can be found in the wide array of constraints that arise. Firstly, the reliability of the multibody model was tested on a Functional Mock-Up Interface (FMI) with the two link payload suspended from the trolley by comparing the experimental video tapping signals in time domain faced with the signals extracted from the multibody model. The FFTs of the simulated and the experimental signal contain the same frequency harmonics only with somewhat different power due to the real world light damping in the joints. The application of this approach may be extended to other cases i.e., the usefulness of mobile hydraulic cranes is limited because the payload is supported by an overhead cable under tension that allows oscillation to occur during crane motion. If the payload size is not negligible small when compared with the cable length may introduce an additional oscillatory mode that creates a multibody double pendulum. To give the insight into the double pendulum dynamics by Lagrangian methods two slender rods as payloads are analyzed dealing with the overhead crane and a composite revolute-revolute joint is proposed to model the cable of the hydraulic crane, both assumptions facilitates an affordable analysis. This allows developing a general

Online Kinematic and Dynamic-State Estimation for Constrained Multibody Systems Based on IMUs

Directory of Open Access Journals (Sweden)

José Luis Torres-Moreno

2016-03-01

Full Text Available This article addresses the problems of online estimations of kinematic and dynamic states of a mechanism from a sequence of noisy measurements. In particular, we focus on a planar four-bar linkage equipped with inertial measurement units (IMUs. Firstly, we describe how the position, velocity, and acceleration of all parts of the mechanism can be derived from IMU signals by means of multibody kinematics. Next, we propose the novel idea of integrating the generic multibody dynamic equations into two variants of Kalman filtering, i.e., the extended Kalman filter (EKF and the unscented Kalman filter (UKF, in a way that enables us to handle closed-loop, constrained mechanisms, whose state space variables are not independent and would normally prevent the direct use of such estimators. The proposal in this work is to apply those estimators over the manifolds of allowed positions and velocities, by means of estimating a subset of independent coordinates only. The proposed techniques are experimentally validated on a testbed equipped with encoders as a means of establishing the ground-truth. Estimators are run online in real-time, a feature not matched by any previous procedure of those reported in the literature on multibody dynamics.

Multibody dynamical modeling for spacecraft docking process with spring-damper buffering device: A new validation approach

Science.gov (United States)

Daneshjou, Kamran; Alibakhshi, Reza

2018-01-01

In the current manuscript, the process of spacecraft docking, as one of the main risky operations in an on-orbit servicing mission, is modeled based on unconstrained multibody dynamics. The spring-damper buffering device is utilized here in the docking probe-cone system for micro-satellites. Owing to the impact occurs inevitably during docking process and the motion characteristics of multibody systems are remarkably affected by this phenomenon, a continuous contact force model needs to be considered. Spring-damper buffering device, keeping the spacecraft stable in an orbit when impact occurs, connects a base (cylinder) inserted in the chaser satellite and the end of docking probe. Furthermore, by considering a revolute joint equipped with torsional shock absorber, between base and chaser satellite, the docking probe can experience both translational and rotational motions simultaneously. Although spacecraft docking process accompanied by the buffering mechanisms may be modeled by constrained multibody dynamics, this paper deals with a simple and efficient formulation to eliminate the surplus generalized coordinates and solve the impact docking problem based on unconstrained Lagrangian mechanics. By an example problem, first, model verification is accomplished by comparing the computed results with those recently reported in the literature. Second, according to a new alternative validation approach, which is based on constrained multibody problem, the accuracy of presented model can be also evaluated. This proposed verification approach can be applied to indirectly solve the constrained multibody problems by minimum required effort. The time history of impact force, the influence of system flexibility and physical interaction between shock absorber and penetration depth caused by impact are the issues followed in this paper. Third, the MATLAB/SIMULINK multibody dynamic analysis software will be applied to build impact docking model to validate computed results and

Analysis of the nonlinear dynamics of a 2-axle freight wagon in curves

DEFF Research Database (Denmark)

Di Gialleonardo, Egidio; Bruni, Stefano; True, Hans

2014-01-01

This paper deals with the study of the nonlinear dynamic behaviour of 2-axle freight wagons in curves, considering the case of one single wagon (neglecting inter-car coupling forces) and of multiple wagons interacting through the buffers and the couplers. A multi-body model of a single wagon...... and of a three-car assembly is introduced, paying particular attention to the nonlinear and nonsmooth modelling of the suspensions and of the inter-car coupling elements. Using this model, a numerical analysis of the steady-state solution reached after the negotiation of curve transition is presented......, it is shown that the coupling forces exchanged by the wagons significantly affect their dynamics in a curve, reducing the amplitude of vibration....

Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates

Energy Technology Data Exchange (ETDEWEB)

Dombrowski, Stefan von [Institute of Robotics and Mechatronics, German Aerospace Center (DLR) (Germany)], E-mail: stefan.von.dombrowski@dlr.de

2002-11-15

To consider large deformation problems in multibody system simulations a finite element approach, called absolute nodal coordinate.formulation,has been proposed. In this formulation absolute nodal coordinates and their material derivatives are applied to represent both deformation and rigid body motion. The choice of nodal variables allows a fully nonlinear representation of rigid body motion and can provide the exact rigid body inertia in the case of large rotations. The methodology is especially suited for but not limited to modeling of beams, cables and shells in multibody dynamics.This paper summarizes the absolute nodal coordinate formulation for a 3D Euler-Bernoulli beam model, in particular the definition of nodal variables, corresponding generalized elastic and inertia forces and equations of motion. The element stiffness matrix is a nonlinear function of the nodal variables even in the case of linearized strain/displacement relations. Nonlinear strain/displacement relations can be calculated from the global displacements using quadrature formulae.Computational examples are given which demonstrate the capabilities of the applied methodology. Consequences of the choice of shape.functions on the representation of internal forces are discussed. Linearized strain/displacement modeling is compared to the nonlinear approach and significant advantages of the latter, when using the absolute nodal coordinate formulation, are outlined.

Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates

International Nuclear Information System (INIS)

Dombrowski, Stefan von

2002-01-01

To consider large deformation problems in multibody system simulations a finite element approach, called absolute nodal coordinate.formulation,has been proposed. In this formulation absolute nodal coordinates and their material derivatives are applied to represent both deformation and rigid body motion. The choice of nodal variables allows a fully nonlinear representation of rigid body motion and can provide the exact rigid body inertia in the case of large rotations. The methodology is especially suited for but not limited to modeling of beams, cables and shells in multibody dynamics.This paper summarizes the absolute nodal coordinate formulation for a 3D Euler-Bernoulli beam model, in particular the definition of nodal variables, corresponding generalized elastic and inertia forces and equations of motion. The element stiffness matrix is a nonlinear function of the nodal variables even in the case of linearized strain/displacement relations. Nonlinear strain/displacement relations can be calculated from the global displacements using quadrature formulae.Computational examples are given which demonstrate the capabilities of the applied methodology. Consequences of the choice of shape.functions on the representation of internal forces are discussed. Linearized strain/displacement modeling is compared to the nonlinear approach and significant advantages of the latter, when using the absolute nodal coordinate formulation, are outlined

Indirect learning control for nonlinear dynamical systems

Science.gov (United States)

Ryu, Yeong Soon; Longman, Richard W.

1993-01-01

In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

Multibody simulations of trolleybus vertical dynamics and influences of spring-damper structural elements

Directory of Open Access Journals (Sweden)

Polach P.

2008-11-01

Full Text Available Vertical dynamic properties of the ŠKODA 21 Tr low-floor trolleybus were investigated on an artificial test track when driving with a real vehicle and when simulating driving with a multibody model along a virtual test track. Driving along the artificial test track was aimed to determine vertical dynamic properties of the real trolleybus and on the basis of them to verify computer trolleybus models. Time histories and extreme values of the air springs relative deflections are the monitored quantities. Due to differences of the experiments and the computer simulations results the influences of the characteristics of the spring-damper structural elements of the axles suspension and the radial characteristics of the tires used in the trolleybus multibody model on the extreme values of the monitored quantities are evaluated.

Multibody Dynamic Stress Simulation of Rigid-Flexible Shovel Crawler Shoes

Directory of Open Access Journals (Sweden)

Samuel Frimpong

2016-06-01

Full Text Available Electric shovels are used in surface mining operations to achieve economic production capacities. The capital investments and operating costs associated with the shovels deployed in the Athabasca oil sands formation are high due to the abrasive conditions. The shovel crawler shoes interact with sharp and abrasive sand particles, and, thus, are subjected to high transient dynamic stresses. These high stresses cause wear and tear leading to crack initiation, propagation and premature fatigue failure. The objective of this paper is to develop a model to characterize the crawler stresses and deformation for the P&H 4100C BOSS during propel and loading using rigid-flexible multi-body dynamic theory. A 3-D virtual prototype model of the rigid-flexible crawler track assembly and its interactions with oil sand formation is simulated to capture the model dynamics within multibody dynamics software MSC ADAMS. The modal and stress shapes and modal loads due to machine weight for each flexible crawler shoes are generated from finite element analysis (FEA. The modal coordinates from the simulation are combined with mode and stress shapes using modal superposition method to calculate real-time stresses and deformation of flexible crawler shoes. The results show a maximum von Mises stress value of 170 MPa occurring in the driving crawler shoe during the propel motion. This study provides a foundation for the subsequent fatigue life analysis of crawler shoes for extending crawler service life.

General background and approach to multibody dynamics for space applications

Science.gov (United States)

Santini, Paolo; Gasbarri, Paolo

2009-06-01

Multibody dynamics for space applications is dictated by space environment such as space-varying gravity forces, orbital and attitude perturbations, control forces if any. Several methods and formulations devoted to the modeling of flexible bodies undergoing large overall motions were developed in recent years. Most of these different formulations were aimed to face one of the main problems concerning the analysis of spacecraft dynamics namely the reduction of computer simulation time. By virtue of this, the use of symbolic manipulation, recursive formulation and parallel processing algorithms were proposed. All these approaches fall into two categories, the one based on Newton/Euler methods and the one based on Lagrangian methods; both of them have their advantages and disadvantages although in general, Newtonian approaches lend to a better understanding of the physics of problems and in particular of the magnitude of the reactions and of the corresponding structural stresses. Another important issue which must be addressed carefully in multibody space dynamics is relevant to a correct choice of kinematics variables. In fact, when dealing with flexible multibody system the resulting equations include two different types of state variables, the ones associated with large (rigid) displacements and the ones associated with elastic deformations. These two sets of variables have generally two different time scales if we think of the attitude motion of a satellite whose period of oscillation, due to the gravity gradient effects, is of the same order of magnitude as the orbital period, which is much bigger than the one associated with the structural vibration of the satellite itself. Therefore, the numerical integration of the equations of the system represents a challenging problem. This was the abstract and some of the arguments that Professor Paolo Santini intended to present for the Breakwell Lecture; unfortunately a deadly disease attacked him and shortly took him

System Reduction in Multibody Dynamics of Wind Turbines

DEFF Research Database (Denmark)

Holm-Jørgensen, Kristian; Nielsen, Søren R.K.

2009-01-01

Abstract A system reduction scheme is devised related to a multibody formulation from which the dynamic response of a wind turbine is determined. In this formulation each substructure is described in its own frame of reference, which is moving freely in the vicinity of the moving substructure....... The Ritz bases spanning the reduced system comprises of rigid body modes and some dynamic low-frequency elastic eigenmodes compatible to the kinematic constraints of the related substructure. The high-frequency elastic modes are presumed to cause merely quasi-static displacements, and thus are included...... in the expansion via a quasi-static correction. The results show that by using the derived reduction scheme it is only necessary with 2 dynamical modes for the blade substructure when the remaining modes are treated as quasi-static. Moreover, it is shown that it has little to none effect if the gyroscopic...

Advances in Chimera Grid Tools for Multi-Body Dynamics Simulations and Script Creation

Science.gov (United States)

Chan, William M.

2004-01-01

This viewgraph presentation contains information about (1) Framework for multi-body dynamics - Geometry Manipulation Protocol (GMP), (2) Simulation procedure using Chimera Grid Tools (CGT) and OVERFLOW-2 (3) Further recent developments in Chimera Grid Tools OVERGRID, Grid modules, Script library and (4) Future work.

How to combine binary collision approximation and multi-body potential for molecular dynamics

International Nuclear Information System (INIS)

Saito, Seiki; Nakamura, Hiroaki; Takayama, Arimichi; Ito, Atsushi M.; Kenmotsu, Takahiro

2010-01-01

Our group has been developing a hybrid simulation of the molecular dynamics (MD) and the binary collision approximation (BCA) simulation. One of the main problems of this hybridization model is that the multi-body potential suddenly appears at the moment when the simulation method switches from the BCA to the MD. This instantaneously emerged multi-body potential causes the acceleration or deceleration of atoms of the system. To solve this problem, the kinetic energy of atoms should be corrected to conserve the total energy in the system. This paper gives the solution. The hybrid simulation for hydrogen atom injection into a graphite material is executed in order to demonstrate the solution. (author)

Virtual design software for mechanical system dynamics using transfer matrix method of multibody system and its application

Directory of Open Access Journals (Sweden)

Hai-gen Yang

2015-09-01

Full Text Available The complex mechanical systems such as high-speed trains, multiple launch rocket system, self-propelled artillery, and industrial robots are becoming increasingly larger in scale and more complicated in structure. Designing these products often requires complex model design, multibody system dynamics calculation, and analysis of large amounts of data repeatedly. In recent 20 years, the transfer matrix method of multibody system has been widely applied in engineering fields and welcomed at home and in abroad for the following features: without global dynamic equations of the system, low orders of involved system matrices, high computational efficiency, and high programming. In order to realize the rapid and visual simulation for complex mechanical system virtual design using transfer matrix method of multibody system, a virtual design software named MSTMMSim is designed and implemented. In the MSTMMSim, the transfer matrix method of multibody system is used as the solver for dynamic modeling and calculation; the Open CASCADE is used for solid geometry modeling. Various auxiliary analytical tools such as curve plot and animation display are provided in the post-processor to analyze and process the simulation results. Two numerical examples are given to verify the validity and accuracy of the software, and a multiple launch rocket system engineering example is given at the end of this article to show that the software provides a powerful platform for complex mechanical systems simulation and virtual design.

Comparative multibody dynamics analysis of falls from playground climbing frames

OpenAIRE

Forero Rueda, Manuel A.; Gilchrist, M. D.

2009-01-01

This paper shows the utility of multibody dynamics in evaluating changes in injury related parameters of the head and lower limbs of children following falls from playground climbing frames. A particular fall case was used as a starting point to analyze the influence of surface properties, posture of the body at impact, and intermediate collisions against the climbing frame before impacting the ground. Simulations were made using the 6-year-old pedestrian MADYMO rigid body model and scaled he...

Multibody Systems

DEFF Research Database (Denmark)

Wagner, Falko Jens

1999-01-01

Multibody Systems is one area, in which methods for solving DAEs are of special interst. This chapter is about multibody systems, why they result in DAE systems and what kind of problems that can arise when dealing with multibody systems and formulating their corresponding DAE system....

Validation of flexible multibody dynamics beam formulations using benchmark problems

Energy Technology Data Exchange (ETDEWEB)

Bauchau, Olivier A., E-mail: obauchau@umd.edu [University of Maryland (United States); Betsch, Peter [Karlsruhe Institute of Technology (Germany); Cardona, Alberto [CIMEC (UNL/Conicet) (Argentina); Gerstmayr, Johannes [Leopold-Franzens Universität Innsbruck (Austria); Jonker, Ben [University of Twente (Netherlands); Masarati, Pierangelo [Politecnico di Milano (Italy); Sonneville, Valentin [Université de Liège (Belgium)

2016-05-15

As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available.

Biomechanical Analysis and Evaluation Technology Using Human Multi-Body Dynamic Model

Energy Technology Data Exchange (ETDEWEB)

Kim, Yoon Hyuk; Shin, June Ho; Khurelbaatar, Tsolmonbaatar [Kyung Hee University, Yongin (Korea, Republic of)

2011-10-15

This paper presents the biomechanical analysis and evaluation technology of musculoskeletal system by multi-body human dynamic model and 3-D motion capture data. First, medical image based geometric model and material properties of tissue were used to develop the human dynamic model and 3-D motion capture data based motion analysis techniques were develop to quantify the in-vivo joint kinematics, joint moment, joint force, and muscle force. Walking and push-up motion was investigated using the developed model. The present model and technologies would be useful to apply the biomechanical analysis and evaluation of human activities.

GPU accelerated tandem traversal of blocked bounding volume hierarchy collision detection for multibody dynamics

DEFF Research Database (Denmark)

Damkjær, Jesper; Erleben, Kenny

2009-01-01

and a simultaneous descend in the tandem traversal. The data structure design and traversal are highly specialized for exploiting the parallel threads in the NVIDIA GPUs. As proof-of-concept we demonstrate a GPU implementation for a multibody dynamics simulation, showing an approximate speedup factor of up to 8...

A new version of transfer matrix method for multibody systems

Energy Technology Data Exchange (ETDEWEB)

Rui, Xiaoting, E-mail: ruixt@163.net [Nanjing University of Science and Technology, Institute of Launch Dynamics (China); Bestle, Dieter, E-mail: bestle@b-tu.de [Brandenburg University of Technology, Engineering Mechanics and Vehicle Dynamics (Germany); Zhang, Jianshu, E-mail: zhangdracpa@sina.com; Zhou, Qinbo, E-mail: zqb912-new@163.com [Nanjing University of Science and Technology, Institute of Launch Dynamics (China)

2016-10-15

In order to avoid the global dynamics equations and increase the computational efficiency for multibody system dynamics (MSD), the transfer matrix method of multibody system (MSTMM) has been developed and applied very widely in research and engineering in recent 20 years. It differs from ordinary methods in multibody system dynamics with respect to the feature that there is no need for a global dynamics equation, and it uses low-order matrices for high computational efficiency. For linear systems, MSTMM is exact even if continuous elements like beams are involved. The discrete time MSTMM, however, has to use local linearization. In order to release the method from such approximations, a new version of MSTMM is presented in this paper where translational and angular accelerations, on the one hand, and internal forces and moments, on the other hand, are used as state variables. Already linear relationships among these quantities are utilized, which results in new element transfer matrices and algorithms making the study of multibody systems as simple as the study of single bodies. The proposed approach also allows combining MSTMM with any general numerical integration procedure. Some numerical examples of MSD are given to demonstrate the proposed method.

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

Science.gov (United States)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Model Reduction in Co-Rotated Multi-Body Dynamics Based on the Dual Craig-Bampton Method

NARCIS (Netherlands)

Weerathunge Kadawathagedara, S.T.; Rixen, D.J.

2011-01-01

A new reduction method for dynamical analsis of multi-body systems is presented in this paper. It fundamentally differs from the ones previously published in the way kinematical constraints are handled. Our approach is based on component mode synthesis, but the specificity of articulated mechanism,

A combined multibody and finite element approach for dynamic interaction analysis of high-speed train and railway structure including post-derailment behavior during an earthquake

International Nuclear Information System (INIS)

Tanabe, M; Wakui, H; Sogabe, M; Matsumoto, N; Tanabe, Y

2010-01-01

A combined multibody and finite element approach is given to solve the dynamic interaction of a Shinkansen train (high-speed train in Japan) and the railway structure including post-derailment during an earthquake effectively. The motion of the train is expressed in multibody dynamics. Efficient mechanical models to express interactions between wheel and track structure including post-derailment are given. Rail and track elements expressed in multibody dynamics and FEM are given to solve contact problems between wheel and long railway components effectively. The motion of a railway structure is modeled with various finite elements and rail and track elements. The computer program has been developed for the dynamic interaction analysis of a Shinkansen train and railway structure including post derailment during an earthquake. Numerical examples are demonstrated.

Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions

Science.gov (United States)

Butler, Jason E.; Shaqfeh, Eric S. G.

2005-01-01

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.

An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part Two: Multibody Systems

Directory of Open Access Journals (Sweden)

Pål Johan From

2012-04-01

Full Text Available This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann--Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann--Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity. The main motivation of these papers is to allow practitioners not familiar with differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.

Evaluation of constraint stabilization procedures for multibody dynamical systems

Science.gov (United States)

Park, K. C.; Chiou, J. C.

1987-01-01

Comparative numerical studies of four constraint treatment techniques for the simulation of general multibody dynamic systems are presented, and results are presented for the example of a classical crank mechanism and for a simplified version of the seven-link manipulator deployment problem. The staggered stabilization technique (Park, 1986) is found to yield improved accuracy and robustness over Baumgarte's (1972) technique, the singular decomposition technique (Walton and Steeves, 1969), and the penalty technique (Lotstedt, 1979). Furthermore, the staggered stabilization technique offers software modularity, and the only data each solution module needs to exchange with the other is a set of vectors plus a common module to generate the gradient matrix of the constraints, B.

A model partitioning method based on dynamic decoupling for the efficient simulation of multibody systems

Energy Technology Data Exchange (ETDEWEB)

Papadopoulos, Alessandro Vittorio, E-mail: alessandro.papadopoulos@control.lth.se [Lund University, Department of Automatic Control (Sweden); Leva, Alberto, E-mail: alberto.leva@polimi.it [Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria (Italy)

2015-06-15

The presence of different time scales in a dynamic model significantly hampers the efficiency of its simulation. In multibody systems the fact is particularly relevant, as the mentioned time scales may be very different, due, for example, to the coexistence of mechanical components controled by electronic drive units, and may also appear in conjunction with significant nonlinearities. This paper proposes a systematic technique, based on the principles of dynamic decoupling, to partition a model based on the time scales that are relevant for the particular simulation studies to be performed and as transparently as possible for the user. In accordance with said purpose, peculiar to the technique is its neat separation into two parts: a structural analysis of the model, which is general with respect to any possible simulation scenario, and a subsequent decoupled integration, which can conversely be (easily) tailored to the study at hand. Also, since the technique does not aim at reducing but rather at partitioning the model, the state space and the physical interpretation of the dynamic variables are inherently preserved. Moreover, the proposed analysis allows us to define some novel indices relative to the separability of the system, thereby extending the idea of “stiffness” in a way that is particularly keen to its use for the improvement of simulation efficiency, be the envisaged integration scheme monolithic, parallel, or even based on cosimulation. Finally, thanks to the way the analysis phase is conceived, the technique is naturally applicable to both linear and nonlinear models. The paper contains a methodological presentation of the proposed technique, which is related to alternatives available in the literature so as to evidence the peculiarities just sketched, and some application examples illustrating the achieved advantages and motivating the major design choice from an operational viewpoint.

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

Science.gov (United States)

Schilder, J.; Ellenbroek, M.; de Boer, A.

2017-12-01

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

Method of Obtaining High Resolution Intrinsic Wire Boom Damping Parameters for Multi-Body Dynamics Simulations

Science.gov (United States)

Yew, Alvin G.; Chai, Dean J.; Olney, David J.

2010-01-01

The goal of NASA's Magnetospheric MultiScale (MMS) mission is to understand magnetic reconnection with sensor measurements from four spinning satellites flown in a tight tetrahedron formation. Four of the six electric field sensors on each satellite are located at the end of 60- meter wire booms to increase measurement sensitivity in the spin plane and to minimize motion coupling from perturbations on the main body. A propulsion burn however, might induce boom oscillations that could impact science measurements if oscillations do not damp to values on the order of 0.1 degree in a timely fashion. Large damping time constants could also adversely affect flight dynamics and attitude control performance. In this paper, we will discuss the implementation of a high resolution method for calculating the boom's intrinsic damping, which was used in multi-body dynamics simulations. In summary, experimental data was obtained with a scaled-down boom, which was suspended as a pendulum in vacuum. Optical techniques were designed to accurately measure the natural decay of angular position and subsequently, data processing algorithms resulted in excellent spatial and temporal resolutions. This method was repeated in a parametric study for various lengths, root tensions and vacuum levels. For all data sets, regression models for damping were applied, including: nonlinear viscous, frequency-independent hysteretic, coulomb and some combination of them. Our data analysis and dynamics models have shown that the intrinsic damping for the baseline boom is insufficient, thereby forcing project management to explore mitigation strategies.

Evaluating the reliability of multi-body mechanisms: A method considering the uncertainties of dynamic performance

International Nuclear Information System (INIS)

Wu, Jianing; Yan, Shaoze; Zuo, Ming J.

2016-01-01

Mechanism reliability is defined as the ability of a certain mechanism to maintain output accuracy under specified conditions. Mechanism reliability is generally assessed by the classical direct probability method (DPM) derived from the first order second moment (FOSM) method. The DPM relies strongly on the analytical form of the dynamic solution so it is not applicable to multi-body mechanisms that have only numerical solutions. In this paper, an indirect probability model (IPM) is proposed for mechanism reliability evaluation of multi-body mechanisms. IPM combines the dynamic equation, degradation function and Kaplan–Meier estimator to evaluate mechanism reliability comprehensively. Furthermore, to reduce the amount of computation in practical applications, the IPM is simplified into the indirect probability step model (IPSM). A case study of a crank–slider mechanism with clearance is investigated. Results show that relative errors between the theoretical and experimental results of mechanism reliability are less than 5%, demonstrating the effectiveness of the proposed method. - Highlights: • An indirect probability model (IPM) is proposed for mechanism reliability evaluation. • The dynamic equation, degradation function and Kaplan–Meier estimator are used. • Then the simplified form of indirect probability model is proposed. • The experimental results agree well with the predicted results.

Development of a multi-body nonlinear model for a seat-occupant system

Science.gov (United States)

Azizi, Yousof

A car seat is an important component of today's cars, which directly affects ride comfort experienced by occupants. Currently, the process of ride comfort evaluation is subjective. Alternatively, the ride comfort can be evaluated by a series of objective metrics in the dynamic response of the occupant. From previous studies it is well known that the dynamic behavior of a seat-occupant system is greatly affected by soft nonlinear viscoelastic materials used in the seat cushion. Therefore, in this research, especial attention was given to efficiently modeling the behavior of seat cushion. In the first part of this research, a phenomenological nonlinear viscoelastic foam model was proposed and its ability to capture uniaxial behavior of foam was investigated. The model is based on the assumption that the total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher order polynomial of strain, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at different rates on two types of low density polyurethane foams and three types of high density CONFOR foams. The performance of the proposed model was compared to that of other traditional continuum models. For each foam type, it was observed that lower order models are sufficient to describe the uniaxial behavior of the foam compressed at different rates. Although, the estimated model parameters were functions of the input strain rate. Alternatively, higher order comprehensive models, with strain independent parameters, were estimated as well. The estimated comprehensive model predicts foam responses under different compression rates. Also, a methodology was proposed to predict the stress-response of a layered foam system using the estimated models of each foam in the layers. Next, the estimated foam model was incorporated into a single

Study on the Dynamics of Laser Gyro Strapdown Inertial Measurement Unit System Based on Transfer Matrix Method for Multibody System

Directory of Open Access Journals (Sweden)

Gangli Chen

2013-01-01

Full Text Available The dynamic test precision of the strapdown inertial measurement unit (SIMU is the basis of estimating accurate motion of various vehicles such as warships, airplanes, spacecrafts, and missiles. So, it is paid great attention in the above fields to increase the dynamic precision of SIMU by decreasing the vibration of the vehicles acting on the SIMU. In this paper, based on the transfer matrix method for multibody system (MSTMM, the multibody system dynamics model of laser gyro strapdown inertial measurement unit (LGSIMU is developed; the overall transfer equation of the system is deduced automatically. The computational results show that the frequency response function of the LGSIMU got by the proposed method and Newton-Euler method have good agreements. Further, the vibration reduction performance and the attitude error responses under harmonic and random excitations are analyzed. The proposed method provides a powerful technique for studying dynamics of LGSIMU because of using MSTMM and its following features: without the global dynamics equations of the system, high programming, low order of system matrix, and high computational speed.

A Coupled Helicopter Rotor/Fuselage Dynamics Model Using Finite Element Multi-body

Directory of Open Access Journals (Sweden)

Cheng Qi-you

2016-01-01

Full Text Available To develop a coupled rotor/flexible fuselage model for vibration reduction studies, the equation of coupled rotor-fuselage is set up based on the theory of multi-body dynamics, and the dynamic analysis model is established with the software MSC.ADMAS and MSC.NASTRAN. The frequencies and vibration acceleration responses of the system are calculated with the model of coupled rotor-fuselage, and the results are compared with those of uncoupled modeling method. Analysis results showed that compared with uncoupled model, the dynamic characteristic obtained by the model of coupled rotor-fuselage are some different. The intrinsic frequency of rotor is increased with the increase of rotational velocities. The results also show that the flying speed has obvious influence on the vibration acceleration responses of the fuselage. The vibration acceleration response in the vertical direction is much higher at the low speed and high speed flight conditions.

Flexible Multibody Systems Models Using Composite Materials Components

International Nuclear Information System (INIS)

Neto, Maria Augusta; Ambr'osio, Jorge A. C.; Leal, Rog'erio Pereira

2004-01-01

The use of a multibody methodology to describe the large motion of complex systems that experience structural deformations enables to represent the complete system motion, the relative kinematics between the components involved, the deformation of the structural members and the inertia coupling between the large rigid body motion and the system elastodynamics. In this work, the flexible multibody dynamics formulations of complex models are extended to include elastic components made of composite materials, which may be laminated and anisotropic. The deformation of any structural member must be elastic and linear, when described in a coordinate frame fixed to one or more material points of its domain, regardless of the complexity of its geometry. To achieve the proposed flexible multibody formulation, a finite element model for each flexible body is used. For the beam composite material elements, the sections properties are found using an asymptotic procedure that involves a two-dimensional finite element analysis of their cross-section. The equations of motion of the flexible multibody system are solved using an augmented Lagrangian formulation and the accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm based on the Gear method

Comparative multibody dynamics analysis of falls from playground climbing frames.

Science.gov (United States)

Forero Rueda, M A; Gilchrist, M D

2009-10-30

This paper shows the utility of multibody dynamics in evaluating changes in injury related parameters of the head and lower limbs of children following falls from playground climbing frames. A particular fall case was used as a starting point to analyze the influence of surface properties, posture of the body at impact, and intermediate collisions against the climbing frame before impacting the ground. Simulations were made using the 6-year-old pedestrian MADYMO rigid body model and scaled head contact characteristics. Energy absorbing surfaces were shown to reduce injury severity parameters by up to 30-80% of those of rigid surfaces, depending on impact posture and surface. Collisions against components of a climbing frame during a fall can increase injury severity of the final impact of the head with the ground by more than 90%. Negligible changes are associated with lower limb injury risks when different surfacing materials are used. Computer reconstructions of actual falls that are intended to quantify the severity of physical injuries rely on accurate knowledge of initial conditions prior to falling, intermediate kinematics of the fall and the orientation of the body when it impacts against the ground. Multibody modelling proved to be a valuable tool to analyze the quality of eyewitness information and analyze the relative injury risk associated with changes in components influencing fall injuries from playground climbing frames. Such simulations can also support forensic investigations by evaluating alternative hypotheses for the sequence of kinematic motion of falls which result in known injuries.

Flexible joints in structural and multibody dynamics

Directory of Open Access Journals (Sweden)

O. A. Bauchau

2013-02-01

Full Text Available Flexible joints, sometimes called bushing elements or force elements, are found in all structural and multibody dynamics codes. In their simplest form, flexible joints simply consist of sets of three linear and three torsional springs placed between two nodes of the model. For infinitesimal deformations, the selection of the lumped spring constants is an easy task, which can be based on a numerical simulation of the joint or on experimental measurements. If the joint undergoes finite deformations, identification of its stiffness characteristics is not so simple, specially if the joint is itself a complex system. When finite deformations occur, the definition of deformation measures becomes a critical issue. This paper proposes a family of tensorial deformation measures suitable for elastic bodies of finite dimension. These families are generated by two parameters that can be used to modify the constitutive behavior of the joint, while maintaining the tensorial nature of the deformation measures. Numerical results demonstrate the objectivity of the deformations measures, a feature that is not shared by the deformations measures presently used in the literature. The impact of the choice of the two parameters on the constitutive behavior of the flexible joint is also investigated.

Parallel Evolutionary Optimization of Multibody Systems with Application to Railway Dynamics

Energy Technology Data Exchange (ETDEWEB)

Eberhard, Peter [University of Erlangen-Nuremberg, Institute of Applied Mechanics (Germany)], E-mail: eberhard@ltm.uni-erlangen.de; Dignath, Florian [University of Stuttgart, Institute B of Mechanics (Germany)], E-mail: fd@mechb.uni-stuttgart.de; Kuebler, Lars [University of Erlangen-Nuremberg, Institute of Applied Mechanics (Germany)], E-mail: kuebler@ltm.uni-erlangen.de

2003-03-15

The optimization of multibody systems usually requires many costly criteria computations since the equations of motion must be evaluated by numerical time integration for each considered design. For actively controlled or flexible multibody systems additional difficulties arise as the criteria may contain non-differentiable points or many local minima. Therefore, in this paper a stochastic evolution strategy is used in combination with parallel computing in order to reduce the computation times whilst keeping the inherent robustness. For the parallelization a master-slave approach is used in a heterogeneous workstation/PC cluster. The pool-of-tasks concept is applied in order to deal with the frequently changing workloads of different machines in the cluster. In order to analyze the performance of the parallel optimization method, the suspension of an ICE passenger coach, modeled as an elastic multibody system, is optimized simultaneously with regard to several criteria including vibration damping and a criterion related to safety against derailment. The iterative and interactive nature of a typical optimization process for technical systems is emphasized.

Parallel Evolutionary Optimization of Multibody Systems with Application to Railway Dynamics

International Nuclear Information System (INIS)

Eberhard, Peter; Dignath, Florian; Kuebler, Lars

2003-01-01

The optimization of multibody systems usually requires many costly criteria computations since the equations of motion must be evaluated by numerical time integration for each considered design. For actively controlled or flexible multibody systems additional difficulties arise as the criteria may contain non-differentiable points or many local minima. Therefore, in this paper a stochastic evolution strategy is used in combination with parallel computing in order to reduce the computation times whilst keeping the inherent robustness. For the parallelization a master-slave approach is used in a heterogeneous workstation/PC cluster. The pool-of-tasks concept is applied in order to deal with the frequently changing workloads of different machines in the cluster. In order to analyze the performance of the parallel optimization method, the suspension of an ICE passenger coach, modeled as an elastic multibody system, is optimized simultaneously with regard to several criteria including vibration damping and a criterion related to safety against derailment. The iterative and interactive nature of a typical optimization process for technical systems is emphasized

Multibody system dynamics and mechatronics. Plenary lecture

Energy Technology Data Exchange (ETDEWEB)

Hiller, M.H.; Hirsch, K. [Duisburg-Essen Univ., Duisburg (Germany). Faculty of Engineering

2006-02-15

Mechatronics as an interdisciplinary combination of domains of mechanical engineering, electrical engineering, electronics, and computer science has developed in industry and universities since the eighties of the last century, and it is meanwhile fully established in many technical areas. The main focus of the mechatronic approach is to extend and to complete the design process of mechanical and more general engineering systems by incorporating from the very beginning sensors and controllers - which includes also the required information processing - and thus being able to generate partly intelligent products. The components and modules of such systems originate from mechanical engineering, from electrical engineering or from other engineering domains. Methods for describing and designing these components and modules are based in the fields of applied mechanics, electrical engineering, system theory, control and automation theory, and information processing. In particular, in mechatronic systems like robots, manipulation systems, machine tools, or all kinds of vehicles, the multibody systems approach offers a powerful tool to model the mechanical properties of the system in an appropriate manner. In this paper, methodologies for the development of formalisms and software for modeling and simulation of multibody and mechatronic systems will be presented and illustrated by examples from automotive systems and robotics. (orig.)

On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation

Science.gov (United States)

Fu, Yao; Song, Jeong-Hoon

2014-08-01

Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. The balance of momentum has been demonstrated to be valid theoretically and tested under various numerical simulation conditions. The validity of momentum conservation justifies the extension of Hardy stress expression to multi-body potential systems. Computed Hardy stress has been observed to converge to the virial stress of the system with increasing spatial averaging volume. This work provides a feasible and reliable linkage between the atomistic and continuum scales for multi-body potential systems.

Nonlinear dynamics and complexity

CERN Document Server

Luo, Albert; Fu, Xilin

2014-01-01

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Research on The Construction of Flexible Multi-body Dynamics Model based on Virtual Components

Science.gov (United States)

Dong, Z. H.; Ye, X.; Yang, F.

2018-05-01

Focus on the harsh operation condition of space manipulator, which cannot afford relative large collision momentum, this paper proposes a new concept and technology, called soft-contact technology. In order to solve the problem of collision dynamics of flexible multi-body system caused by this technology, this paper also proposes the concepts of virtual components and virtual hinges, and constructs flexible dynamic model based on virtual components, and also studies on its solutions. On this basis, this paper uses NX to carry out model and comparison simulation for space manipulator in 3 different modes. The results show that using the model of multi-rigid body + flexible body hinge + controllable damping can make effective control on amplitude for the force and torque caused by target satellite collision.

Attitude coordination of multi-HUG formation based on multibody system theory

Science.gov (United States)

Xue, Dong-yang; Wu, Zhi-liang; Qi, Er-mai; Wang, Yan-hui; Wang, Shu-xin

2017-04-01

Application of multiple hybrid underwater gliders (HUGs) is a promising method for large scale, long-term ocean survey. Attitude coordination has become a requisite for task execution of multi-HUG formation. In this paper, a multibody model is presented for attitude coordination among agents in the HUG formation. The HUG formation is regarded as a multi-rigid body system. The interaction between agents in the formation is described by artificial potential field (APF) approach. Attitude control torque is composed of a conservative torque generated by orientation potential field and a dissipative term related with angular velocity. Dynamic modeling of the multibody system is presented to analyze the dynamic process of the HUG formation. Numerical calculation is carried out to simulate attitude synchronization with two kinds of formation topologies. Results show that attitude synchronization can be fulfilled based on the multibody method described in this paper. It is also indicated that different topologies affect attitude control quality with respect to energy consumption and adjusting time. Low level topology should be adopted during formation control scheme design to achieve a better control effect.

Dynamic Behavior of Wind Turbine by a Mixed Flexible-Rigid Multi-Body Model

Science.gov (United States)

Wang, Jianhong; Qin, Datong; Ding, Yi

A mixed flexible-rigid multi-body model is presented to study the dynamic behavior of a horizontal axis wind turbine. The special attention is given to flexible body: flexible rotor is modeled by a newly developed blade finite element, support bearing elasticities, variations in the number of teeth in contact as well as contact tooth's elasticities are mainly flexible components in the power train. The couple conditions between different subsystems are established by constraint equations. The wind turbine model is generated by coupling models of rotor, power train and generator with constraint equations together. Based on this model, an eigenproblem analysis is carried out to show the mode shape of rotor and power train at a few natural frequencies. The dynamic responses and contact forces among gears under constant wind speed and fixed pitch angle are analyzed.

Exploration of molecular interactions in cholesterol superlattices: effect of multibody interactions.

Science.gov (United States)

Huang, Juyang

2002-08-01

Experimental evidences have indicated that cholesterol may adapt highly regular lateral distributions (i.e., superlattices) in a phospholipid bilayer. We investigated the formations of superlattices at cholesterol mole fraction of 0.154, 0.25, 0.40, and 0.5 using Monte Carlo simulation. We found that in general, conventional pairwise-additive interactions cannot produce superlattices. Instead, a multibody (nonpairwise) interaction is required. Cholesterol superlattice formation reveals that although the overall interaction between cholesterol and phospholipids is favorable, it contains two large opposing components: an interaction favoring cholesterol-phospholipid mixing and an unfavorable acyl chain multibody interaction that increases nonlinearly with the number of cholesterol contacts. The magnitudes of interactions are in the order of kT. The physical origins of these interactions can be explained by our umbrella model. They most likely come from the requirement for polar phospholipid headgroups to cover the nonpolar cholesterol to avoid the exposure of cholesterol to water and from the sharp decreasing of acyl chain conformation entropy due to cholesterol contact. This study together with our previous work demonstrate that the driving force of cholesterol-phospholipid mixing is a hydrophobic interaction, and multibody interactions dominate others over a wide range of cholesterol concentration.

Active vibration control of spatial flexible multibody systems

International Nuclear Information System (INIS)

Neto, Maria Augusta; Ambrósio, Jorge A. C.; Roseiro, Luis M.; Amaro, A.; Vasques, C. M. A.

2013-01-01

In this work a flexible multibody dynamics formulation of complex models including elastic components made of composite materials is extended to include piezoelectric sensors and actuators. The only limitation for the deformation of a structural member is that they must remain elastic and linear when described in a coordinate frame fixed to a material point or region of its domain. The flexible finite-element model of each flexible body is obtained referring the flexible body nodal coordinates to the body fixed frame and using a diagonalized mass description of the inertia in the mass matrix and on the gyroscopic force vector. The modal superposition technique is used to reduce the number of generalized coordinates to a reasonable dimension for complex shaped structural models of flexible bodies. The active vibration control of the flexible multibody components is implemented using an asymmetric collocated piezoelectric sensor/actuator pair. An electromechanically coupled model is taken into account to properly consider the surface-bonded piezoelectric transducers and their effects on the time and spatial response of the flexible multibody components. The electromechanical effects are introduced in the flexible multibody equations of motion by the use of beam and plate/shell elements, developed to this purpose. A comparative study between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategy, linear quadratic regulator (LQR), is performed in order to investigate their effectiveness to suppress vibrations in structures with piezoelectric sensing and actuating patches.

Active vibration control of spatial flexible multibody systems

Energy Technology Data Exchange (ETDEWEB)

Neto, Maria Augusta, E-mail: augusta.neto@dem.uc.pt [Universidade de Coimbra (Polo II), Departamento de Engenharia Mecanica, Faculdade de Ciencia e Tecnologia (Portugal); Ambrosio, Jorge A. C., E-mail: jorge@dem.ist.utl.pt [Instituto Superior Tecnico, Instituto de Engenharia Mecanica (Portugal); Roseiro, Luis M., E-mail: lroseiro@isec.pt [Instituto Superior de Engenharia de Coimbra, Departamento de Engenharia Mecanica (Portugal); Amaro, A., E-mail: ana.amaro@dem.uc.pt [Universidade de Coimbra (Polo II), Departamento de Engenharia Mecanica, Faculdade de Ciencia e Tecnologia (Portugal); Vasques, C. M. A., E-mail: cvasques@inegi.up.pt [Universidade do Porto, INEGI-Instituto de Engenharia Mecanica e Gestao Industrial (Portugal)

2013-06-15

In this work a flexible multibody dynamics formulation of complex models including elastic components made of composite materials is extended to include piezoelectric sensors and actuators. The only limitation for the deformation of a structural member is that they must remain elastic and linear when described in a coordinate frame fixed to a material point or region of its domain. The flexible finite-element model of each flexible body is obtained referring the flexible body nodal coordinates to the body fixed frame and using a diagonalized mass description of the inertia in the mass matrix and on the gyroscopic force vector. The modal superposition technique is used to reduce the number of generalized coordinates to a reasonable dimension for complex shaped structural models of flexible bodies. The active vibration control of the flexible multibody components is implemented using an asymmetric collocated piezoelectric sensor/actuator pair. An electromechanically coupled model is taken into account to properly consider the surface-bonded piezoelectric transducers and their effects on the time and spatial response of the flexible multibody components. The electromechanical effects are introduced in the flexible multibody equations of motion by the use of beam and plate/shell elements, developed to this purpose. A comparative study between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategy, linear quadratic regulator (LQR), is performed in order to investigate their effectiveness to suppress vibrations in structures with piezoelectric sensing and actuating patches.

Development of an anisotropic beam finite element for composite wind turbine blades in multibody system

DEFF Research Database (Denmark)

Kim, Taeseong; Hansen, Anders Melchior; Branner, Kim

2013-01-01

In this paper a new anisotropic beam finite element for composite wind turbine blades is developed and implemented into the aeroelastic nonlinear multibody code, HAWC2, intended to be used to investigate if use of anisotropic material layups in wind turbine blades can be tailored for improved...

Global Analysis of Nonlinear Dynamics

CERN Document Server

Luo, Albert

2012-01-01

Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.  

6 DOF articulated-arm robot and mobile platform: Dynamic modelling as Multibody System and its validation via Experimental Modal Analysis.

Science.gov (United States)

Toledo Fuentes, A.; Kipfmueller, M.; José Prieto, M. A.

2017-10-01

Mobile manipulators are becoming a key instrument to increase the flexibility in industrial processes. Some of their requirements include handling of objects with different weights and sizes and their “fast” transportation, without jeopardizing production workers and machines. The compensation of forces affecting the system dynamic is therefore needed to avoid unwanted oscillations and tilting by sudden accelerations and decelerations. One general solution may be the implementation of external positioning elements to active stabilize the system. To accomplish the approach, the dynamic behavior of a robotic arm and a mobile platform was investigated to develop the stabilization mechanism using multibody simulations. The methodology used was divided into two phases for each subsystem: their natural frequencies and modal shapes were obtained using experimental modal analyses. Then, based on these experimental results, multibody simulation models (MBS) were set up and its dynamical parameters adjusted. Their modal shapes together with their obtained natural frequencies allowed a quantitative and qualitative analysis. In summary, the MBS models were successfully validated with the real subsystems, with a maximal percentage error of 15%. These models will serve as the basis for future steps in the design of the external actuators and its control strategy using a co-simulation tool.

Nonlinear dynamics aspects of particle accelerators

International Nuclear Information System (INIS)

Jowett, J.M.; Turner, S.; Month, M.

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI)

Path lumping: An efficient algorithm to identify metastable path channels for conformational dynamics of multi-body systems

Science.gov (United States)

Meng, Luming; Sheong, Fu Kit; Zeng, Xiangze; Zhu, Lizhe; Huang, Xuhui

2017-07-01

Constructing Markov state models from large-scale molecular dynamics simulation trajectories is a promising approach to dissect the kinetic mechanisms of complex chemical and biological processes. Combined with transition path theory, Markov state models can be applied to identify all pathways connecting any conformational states of interest. However, the identified pathways can be too complex to comprehend, especially for multi-body processes where numerous parallel pathways with comparable flux probability often coexist. Here, we have developed a path lumping method to group these parallel pathways into metastable path channels for analysis. We define the similarity between two pathways as the intercrossing flux between them and then apply the spectral clustering algorithm to lump these pathways into groups. We demonstrate the power of our method by applying it to two systems: a 2D-potential consisting of four metastable energy channels and the hydrophobic collapse process of two hydrophobic molecules. In both cases, our algorithm successfully reveals the metastable path channels. We expect this path lumping algorithm to be a promising tool for revealing unprecedented insights into the kinetic mechanisms of complex multi-body processes.

Study on Parallel Processing for Efficient Flexible Multibody Analysis based on Subsystem Synthesis Method

Energy Technology Data Exchange (ETDEWEB)

Han, Jong-Boo; Song, Hajun; Kim, Sung-Soo [Chungnam Nat’l Univ., Daejeon (Korea, Republic of)

2017-06-15

Flexible multibody simulations are widely used in the industry to design mechanical systems. In flexible multibody dynamics, deformation coordinates are described either relatively in the body reference frame that is floating in the space or in the inertial reference frame. Moreover, these deformation coordinates are generated based on the discretization of the body according to the finite element approach. Therefore, the formulation of the flexible multibody system always deals with a huge number of degrees of freedom and the numerical solution methods require a substantial amount of computational time. Parallel computational methods are a solution for efficient computation. However, most of the parallel computational methods are focused on the efficient solution of large-sized linear equations. For multibody analysis, we need to develop an efficient formulation that could be suitable for parallel computation. In this paper, we developed a subsystem synthesis method for a flexible multibody system and proposed efficient parallel computational schemes based on the OpenMP API in order to achieve efficient computation. Simulations of a rotating blade system, which consists of three identical blades, were carried out with two different parallel computational schemes. Actual CPU times were measured to investigate the efficiency of the proposed parallel schemes.

Nonlinear dynamics of structures

CERN Document Server

Oller, Sergio

2014-01-01

This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

Hard real-time multibody simulations using ARM-based embedded systems

Energy Technology Data Exchange (ETDEWEB)

Pastorino, Roland, E-mail: roland.pastorino@kuleuven.be, E-mail: rpastorino@udc.es; Cosco, Francesco, E-mail: francesco.cosco@kuleuven.be; Naets, Frank, E-mail: frank.naets@kuleuven.be; Desmet, Wim, E-mail: wim.desmet@kuleuven.be [KU Leuven, PMA division, Department of Mechanical Engineering (Belgium); Cuadrado, Javier, E-mail: javicuad@cdf.udc.es [Universidad de La Coruña, Laboratorio de Ingeniería Mecánica (Spain)

2016-05-15

The real-time simulation of multibody models on embedded systems is of particular interest for controllers and observers such as model predictive controllers and state observers, which rely on a dynamic model of the process and are customarily executed in electronic control units. This work first identifies the software techniques and tools required to easily write efficient code for multibody models to be simulated on ARM-based embedded systems. Automatic Programming and Source Code Translation are the two techniques that were chosen to generate source code for multibody models in different programming languages. Automatic Programming is used to generate procedural code in an intermediate representation from an object-oriented library and Source Code Translation is used to translate the intermediate representation automatically to an interpreted language or to a compiled language for efficiency purposes. An implementation of these techniques is proposed. It is based on a Python template engine and AST tree walkers for Source Code Generation and on a model-driven translator for the Source Code Translation. The code is translated from a metalanguage to any of the following four programming languages: Python-Numpy, Matlab, C++-Armadillo, C++-Eigen. Two examples of multibody models were simulated: a four-bar linkage with multiple loops and a 3D vehicle steering system. The code for these examples has been generated and executed on two ARM-based single-board computers. Using compiled languages, both models could be simulated faster than real-time despite the low resources and performance of these embedded systems. Finally, the real-time performance of both models was evaluated when executed in hard real-time on Xenomai for both embedded systems. This work shows through measurements that Automatic Programming and Source Code Translation are valuable techniques to develop real-time multibody models to be used in embedded observers and controllers.

Hard real-time multibody simulations using ARM-based embedded systems

International Nuclear Information System (INIS)

Pastorino, Roland; Cosco, Francesco; Naets, Frank; Desmet, Wim; Cuadrado, Javier

2016-01-01

The real-time simulation of multibody models on embedded systems is of particular interest for controllers and observers such as model predictive controllers and state observers, which rely on a dynamic model of the process and are customarily executed in electronic control units. This work first identifies the software techniques and tools required to easily write efficient code for multibody models to be simulated on ARM-based embedded systems. Automatic Programming and Source Code Translation are the two techniques that were chosen to generate source code for multibody models in different programming languages. Automatic Programming is used to generate procedural code in an intermediate representation from an object-oriented library and Source Code Translation is used to translate the intermediate representation automatically to an interpreted language or to a compiled language for efficiency purposes. An implementation of these techniques is proposed. It is based on a Python template engine and AST tree walkers for Source Code Generation and on a model-driven translator for the Source Code Translation. The code is translated from a metalanguage to any of the following four programming languages: Python-Numpy, Matlab, C++-Armadillo, C++-Eigen. Two examples of multibody models were simulated: a four-bar linkage with multiple loops and a 3D vehicle steering system. The code for these examples has been generated and executed on two ARM-based single-board computers. Using compiled languages, both models could be simulated faster than real-time despite the low resources and performance of these embedded systems. Finally, the real-time performance of both models was evaluated when executed in hard real-time on Xenomai for both embedded systems. This work shows through measurements that Automatic Programming and Source Code Translation are valuable techniques to develop real-time multibody models to be used in embedded observers and controllers.

Nonlinear dynamics and astrophysics

International Nuclear Information System (INIS)

Vallejo, J. C.; Sanjuan, M. A. F.

2000-01-01

Concepts and techniques from Nonlinear Dynamics, also known as Chaos Theory, have been applied successfully to several astrophysical fields such as orbital motion, time series analysis or galactic dynamics, providing answers to old questions but also opening a few new ones. Some of these topics are described in this review article, showing the basis of Nonlinear Dynamics, and how it is applied in Astrophysics. (Author)

Gradient-based optimization in nonlinear structural dynamics

DEFF Research Database (Denmark)

Dou, Suguang

The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...

Development of Constraint Force Equation Methodology for Application to Multi-Body Dynamics Including Launch Vehicle Stage Seperation

Science.gov (United States)

Pamadi, Bandu N.; Toniolo, Matthew D.; Tartabini, Paul V.; Roithmayr, Carlos M.; Albertson, Cindy W.; Karlgaard, Christopher D.

2016-01-01

The objective of this report is to develop and implement a physics based method for analysis and simulation of multi-body dynamics including launch vehicle stage separation. The constraint force equation (CFE) methodology discussed in this report provides such a framework for modeling constraint forces and moments acting at joints when the vehicles are still connected. Several stand-alone test cases involving various types of joints were developed to validate the CFE methodology. The results were compared with ADAMS(Registered Trademark) and Autolev, two different industry standard benchmark codes for multi-body dynamic analysis and simulations. However, these two codes are not designed for aerospace flight trajectory simulations. After this validation exercise, the CFE algorithm was implemented in Program to Optimize Simulated Trajectories II (POST2) to provide a capability to simulate end-to-end trajectories of launch vehicles including stage separation. The POST2/CFE methodology was applied to the STS-1 Space Shuttle solid rocket booster (SRB) separation and Hyper-X Research Vehicle (HXRV) separation from the Pegasus booster as a further test and validation for its application to launch vehicle stage separation problems. Finally, to demonstrate end-to-end simulation capability, POST2/CFE was applied to the ascent, orbit insertion, and booster return of a reusable two-stage-to-orbit (TSTO) vehicle concept. With these validation exercises, POST2/CFE software can be used for performing conceptual level end-to-end simulations, including launch vehicle stage separation, for problems similar to those discussed in this report.

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

Nonlinear dynamics aspects of particle accelerators. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Jowett, J M; Turner, S; Month, M

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI).

Nonlinear dynamics in Nuclotron

International Nuclear Information System (INIS)

Dinev, D.

1997-01-01

The paper represents an extensive study of the nonlinear beam dynamics in the Nuclotron. Chromatic effects, including the dependence of the betatron tunes on the amplitude, and chromatic perturbations have been investigated taking into account the measured field imperfections. Beam distortion, smear, dynamic aperture and nonlinear acceptance have been calculated for different particle energies and betatron tunes

Nonlinear Dynamic Phenomena in Mechanics

CERN Document Server

Warminski, Jerzy; Cartmell, Matthew P

2012-01-01

Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

Science.gov (United States)

Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

2018-05-01

In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

Nonlinear dynamics aspects of particle accelerators

International Nuclear Information System (INIS)

Araki, H.; Ehlers, J.; Hepp, K.; Kippenhahn, R.; Weidenmuller, A.; Zittartz, J.

1986-01-01

This book contains 18 selections. Some of the titles are: Integrable and Nonintegrable Hamiltonian Systems; Nonlinear Dynamics Aspects of Modern Storage Rings; Nonlinear Beam-Beam Resonances; Synchro-Betatron Resonances; Review of Beam-Beam Simulations; and Perturbation Method in Nonlinear Dynamics

Nonlinear transport of dynamic system phase space

International Nuclear Information System (INIS)

Xie Xi; Xia Jiawen

1993-01-01

The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

Applications of Lie Group Theory to the Modeling and Control of Multibody Systems

International Nuclear Information System (INIS)

Mladenova, Clementina D.

1999-01-01

This paper reviews our research activities concerning the modeling and control of rigid and elastic joint multibody mechanical systems, including some investigations into nonholonomic systems. Bearing in mind the different parameterizations of the rotation group in three-dimensional space SO(3), and the fact that the properties of the parameterization more or less influence the efficiency of the dynamics model, here the so-called vector parameter is used for parallel considerations of rigid body motion and of rigid and elastic joint multibody mechanical systems. Besides the fundamental role of this study, the vector-parameter approach is efficient in its computational aspect and quite convenient for real time simulation and control. The consideration of the mechanical system on the configuration space of pure vector parameters with a group structure opens the possibilities for the Lie group theory to be applied in problems of dynamics and control

Nonlinear dynamics in biological systems

CERN Document Server

Carballido-Landeira, Jorge

2016-01-01

This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...

International Conference on Applications in Nonlinear Dynamics

CERN Document Server

Longhini, Patrick; Palacios, Antonio

2017-01-01

This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

Beam Stability and Nonlinear Dynamics. Proceedings

International Nuclear Information System (INIS)

Parsa, Z.

1997-01-01

These proceedings represent papers presented at the Beam Stability and Nonlinear Dynamics symposium held in Santa Barbara in December 1996. The symposium was sponsored by the National Science Foundation as part of the United States long term accelerator research. The focus of this symposium was on nonlinear dynamics and beam stability. The topics included single-particle and many-particle dynamics, and stability in large circular accelerators such as the Large Hadron Collider(LHC). Other subjects covered were spin dynamics, nonlinear aberration correction, collective effects in the LHC, sawtooth instability and Landau damping in the presence of strong nonlinearity. There were presentations concerning plasma physics including the effect of beam echo. There are 17 papers altogether in these proceedings and 8 of them have been abstracted for the Energy Science and Technology database

Nonlinear dynamics experiment in the Tevatron

International Nuclear Information System (INIS)

Merminga, N.; Edwards, D.; Finley, D.

1989-01-01

Results of the continuing analysis of the nonlinear dynamics experiment E778 are presented. Sixteen special sextupoles introduced nonlinearities in the Tevatron. 'Smear,' which is one of the parameters used to quantify the degree of nonlinearity, was extracted from the data and compared with calculation. Injection efficiency in the presence of nonlinearities was studied. Measurements of the dynamic aperture were performed. The final results in one degree of freedom of the smear, the injection efficiency and the dynamic aperture are presented. Particles captured on nonlinear resonance islands were directly observed and measurements were performed. The capture efficiency was extracted from the data and compared with prediction. The influence of tune modulation on the stability of these islands was investigated. Plans for future measurements are discussed. 4 refs., 6 figs

A 3D Finite Element Method for Flexible Multibody Systems

International Nuclear Information System (INIS)

Gerstmayr, Johannes; Schoeberl, Joachim

2006-01-01

An efficient finite element (FE) formulation for the simulation of multibody systems is derived from Hamilton's principle. According to the classical assumptions of multibody systems, a large rotation formulation has been chosen, where large rotations and large displacements, but only small deformations of the single bodies are taken into account. The strain tensor is linearized with respect to a co-rotated frame. The present approach uses absolute coordinates for the degrees of freedom and forms an alternative to the floating frame of reference formulation that is based on relative coordinates and describes deformation with respect to a co-rotated frame. Due to the modified strain tensor, the present formulation distinguishes significantly from standard nodal based nonlinear FE methods. Constraints are defined in integral form for every pair of surfaces of two bodies. This leads to a small number of constraint equations and avoids artificial stress singularities. The resulting mass and stiffness matrices are constant apart from a transformation based on a single rotation matrix for each body. The particular structure of this transformation allows to prevent from the usually expensive factorization of the system Jacobian within implicit time--integration methods. The present method has been implemented and tested with the FE-package NGSolve and specific 3D examples are verified with a standard beam formulation

Nonlinear Dynamics in Spear Wigglers

International Nuclear Information System (INIS)

2002-01-01

BL11, the most recently installed wiggler in the SPEAR storage ring at SSRL, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and with closed orbit shifts were used to characterize the nonlinear fields of the SPEAR insertion devices (IDs). Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different than the flip coil measurements made along a straight line. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Corrector magnets to cancel the BL11 nonlinear fields are presently under construction

Structural stability of nonlinear population dynamics.

Science.gov (United States)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

Science.gov (United States)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Physical essence of the multibody contact-sliding at atomic scale

Science.gov (United States)

Han, Xuesong

2014-01-01

Investigation the multibody contact-sliding occurred at atomic discrete contact spot will play an important role in determine the origin of tribology behavior and evaluates the micro-mechanical property of nanomaterials and thus optimizing the design of surface texture. This paper carries out large scale parallel molecular dynamics simulation on contact-sliding at atomic scale to uncover the special physical essence. The research shows that some kind of force field exists between nanodot pair and the interaction can be expressed by the linear combination of exponential function while the effective interaction distance limited in 1 angstrom for nanodot with several tens of nanometer diameter. The variation tendency about the interaction force between nanodot array is almost the same between nanodot pairs and thus the interaction between two nanodot array can be characterized by parallel mechanical spring. Multibody effect which dominates the interaction between atoms or molecules will gradually diminish with the increasing of length scales.

Dynamics of nonlinear feedback control.

Science.gov (United States)

Snippe, H P; van Hateren, J H

2007-05-01

Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input steps, the dynamics of gain and attenuation can be very different, depending on the mathematical form of the nonlinearity and the ordering of the nonlinearity and the filtering in the feedback loop. Further, the dynamics of feedback control can be strongly asymmetrical for increment versus decrement steps of the input. Nevertheless, for each of the models studied, the nonlinearity in the feedback loop can be chosen such that immediately after an input step, the dynamics of feedback control is symmetric with respect to increments versus decrements. Finally, we study the dynamics of the output of the control loops and find conditions under which overshoots and undershoots of the output relative to the steady-state output occur when the models are stimulated with low-pass filtered steps. For small steps at the input, overshoots and undershoots of the output do not occur when the filtering in the control path is faster than the low-pass filtering at the input. For large steps at the input, however, results depend on the model, and for some of the models, multiple overshoots and undershoots can occur even with a fast control path.

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig

Nonlinear analysis of pupillary dynamics.

Science.gov (United States)

Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo

2016-02-01

Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (pnonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. (c) autonomic stimulation is partially reflected in nonlinear dynamics.

Device Applications of Nonlinear Dynamics

CERN Document Server

Baglio, Salvatore

2006-01-01

This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.

Comparison of stochastic resonance in static and dynamical nonlinearities

International Nuclear Information System (INIS)

Ma, Yumei; Duan, Fabing

2014-01-01

We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution. - Highlights: • Comparison of SR effects in arrays of both static and dynamical nonlinearities. • Static nonlinearity is easily implementable for the SNR enhancement. • Dynamical nonlinearity yields a better output SNR for external Laplacian noise

Nonlinear dynamics and numerical uncertainties in CFD

Science.gov (United States)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Perspectives of nonlinear dynamics

International Nuclear Information System (INIS)

Jackson, E.A.

1985-03-01

Four lectures were given weekly in October and November, 1984, and some of the ideas presented here will be of use in the future. First, a brief survey of the historical development of nonlinear dynamics since about 1890 was given, and then, a few topics were discussed in detail. The objective was to introduce some of many concepts and methods which are presently used for describing nonlinear dynamics. The symbiotic relationship between sciences of all types and mathematics, two main categories of the models describing nature, the method for describing the dynamics of a system, the idea of control parameters and topological dimension, the asymptotic properties of dynamics, abstract dynamics, the concept of embedding, singular perturbation theory, strange attractor, Fermi-Pasta-Ulam phenomena, an example of computer heuristics, the idea of elementary catastrophe theory and so on were explained. The logistic map is the simplest introduction to complex dynamics. The complicated dynamics is referred to as strange attractors. Two-dimensional maps are the highest dimensional maps commonly studied. These were discussed in detail. (Kako, I.)

Investigating the running abilities of Tyrannosaurus rex using stress-constrained multibody dynamic analysis

Directory of Open Access Journals (Sweden)

William I. Sellers

2017-07-01

Full Text Available The running ability of Tyrannosaurus rex has been intensively studied due to its relevance to interpretations of feeding behaviour and the biomechanics of scaling in giant predatory dinosaurs. Different studies using differing methodologies have produced a very wide range of top speed estimates and there is therefore a need to develop techniques that can improve these predictions. Here we present a new approach that combines two separate biomechanical techniques (multibody dynamic analysis and skeletal stress analysis to demonstrate that true running gaits would probably lead to unacceptably high skeletal loads in T. rex. Combining these two approaches reduces the high-level of uncertainty in previous predictions associated with unknown soft tissue parameters in dinosaurs, and demonstrates that the relatively long limb segments of T. rex—long argued to indicate competent running ability—would actually have mechanically limited this species to walking gaits. Being limited to walking speeds contradicts arguments of high-speed pursuit predation for the largest bipedal dinosaurs like T. rex, and demonstrates the power of multiphysics approaches for locomotor reconstructions of extinct animals.

Nonlinear PDEs a dynamical systems approach

CERN Document Server

Schneider, Guido

2017-01-01

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced...

Some Aspects of Nonlinear Dynamics and CFD

Science.gov (United States)

Yee, Helen C.; Merriam, Marshal (Technical Monitor)

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

DEFF Research Database (Denmark)

True, Hans

1999-01-01

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed......., and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice...

Spin-current emission governed by nonlinear spin dynamics.

Science.gov (United States)

Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya

2015-10-16

Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

NARCIS (Netherlands)

Schilder, Jurnan Paul; Ellenbroek, Marcellinus Hermannus Maria; de Boer, A.

2017-01-01

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of

Describing pediatric dysphonia with nonlinear dynamic parameters

Science.gov (United States)

Meredith, Morgan L.; Theis, Shannon M.; McMurray, J. Scott; Zhang, Yu; Jiang, Jack J.

2008-01-01

Objective Nonlinear dynamic analysis has emerged as a reliable and objective tool for assessing voice disorders. However, it has only been tested on adult populations. In the present study, nonlinear dynamic analysis was applied to normal and dysphonic pediatric populations with the goal of collecting normative data. Jitter analysis was also applied in order to compare nonlinear dynamic and perturbation measures. This study’s findings will be useful in creating standards for the use of nonlinear dynamic analysis as a tool to describe dysphonia in the pediatric population. Methods The study included 38 pediatric subjects (23 children with dysphonia and 15 without). Recordings of sustained vowels were obtained from each subject and underwent nonlinear dynamic analysis and percent jitter analysis. The resulting correlation dimension (D2) and percent jitter values were compared across the two groups using t-tests set at a significance level of p = 0.05. Results It was shown that D2 values covary with the presence of pathology in children. D2 values were significantly higher in dysphonic children than in normal children (p = 0.002). Standard deviations indicated a higher level of variation in normal children’s D2 values than in dysphonic children’s D2 values. Jitter analysis showed markedly higher percent jitter in dysphonic children than in normal children (p = 0.025) and large standard deviations for both groups. Conclusion This study indicates that nonlinear dynamic analysis could be a viable tool for the detection and assessment of dysphonia in children. Further investigations and more normative data are needed to create standards for using nonlinear dynamic parameters for the clinical evaluation of pediatric dysphonia. PMID:18947887

Dynamics and vibrations progress in nonlinear analysis

CERN Document Server

Kachapi, Seyed Habibollah Hashemi

2014-01-01

Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...

On the dynamics of Airy beams in nonlinear media with nonlinear losses.

Science.gov (United States)

Ruiz-Jiménez, Carlos; Nóbrega, K Z; Porras, Miguel A

2015-04-06

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

4th International Conference on Structural Nonlinear Dynamics and Diagnosis

CERN Document Server

2018-01-01

This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...

Dynamics of nonlinear feedback control

OpenAIRE

Snippe, H.P.; Hateren, J.H. van

2007-01-01

Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input step...

Experimental validation of flexible multibody dynamics beam formulations

Energy Technology Data Exchange (ETDEWEB)

Bauchau, Olivier A., E-mail: olivier.bauchau@sjtu.edu.cn; Han, Shilei [University of Michigan-Shanghai Jiao Tong University Joint Institute (China); Mikkola, Aki; Matikainen, Marko K. [Lappeenranta University of Technology, Department of Mechanical Engineering (Finland); Gruber, Peter [Austrian Center of Competence in Mechatronics GmbH (Austria)

2015-08-15

In this paper, the accuracies of the geometrically exact beam and absolute nodal coordinate formulations are studied by comparing their predictions against an experimental data set referred to as the “Princeton beam experiment.” The experiment deals with a cantilevered beam experiencing coupled flap, lag, and twist deformations. In the absolute nodal coordinate formulation, two different beam elements are used. The first is based on a shear deformable approach in which the element kinematics is described using two nodes. The second is based on a recently proposed approach featuring three nodes. The numerical results for the geometrically exact beam formulation and the recently proposed three-node absolute nodal coordinate formulation agree well with the experimental data. The two-node beam element predictions are similar to those of linear beam theory. This study suggests that a careful and thorough evaluation of beam elements must be carried out to assess their ability to deal with the three-dimensional deformations typically found in flexible multibody systems.

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

Intramolecular and nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Davis, M.J. [Argonne National Laboratory, IL (United States)

1993-12-01

Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.

Quantitative theory of driven nonlinear brain dynamics.

Science.gov (United States)

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

A Non-smooth Newton Method for Multibody Dynamics

International Nuclear Information System (INIS)

Erleben, K.; Ortiz, R.

2008-01-01

In this paper we deal with the simulation of rigid bodies. Rigid body dynamics have become very important for simulating rigid body motion in interactive applications, such as computer games or virtual reality. We present a novel way of computing contact forces using a Newton method. The contact problem is reformulated as a system of non-linear and non-smooth equations, and we solve this system using a non-smooth version of Newton's method. One of the main contribution of this paper is the reformulation of the complementarity problems, used to model impacts, as a system of equations that can be solved using traditional methods.

Nonlinear Deformable-body Dynamics

CERN Document Server

Luo, Albert C J

2010-01-01

"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...

An Efficient Method for Synthesis of Planar Multibody Systems including Shape of Bodies as Design Variables

DEFF Research Database (Denmark)

Hansen, Michael R.; Hansen, John Michael

1998-01-01

A point contact joint has been developed and implemented in a joint coordinate based planar multibody dynamics analysis program that also supports revolute and translational joints. Further, a segment library for the definition of the contours of the point contact joints has been integrated...

Overview of magnetic nonlinear beam dynamics in the RHIC

International Nuclear Information System (INIS)

Luo, Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, F.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, G.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.

2009-01-01

In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed

Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements

International Nuclear Information System (INIS)

Garcia-Vallejo, D.; Mayo, J.; Escalona, J. L.; Dominguez, J.

2008-01-01

Multibody systems generally contain solids with appreciable deformations and which decisively influence the dynamics of the system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a rigid-flexible multibody system, two types of formulations coexist in the equations of the system. Among the different possibilities provided in the literature on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates are utilized in this paper to model the rigid and flexible solids, respectively. This paper contains a mixed formulation based on the possibility of sharing coordinates between a rigid solid and a flexible solid. The global mass matrix of the system is shown to be constant and, in addition, many of the constraint equations obtained upon utilizing these formulations are linear and can be eliminated

Periodic precursors of nonlinear dynamical transitions

International Nuclear Information System (INIS)

Jiang Yu; Dong Shihai; Lozada-Cassou, M.

2004-01-01

We study the resonant response of a nonlinear system to external periodic perturbations. We show by numerical simulation that the periodic resonance curve may anticipate the dynamical instability of the unperturbed nonlinear periodic system, at parameter values far away from the bifurcation points. In the presence of noise, the buried intrinsic periodic dynamics can be picked out by analyzing the system's response to periodic modulation of appropriate intensity

Teaching nonlinear dynamics through elastic cords

International Nuclear Information System (INIS)

Chacon, R; Galan, C A; Sanchez-Bajo, F

2011-01-01

We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

Self-Organized Biological Dynamics and Nonlinear Control

Science.gov (United States)

Walleczek, Jan

2006-04-01

The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological

Nonlinear switching dynamics in a photonic-crystal nanocavity

International Nuclear Information System (INIS)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.

Nonlinear switching dynamics in a photonic-crystal nanocavity

DEFF Research Database (Denmark)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...

Nonlinear and Nonequilibrium Dynamics in Geomaterials

OpenAIRE

TenCate, James A.; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A.

2004-01-01

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a s...

Nonlinear Dynamic Models in Advanced Life Support

Science.gov (United States)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Report of the working group on single-particle nonlinear dynamics

International Nuclear Information System (INIS)

Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M.

1999-01-01

The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of accelerators. (AIP) copyright 1999 American Institute of Physics

Nonlinear and stochastic dynamics of coherent structures

DEFF Research Database (Denmark)

Rasmussen, Kim

1997-01-01

This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...

MEMS linear and nonlinear statics and dynamics

CERN Document Server

Younis, Mohammad I

2011-01-01

MEMS Linear and Nonlinear Statics and Dynamics presents the necessary analytical and computational tools for MEMS designers to model and simulate most known MEMS devices, structures, and phenomena. This book also provides an in-depth analysis and treatment of the most common static and dynamic phenomena in MEMS that are encountered by engineers. Coverage also includes nonlinear modeling approaches to modeling various MEMS phenomena of a nonlinear nature, such as those due to electrostatic forces, squeeze-film damping, and large deflection of structures. The book also: Includes examples of nume

Analysis of Nonlinear Dynamics by Square Matrix Method

Energy Technology Data Exchange (ETDEWEB)

Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II

2016-07-25

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.

Dynamics of nonlinear feedback control

NARCIS (Netherlands)

Snippe, H.P.; Hateren, J.H. van

Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain

Development of Viscoelastic Multi-Body Simulation and Impact Response Analysis of a Ballasted Railway Track under Cyclic Loading

Directory of Open Access Journals (Sweden)

Daisuke Nishiura

2017-06-01

Full Text Available Simulation of a large number of deformable bodies is often difficult because complex high-level modeling is required to address both multi-body contact and viscoelastic deformation. This necessitates the combined use of a discrete element method (DEM and a finite element method (FEM. In this study, a quadruple discrete element method (QDEM was developed for dynamic analysis of viscoelastic materials using a simpler algorithm compared to the standard FEM. QDEM easily incorporates the contact algorithm used in DEM. As the first step toward multi-body simulation, the fundamental performance of QDEM was investigated for viscoelastic analysis. The amplitude and frequency of cantilever elastic vibration were nearly equal to those obtained by the standard FEM. A comparison of creep recovery tests with an analytical solution showed good agreement between them. In addition, good correlation between the attenuation degree and the real physical viscosity was confirmed for viscoelastic vibration analysis. Therefore, the high accuracy of QDEM in the fundamental analysis of infinitesimal viscoelastic deformations was verified. Finally, the impact response of a ballast and sleeper under cyclic loading on a railway track was analyzed using QDEM as an application of deformable multi-body dynamics. The results showed that the vibration of the ballasted track was qualitatively in good agreement with the actual measurements. Moreover, the ballast layer with high friction reduced the ballasted track deterioration. This study suggests that QDEM, as an alternative to DEM and FEM, can provide deeper insights into the contact dynamics of a large number of deformable bodies.

Nonlinear dynamics and chaotic phenomena an introduction

CERN Document Server

Shivamoggi, Bhimsen K

2014-01-01

This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics  -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special...

Application of stabilization techniques in the dynamic analysis of multibody systems

Directory of Open Access Journals (Sweden)

Hajžman M.

2007-11-01

Full Text Available This paper is intended to the discussion of possible methods for the solution of the motion equations of constrained multibody systems. They can be formulated in the form of differential-algebraic equations and their numerical solution brings the problems of constraint violation and numerical stability. Therefore special methods were proposed to handle these problems. Various approaches for the numerical solution of equations are briefly reviewed and the application of the Baumgarte’s stabilization method on testing examples is shown. The paper was motivated by the effort to find the suitable solution methods for the equations of motion in the form of differentialalgebraic equations using the MATLAB standard computational system.

Nonlinear Dynamics of Nanomechanical Resonators

Science.gov (United States)

Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym

2007-03-01

Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004).

Predictable nonlinear dynamics: Advances and limitations

International Nuclear Information System (INIS)

Anosov, L.A.; Butkovskii, O.Y.; Kravtsov, Y.A.; Surovyatkina, E.D.

1996-01-01

Methods for reconstruction chaotic dynamical system structure directly from experimental time series are described. Effectiveness of general methods is illustrated with the results of numerical simulation. It is of common interest that from the single time series it is possible to reconstruct a set of interconnected variables. Predictive power of dynamical models, provided by the nonlinear dynamics inverse problem solution, is limited firstly by the noise level in the system under study and is characterized by the horizon of predictability. New physical results are presented, concerning nonstationary and bifurcation nonlinear systems: (1) algorithms for revealing of nonstationarity in random-like chaotic time-series are suggested based on discriminant analysis with nonlinear discriminant function; (2) an opportunity is established to predict the final state in bifurcation system with quickly varying control parameters; (3) hysteresis is founded out in bifurcation system with quickly varying parameters; (4) delayed correlation left-angle noise-prediction error right-angle in chaotic systems is revealed. copyright 1996 American Institute of Physics

An investigation of the structural dynamic behaviour of a vehicle transmission by means of multibody simulation; Untersuchung des strukturdynamischen und akustischen Verhaltens eines Fahrzeuggetriebes mit MKS

Energy Technology Data Exchange (ETDEWEB)

Gross, Volker [ZF Friedrichshafen AG, Friedrichshafen (Germany)

2011-07-01

The legal regulations and the customers' requirements as regards vehicle comfort are growing more and more stringent. This also includes the transmission systems, as they are expected not so show any obvious acoustic or dynamic weaknesses. Modern simulation methods permit evaluation and optimization of structure-borne and airborne noise in the early stage of development. Especially the FE method is a well-established technique for the simulation of structure-borne sound. With regard to complex transmissions, multibody simulations (MBS) can provide valuable insights for a realistic evaluation of the dynamic behaviour of a transmission. This is demonstrated using a truck transmission as an example. (orig.)

Experimental studies of nonlinear beam dynamics

International Nuclear Information System (INIS)

Caussyn, D.D.; Ball, M.; Brabson, B.; Collins, J.; Curtis, S.A.; Derenchuck, V.; DuPlantis, D.; East, G.; Ellison, M.; Ellison, T.; Friesel, D.; Hamilton, B.; Jones, W.P.; Lamble, W.; Lee, S.Y.; Li, D.; Minty, M.G.; Sloan, T.; Xu, G.; Chao, A.W.; Ng, K.Y.; Tepikian, S.

1992-01-01

The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the Indiana University Cyclotron Facility cooler ring. Motion in one dimension was measured for betatron tunes near the third, fourth, fifth, and seventh integer resonances. This motion is described by coupling between the transverse modes of motion and nonlinear field errors. The Hamiltonian for nonlinear particle motion near the third- and fourth-integer-resonance conditions has been deduced

Nonlinear dynamic range transformation in visual communication channels.

Science.gov (United States)

Alter-Gartenberg, R

1996-01-01

The article evaluates nonlinear dynamic range transformation in the context of the end-to-end continuous-input/discrete processing/continuous-display imaging process. Dynamic range transformation is required when we have the following: (i) the wide dynamic range encountered in nature is compressed into the relatively narrow dynamic range of the display, particularly for spatially varying irradiance (e.g., shadow); (ii) coarse quantization is expanded to the wider dynamic range of the display; and (iii) nonlinear tone scale transformation compensates for the correction in the camera amplifier.

Energy flow theory of nonlinear dynamical systems with applications

CERN Document Server

Xing, Jing Tang

2015-01-01

This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

The numerical dynamic for highly nonlinear partial differential equations

Science.gov (United States)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Modelling of joints with clearance and friction in multibody dynamic simulation of automotive differentials

OpenAIRE

Virlez, Geoffrey; Bruls, Olivier; Tromme, Emmanuel; Duysinx, Pierre

2012-01-01

Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the lubrication and the flexibility affect the transient behaviour, reduce the component life and produce noise and vibration for classical joints such as prismatic, cylindric or universal joint. In this work, a new 3D cylindrical joint model which accounts for the clearance, the misalignment and the...

Comparison between vertical acceleration data from acquired signals and multibody model for an off-road vehicle

Directory of Open Access Journals (Sweden)

Cristian Padilha Fontoura

2018-02-01

Full Text Available SAE Mini Baja competitions require efforts in developing a reliable vehicle project that enables their teams to manage time and resources wisely. Vehicle simulations are one the best ways to deal with these conditions and prevent failure during a test. This work outlines the methodology that was carried out for validating the multibody dynamics model of a Mini Baja vehicle through vertical acceleration data acquisition. The data was acquired with the vehicle in different sets of obstacles, based on those seen in previously held competitions. Simulation was done through ADAMS/Car, with the vehicle’s multibody model being simulated in different three-dimensional roads, counterpart to those where data acquisition took place. Simulation data, when compared to acquired acceleration signals for most of the obstacles, exhibited equivalence. Additional data computation revealed that the spectra in the frequency domain presented most severe loads concentrated between 0 and 20 Hz, incoming mostly from road unevenness. Gathering such data, by the presented approach can assist future analyses and guide the Baja Team in defining an improved project by predicting its dynamic behavior.

Digital Communication Devices Based on Nonlinear Dynamics and Chaos

National Research Council Canada - National Science Library

Larson, Lawrence

2003-01-01

The final report of the ARO MURI "Digital Communications Based on Chaos and Nonlinear Dynamics" contains research results in the areas of chaos and nonlinear dynamics applied to wireless and optical communications...

Nonlinear Dynamical Analysis for a Plain Bearing

Directory of Open Access Journals (Sweden)

Ali Belhamra

2014-03-01

Full Text Available This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film. The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance and asynchrony (whipping amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances.

COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

Energy Technology Data Exchange (ETDEWEB)

Sun, Y.; Borland, Michael

2017-06-25

Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

Nonlinear dynamics as an engine of computation.

Science.gov (United States)

Kia, Behnam; Lindner, John F; Ditto, William L

2017-03-06

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

Science.gov (United States)

Chiou, Jin-Chern

1990-01-01

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Nonlinear dynamics between linear and impact limits

CERN Document Server

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

Is DNA a nonlinear dynamical system where solitary conformational ...

Indian Academy of Sciences (India)

Unknown

DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.

International Conference on Structural Nonlinear Dynamics and Diagnosis

CERN Document Server

CSNDD 2012; CSNDD 2014

2015-01-01

This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics.  Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characteriz...

Nonlinear dynamics of quadratically cubic systems

International Nuclear Information System (INIS)

Rudenko, O V

2013-01-01

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

Nonlinear dynamical system approaches towards neural prosthesis

International Nuclear Information System (INIS)

Torikai, Hiroyuki; Hashimoto, Sho

2011-01-01

An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

Criteria of benchmark selection for efficient flexible multibody system formalisms

Directory of Open Access Journals (Sweden)

Valášek M.

2007-10-01

Full Text Available The paper deals with the selection process of benchmarks for testing and comparing efficient flexible multibody formalisms. The existing benchmarks are briefly summarized. The purposes for benchmark selection are investigated. The result of this analysis is the formulation of the criteria of benchmark selection for flexible multibody formalisms. Based on them the initial set of suitable benchmarks is described. Besides that the evaluation measures are revised and extended.

A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics

International Nuclear Information System (INIS)

Johnson, Jay R.; Wing, Simon

2004-01-01

Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach

Nonlinear dynamics of the human lumbar intervertebral disc.

Science.gov (United States)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

Nonlinear beam dynamics experimental program at SPEAR

International Nuclear Information System (INIS)

Tran, P.; Pellegrini, C.; Cornacchia, M.; Lee, M.; Corbett, W.

1995-01-01

Since nonlinear effects can impose strict performance limitations on modern colliders and storage rings, future performance improvements depend on further understanding of nonlinear beam dynamics. Experimental studies of nonlinear beam motion in three-dimensional space have begun in SPEAR using turn-by-turn transverse and longitudinal phase-space monitors. This paper presents preliminary results from an on-going experiment in SPEAR

Nonlinear amplitude dynamics in flagellar beating.

Science.gov (United States)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-01-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map (ST). Thus, it is natural to pose the question asking how the relativistic effects change the nonlinear dynamical behavior described by the classical ST map. The authors show that the speed of light limits the rate of advance of the phase in the relativistic standard map (RST) and introduces KAM surfaces persisting in the high momentum region. The RST map is a two parameter (k, β = ω/kc) family of dynamics reducing to the ST map when β → 0. For β ≠ 0 the relativity suppresses the onset of stochasticity. Chernikov et al. has also reported this effect. They have carried out extensive studies of nonlinear dynamics of the RST map and found very intricate structure of mixing of the higher order periodic orbits and chaotic orbits. They have shown that no matter how its gets chaotic the symmetry properties of the RST map determines its nonlinear dynamical behavior. 1 ref

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

Science.gov (United States)

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

An Improved Rigid Multibody Model for the Dynamic Analysis of the Planetary Gearbox in a Wind Turbine

Directory of Open Access Journals (Sweden)

Wenguang Yang

2016-01-01

Full Text Available This paper proposes an improved rigid multibody model for the dynamic analysis of the planetary gearbox in a wind turbine. The improvements mainly include choosing the inertia frame as the reference frame of the carrier, the ring, and the sun and adding a new degree of freedom for each planet. An element assembly method is introduced to build the model, and a time-varying mesh stiffness model is presented. A planetary gear study case is employed to verify the validity of the improved model. Comparisons between the improvement model and the traditional model show that the natural characteristics are very close; the improved model can obtain the right equivalent moment of inertia of the planetary gear in the transient simulation, and all the rotation speeds satisfy the transmission relationships well; harmonic resonance and resonance modulation phenomena can be found in their vibration signals. The improved model is applied in a multistage gearbox dynamics analysis to reveal the prospects of the model. Modal analysis and transient analysis with and without time-varying mesh stiffness considered are conducted. The rotation speeds from the transient analysis are consistent with the theory, and resonance modulation can be found in the vibration signals.

Nonlinear analysis of dynamic signature

Science.gov (United States)

Rashidi, S.; Fallah, A.; Towhidkhah, F.

2013-12-01

Signature is a long trained motor skill resulting in well combination of segments like strokes and loops. It is a physical manifestation of complex motor processes. The problem, generally stated, is that how relative simplicity in behavior emerges from considerable complexity of perception-action system that produces behavior within an infinitely variable biomechanical and environmental context. To solve this problem, we present evidences which indicate that motor control dynamic in signing process is a chaotic process. This chaotic dynamic may explain a richer array of time series behavior in motor skill of signature. Nonlinear analysis is a powerful approach and suitable tool which seeks for characterizing dynamical systems through concepts such as fractal dimension and Lyapunov exponent. As a result, they can be analyzed in both horizontal and vertical for time series of position and velocity. We observed from the results that noninteger values for the correlation dimension indicates low dimensional deterministic dynamics. This result could be confirmed by using surrogate data tests. We have also used time series to calculate the largest Lyapunov exponent and obtain a positive value. These results constitute significant evidence that signature data are outcome of chaos in a nonlinear dynamical system of motor control.

Parameter and Structure Inference for Nonlinear Dynamical Systems

Science.gov (United States)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Nonlinear dynamics non-integrable systems and chaotic dynamics

CERN Document Server

Borisov, Alexander

2017-01-01

This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.

Nonlinear and Complex Dynamics in Real Systems

OpenAIRE

William Barnett; Apostolos Serletis; Demitre Serletis

2005-01-01

This paper was produced for the El-Naschie Symposium on Nonlinear Dynamics in Shanghai in December 2005. In this paper we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems with nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could p...

Nonlinear dynamics new directions models and applications

CERN Document Server

Ugalde, Edgardo

2015-01-01

This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: ·         Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...

Robust flight control using incremental nonlinear dynamic inversion and angular acceleration prediction

NARCIS (Netherlands)

Sieberling, S.; Chu, Q.P.; Mulder, J.A.

2010-01-01

This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of

Nonlinear dynamics: Challenges and perspectives

Indian Academy of Sciences (India)

fields such as economics, social dynamics and so on [6–10]. These nonlinear ..... developing all-optical computers in homogeneous bulk media such as pho- ... suggestions have been given to develop effective chaos-based cryptographic.

Bubble nonlinear dynamics and stimulated scattering process

Science.gov (United States)

Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu

2016-02-01

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).

The application of nonlinear dynamics in the study of ferroelectric materials

International Nuclear Information System (INIS)

Blochwitz, S.; Habel, R.; Diestelhorst, M.; Beige, H.

1996-01-01

It is well known that the structural phase transitions in ferroelectric materials are connected with strong nonlinear properties. So we can expect all features of nonlinear dynamical systems such as period-doubling cascades and chaos in a dynamical system that contains ferroelectric materials. Therefore we can apply nonlinear dynamics to these ferroelectric materials and we are doing it in two directions: (i) We study the structural phase transitions by analyzing the large signal behaviour with means of nonlinear dynamics. (ii) We control the chaotic behaviour of the system with the method proposed by Ott, Grebogi and Yorke. (authors)

Nonlinear dynamics of two-phase flow

International Nuclear Information System (INIS)

Rizwan-uddin

1986-01-01

Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques

Model-free inference of direct network interactions from nonlinear collective dynamics.

Science.gov (United States)

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.

Science.gov (United States)

Jin, Leisheng; Li, Lijie

2017-12-01

In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.

Bifurcation methods of dynamical systems for handling nonlinear ...

Indian Academy of Sciences (India)

physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

The authors try to address the following two questions: a. Why should accelerator physicists to be interested in the recent, sometimes abstract, developments in Nonlinear Dynamics, a field which will recently was mainly studied by mathematicians, theoretical physicists and astronomers? That such an interest to some extent already exists is apparent from the fact that many accelerator physicists attended this School and several analogous meetings in the past. b. Why should researchers from nonlinear dynamics be interested in modern Storage Rings which are largely designed and built by experimental physicists and engineers? At the moment few 'nonlinear scientists' work on storage rings (or in the field of accelerator physics). It is a hopeful sign that many (more) attended this School

Influence of forced respiration on nonlinear dynamics in heart rate variability

DEFF Research Database (Denmark)

Kanters, J K; Højgaard, M V; Agner, E

1997-01-01

Although it is doubtful whether the normal sinus rhythm can be described as low-dimensional chaos, there is evidence for inherent nonlinear dynamics and determinism in time series of consecutive R-R intervals. However, the physiological origin for these nonlinearities is unknown. The aim...... with a metronome set to 12 min(-1). Nonlinear dynamics were measured as the correlation dimension and the nonlinear prediction error. Complexity expressed as correlation dimension was unchanged from normal respiration, 9.1 +/- 0.5, compared with forced respiration, 9.3 +/- 0.6. Also, nonlinear determinism...... expressed as the nonlinear prediction error did not differ between spontaneous respiration, 32.3 +/- 3.4 ms, and forced respiration, 31.9 +/- 5.7. It is concluded that the origin of the nonlinear dynamics in heart rate variability is not a nonlinear input from the respiration into the cardiovascular...

Nonlinear dynamic characterization of two-dimensional materials

NARCIS (Netherlands)

Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.

2017-01-01

Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's

Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors

Science.gov (United States)

Schöll, Eckehard

2005-08-01

Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.

Dynamics and control for Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Partll

International Nuclear Information System (INIS)

Amengonu, Yawo H; Kakad, Yogendra P

2014-01-01

Quasivelocity techniques were applied to derive the dynamics of a Differential Wheeled Mobile Robot (DWMR) in the companion paper. The present paper formulates a control system design for trajectory tracking of this class of robots. The method develops a feedback linearization technique for the nonlinear system using dynamic extension algorithm. The effectiveness of the nonlinear controller is illustrated with simulation example

A multibody motorcycle model with rigid-ring tyres: formulation and validation

Science.gov (United States)

Leonelli, Luca; Mancinelli, Nicolò

2015-06-01

The aim of this paper is the development and validation of a three-dimensional multibody motorcycle model including a rigid-ring tyre model, taking into account both the slopes and elevation of the road surface. In order to achieve accurate assessment of ride and handling performances of a road racing motorcycle, a tyre model capable of reproducing the dynamic response to actual road excitation is required. While a number of vehicle models with such feature are available for car application, the extension to the motorcycle modelling has not been addressed yet. To do so, a novel parametrisation for the general motorcycle kinematics is proposed, using a mixed reference point and relative coordinates approach. The resulting description, developed in terms of dependent coordinates, makes it possible to include the rigid-ring kinematics as well as road elevation and slopes, without affecting computational efficiency. The equations of motion for the whole multibody system are derived symbolically and the constraint equations arising from the dependent coordinate formulation are handled using the position and velocity vector projection technique. The resulting system of equations is integrated in time domain using a standard ordinary differential equation (ODE) algorithm. Finally, the model is validated with respect to experimentally measured data in both time and frequency domains.

Nonlinear Dynamic Response of Compliant Journal Bearings

Directory of Open Access Journals (Sweden)

Glavatskih S.

2012-07-01

Full Text Available This paper investigates the dynamic response of the compliant tilting pad journal bearings subjected to synchronous excitation. Bearing compliance is affected by the properties of pad liner and pad support geometry. Different unbalance eccentricities are considered. It is shown that bearing dynamic response is non-linear. Journal orbit complexity increases with pad compliance though the orbit amplitudes are marginally affected at low loads. At high loads, the journal is forced to operate outside the bearing clearance. The polymer liner reduces the maximum oil film pressure by a factor of 2 when compared to the white metal liner. The nonlinear dynamic response of compliant tilting pad journal bearings is thoroughly discussed.

Nonlinear dynamics of a coherent polariton-biexciton system

International Nuclear Information System (INIS)

Nguyen Trung Dan; Vo Tinh

1994-08-01

The nonlinear dynamics of a coherent interacting polariton-biexciton system in optically excited semiconductors is investigated. We consider the case when two macroscopically coherent modes - a lower branch polariton and a biexciton existing simultaneously in a direct-gap semiconductor. The conditions for exhibiting optical bistability in stationary regime are obtained. Numerical simulation for the nonlinear dynamics equations of the system is also carried out. (author). 16 refs, 4 figs

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

Science.gov (United States)

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Science.gov (United States)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Sliding mode-based lateral vehicle dynamics control using tyre force measurements

Science.gov (United States)

Kunnappillil Madhusudhanan, Anil; Corno, Matteo; Holweg, Edward

2015-11-01

In this work, a lateral vehicle dynamics control based on tyre force measurements is proposed. Most of the lateral vehicle dynamics control schemes are based on yaw rate whereas tyre forces are the most important variables in vehicle dynamics as tyres are the only contact points between the vehicle and road. In the proposed method, active front steering is employed to uniformly distribute the required lateral force among the front left and right tyres. The force distribution is quantified through the tyre utilisation coefficients. In order to address the nonlinearities and uncertainties of the vehicle model, a gain scheduling sliding-mode control technique is used. In addition to stabilising the lateral dynamics, the proposed controller is able to maintain maximum lateral acceleration. The proposed method is tested and validated on a multi-body vehicle simulator.

Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

International Nuclear Information System (INIS)

Liang, Guo; Guo, Qi; Shou, Qian; Ren, Zhanmei

2014-01-01

We have introduced a class of dynamic elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behavior for the dynamic breathers, rotations and molecule-like librations, are both predicted by the variational approach, and confirmed in numerical simulations. The dynamic elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). As the media are linear anisotropic, OAM is no longer conserved, and hence the angular velocity is not constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the dynamic elliptic breathers librate like molecules. The dynamic elliptic breathers are present in media with not only saturable nonlinearity but also nonlocal nonlinearity; indeed, they are universal in nonlinear media with linear anisotropy. (paper)

General relativistic chaos and nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Barrow, J D [California Univ., Berkeley (USA). Dept. of Physics

1982-06-01

How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations.

General relativistic chaos and nonlinear dynamics

International Nuclear Information System (INIS)

Barrow, J.D.

1982-01-01

How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations. (author)

Analysis of Nonlinear Dynamic Structures

African Journals Online (AJOL)

Bheema

work a two degrees of freedom nonlinear system with zero memory was ... FRF is the most widely used method in structural dynamics which gives information about the ..... 3.6, which is the waterfall diagram of the same response, as well.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

Science.gov (United States)

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

XXIII International Conference on Nonlinear Dynamics of Electronic Systems

CERN Document Server

Stoop, Ruedi; Stramaglia, Sebastiano

2017-01-01

This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.

NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

A joint-space numerical model of metabolic energy expenditure for human multibody dynamic system.

Science.gov (United States)

Kim, Joo H; Roberts, Dustyn

2015-09-01

Metabolic energy expenditure (MEE) is a critical performance measure of human motion. In this study, a general joint-space numerical model of MEE is derived by integrating the laws of thermodynamics and principles of multibody system dynamics, which can evaluate MEE without the limitations inherent in experimental measurements (phase delays, steady state and task restrictions, and limited range of motion) or muscle-space models (complexities and indeterminacies from excessive DOFs, contacts and wrapping interactions, and reliance on in vitro parameters). Muscle energetic components are mapped to the joint space, in which the MEE model is formulated. A constrained multi-objective optimization algorithm is established to estimate the model parameters from experimental walking data also used for initial validation. The joint-space parameters estimated directly from active subjects provide reliable MEE estimates with a mean absolute error of 3.6 ± 3.6% relative to validation values, which can be used to evaluate MEE for complex non-periodic tasks that may not be experimentally verifiable. This model also enables real-time calculations of instantaneous MEE rate as a function of time for transient evaluations. Although experimental measurements may not be completely replaced by model evaluations, predicted quantities can be used as strong complements to increase reliability of the results and yield unique insights for various applications. Copyright © 2015 John Wiley & Sons, Ltd.

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

International Nuclear Information System (INIS)

Hedrih, K

2008-01-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

Science.gov (United States)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Dynamic nonlinear interaction of elastic plates on discrete supports

International Nuclear Information System (INIS)

Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

1984-01-01

A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

Structural optimization for nonlinear dynamic response

DEFF Research Database (Denmark)

Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.

2015-01-01

by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance......Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...

Nonlinear dynamics research in the former Soviet Union

International Nuclear Information System (INIS)

McKenney, B.L.; Krafsig, J.; Moon, F.C.; Shlesinger, M.F.

1992-08-01

This assessment of nonlinear dynamics research in the former Soviet Union was performed by seven US scientists and engineers active in the fields examined. The topics covered include: solid-state systems and circuits, information theory and signal analysis, chaos in mechanical systems, turbulence and vortex dynamics, ocean processes, image processing, and lasers and nonlinear optics. The field of nonlinear dynamics and chaos blossomed in academic settings in both the West and the former Soviet Union during the 1980s. The field went from mathematical abstraction to interesting engineering application areas. Several generalizations can be drawn from the review of Soviet work: Soviet work generally began earlier than Western work, and, in areas that do not require extensive computational resources, that work has kept up with, and often leads, the West. This is especially true in the mathematical analysis of nonlinear phenomena. Soviet researchers have shown an ability to combine numerical or analytic ideas with laboratory experimentation in a smoother, less erratic fashion than Western researchers. Furthermore, contrary to Western practice, the same researchers often do both theoretical and experimental work. In areas that require numerical verification of ideas in the field, the Western work is leading that of the former Soviet Union. This is especially true in the areas of signal processing, simulations of turbulence, and communications. No evidence was found of any significant penetration of ideas of nonlinear dynamics into technological applications of a military or commercial area in the former Soviet Union. Opportunities abound, but specific applications are not apparent

Nonlinear dynamics of the magnetosphere and space weather

Science.gov (United States)

Sharma, A. Surjalal

1996-01-01

The solar wind-magnetosphere system exhibits coherence on the global scale and such behavior can arise from nonlinearity on the dynamics. The observational time series data were used together with phase space reconstruction techniques to analyze the magnetospheric dynamics. Analysis of the solar wind, auroral electrojet and Dst indices showed low dimensionality of the dynamics and accurate prediction can be made with an input/output model. The predictability of the magnetosphere in spite of the apparent complexity arises from its dynamical synchronism with the solar wind. The electrodynamic coupling between different regions of the magnetosphere yields its coherent, low dimensional behavior. The data from multiple satellites and ground stations can be used to develop a spatio-temporal model that identifies the coupling between different regions. These nonlinear dynamical models provide space weather forecasting capabilities.

Particle-based solid for nonsmooth multidomain dynamics

Science.gov (United States)

Nordberg, John; Servin, Martin

2018-04-01

A method for simulation of elastoplastic solids in multibody systems with nonsmooth and multidomain dynamics is developed. The solid is discretised into pseudo-particles using the meshfree moving least squares method for computing the strain tensor. The particle's strain and stress tensor variables are mapped to a compliant deformation constraint. The discretised solid model thus fit a unified framework for nonsmooth multidomain dynamics simulations including rigid multibodies with complex kinematic constraints such as articulation joints, unilateral contacts with dry friction, drivelines, and hydraulics. The nonsmooth formulation allows for impact impulses to propagate instantly between the rigid multibody and the solid. Plasticity is introduced through an associative perfectly plastic modified Drucker-Prager model. The elastic and plastic dynamics are verified for simple test systems, and the capability of simulating tracked terrain vehicles driving on a deformable terrain is demonstrated.

Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

Directory of Open Access Journals (Sweden)

Zhenhua Hu

2013-01-01

Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

Nonlinear dynamics of fractional order Duffing system

International Nuclear Information System (INIS)

Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

2015-01-01

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

Science.gov (United States)

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Role of nonlinear dynamics and chaos in applied sciences

International Nuclear Information System (INIS)

Lawande, Quissan V.; Maiti, Nirupam

2000-02-01

Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. However, little attention was being paid to this dynamically rich field. With the advent of high speed computers with visual graphics, the field has proliferated over past few years. One of the most rewarding realization from nonlinear dynamics is the universally acclaimed field of chaos. Chaos has brought in order and has broken the disciplinary boundaries that existed until recently. With its universal phenomena, almost all disciplines following an evolutionary character can be treated on same footing. Chaotic dynamics has its grounding in the multidisciplinary field of synergetics founded by Professor Hermann Haken. In this report, we address some of the basics related to the field of chaos. We have discussed simple mechanisms for generating chaotic trajectories, ways and means of characterizing such systems and the manifestation of their signatures in the evolutions. We have mentioned the links of this field with other existing theories. We have outlined the topics on bifurcation and stability of dynamical systems. Information theoretic aspects and notions on fractal geometry are reviewed in the light of dynamical characterization of chaotic systems. Application oriented views of this novel dynamical phenomena are discussed through examples on simple nonlinear electronic circuits and a BWR reactor. Some ideas relating to control and synchronization in chaotic systems also addressed. In conclusion, we have explored the possibilities of exploiting nonlinear dynamics and chaos in the context of multidisciplinary character of BARC. (author)

Statistical methods in nonlinear dynamics

Indian Academy of Sciences (India)

Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical ...

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

Substructuring of multibody systems for numerical transfer path analysis in internal combustion engines

Science.gov (United States)

Acri, Antonio; Offner, Guenter; Nijman, Eugene; Rejlek, Jan

2016-10-01

Noise legislations and the increasing customer demands determine the Noise Vibration and Harshness (NVH) development of modern commercial vehicles. In order to meet the stringent legislative requirements for the vehicle noise emission, exact knowledge of all vehicle noise sources and their acoustic behavior is required. Transfer path analysis (TPA) is a fairly well established technique for estimating and ranking individual low-frequency noise or vibration contributions via the different transmission paths. Transmission paths from different sources to target points of interest and their contributions can be analyzed by applying TPA. This technique is applied on test measurements, which can only be available on prototypes, at the end of the designing process. In order to overcome the limits of TPA, a numerical transfer path analysis methodology based on the substructuring of a multibody system is proposed in this paper. Being based on numerical simulation, this methodology can be performed starting from the first steps of the designing process. The main target of the proposed methodology is to get information of noise sources contributions of a dynamic system considering the possibility to have multiple forces contemporary acting on the system. The contributions of these forces are investigated with particular focus on distribute or moving forces. In this paper, the mathematical basics of the proposed methodology and its advantages in comparison with TPA will be discussed. Then, a dynamic system is investigated with a combination of two methods. Being based on the dynamic substructuring (DS) of the investigated model, the methodology proposed requires the evaluation of the contact forces at interfaces, which are computed with a flexible multi-body dynamic (FMBD) simulation. Then, the structure-borne noise paths are computed with the wave based method (WBM). As an example application a 4-cylinder engine is investigated and the proposed methodology is applied on the

Structure Learning in Stochastic Non-linear Dynamical Systems

Science.gov (United States)

Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.

2005-12-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.

Neural network based adaptive control for nonlinear dynamic regimes

Science.gov (United States)

Shin, Yoonghyun

Adaptive control designs using neural networks (NNs) based on dynamic inversion are investigated for aerospace vehicles which are operated at highly nonlinear dynamic regimes. NNs play a key role as the principal element of adaptation to approximately cancel the effect of inversion error, which subsequently improves robustness to parametric uncertainty and unmodeled dynamics in nonlinear regimes. An adaptive control scheme previously named 'composite model reference adaptive control' is further developed so that it can be applied to multi-input multi-output output feedback dynamic inversion. It can have adaptive elements in both the dynamic compensator (linear controller) part and/or in the conventional adaptive controller part, also utilizing state estimation information for NN adaptation. This methodology has more flexibility and thus hopefully greater potential than conventional adaptive designs for adaptive flight control in highly nonlinear flight regimes. The stability of the control system is proved through Lyapunov theorems, and validated with simulations. The control designs in this thesis also include the use of 'pseudo-control hedging' techniques which are introduced to prevent the NNs from attempting to adapt to various actuation nonlinearities such as actuator position and rate saturations. Control allocation is introduced for the case of redundant control effectors including thrust vectoring nozzles. A thorough comparison study of conventional and NN-based adaptive designs for a system under a limit cycle, wing-rock, is included in this research, and the NN-based adaptive control designs demonstrate their performances for two highly maneuverable aerial vehicles, NASA F-15 ACTIVE and FQM-117B unmanned aerial vehicle (UAV), operated under various nonlinearities and uncertainties.

Nonlinear dynamics and cavity cooling of levitated nanoparticles

Science.gov (United States)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-09-01

We investigate a dynamic nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. Through the rich sideband structure displayed by the cavity output we can observe cooling of the linear and non-linear particle's motion. Here we present an experimental setup which allows full control over the cavity resonant frequencies, and shows cooling of the particle's motion as a function of the detuning. This work paves the way to strong-coupled quantum dynamics between a cavity and a mesoscopic object largely decoupled from its environment.

Nonlinear dynamics of zigzag molecular chains (in Russian)

DEFF Research Database (Denmark)

Savin, A. V.; Manevitsch, L. I.; Christiansen, Peter Leth

1999-01-01

models (two-dimensional alpha-spiral, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure essentially limits the soliton dynamics to finite, relatively narrow, supersonic soliton velocity intervals and may also result in that several acoustic soliton......Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry...

Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Devine, N., E-mail: nnd124@rsphysse.anu.edu.au [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Ankiewicz, A. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Genty, G. [Tampere University of Technology, Optics Laboratory, FI-33101 Tampere (Finland); Dudley, J.M. [Institut FEMTO-ST UMR 6174 CNRS/Universite de Franche-Comte, Besancon (France); Akhmediev, N. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia)

2011-11-07

We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schroedinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. -- Highlights: → The dynamics of FPU recurrence is associated with a phase shift between initial and final states. → The properties of this phase shift are studied for the self-focussing NLS equation. → This phase shift is a previously-unremarked feature of the FPU growth-return cycle. → We anticipate its wide significance as an essential feature of related dynamics in other systems.

Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

International Nuclear Information System (INIS)

Devine, N.; Ankiewicz, A.; Genty, G.; Dudley, J.M.; Akhmediev, N.

2011-01-01

We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schroedinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. -- Highlights: → The dynamics of FPU recurrence is associated with a phase shift between initial and final states. → The properties of this phase shift are studied for the self-focussing NLS equation. → This phase shift is a previously-unremarked feature of the FPU growth-return cycle. → We anticipate its wide significance as an essential feature of related dynamics in other systems.

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics.

Science.gov (United States)

Linnemann, D; Strobel, H; Muessel, W; Schulz, J; Lewis-Swan, R J; Kheruntsyan, K V; Oberthaler, M K

2016-07-01

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Dynamic simulation of the NET In-Vessel Handling Unit

International Nuclear Information System (INIS)

Reim, J.

1991-01-01

During the conceptual design phase of the Next European Torus (NET) a large remote maintenance transporter system, the In-Vessel Handling Unit (IVHU), is being developed. It consists of an articulated boom with four rotational joints, which is mounted on a carrier outside the vessel. This boom will be able to carry master-slave manipulators or special work units. The engineering design is supported by dynamic computations. Main topics of the dynamic simulation are the evaluation of IVHU performance, selection and optimisation of the actuator design and of the control algorithms. This simulation task requires full three-dimensional modelling regarding structural elasticity and non-linear actuator dynamics. The Multibody dynamics of the transporter system are modelled with a commerical analysis package. Elastic links and a precise dynamic actuator model are introduced by applied forces, spring elements and differential equations. The actuator model comprises electric motors, gears and linear control algorithms. Non-linear effects which have an influence on control stability and accuracy are taken into account. Most important effects are backlash and static friction. The simulations concentrate on test and optimisation of the control layout and performance studies for critical remote handling tasks. Simulations for control layout and critical remote maintenance tasks correspond to the design objectives of the transporter system. (orig.)

GENERAL APROACH TO MODELING NONLINEAR AMPLITUDE AND FREQUENCY DEPENDENT HYSTERESIS EFFECTS BASED ON EXPERIMENTAL RESULTS

Directory of Open Access Journals (Sweden)

Christopher Heine

2014-08-01

Full Text Available A detailed description of the rubber parts’ properties is gaining in importance in the current simulation models of multi-body simulation. One application example is a multi-body simulation of the washing machine movement. Inside the washing machine, there are different force transmission elements, which consist completely or partly of rubber. Rubber parts or, generally, elastomers usually have amplitude-dependant and frequency-dependent force transmission properties. Rheological models are used to describe these properties. A method for characterization of the amplitude and frequency dependence of such a rheological model is presented within this paper. Within this method, the used rheological model can be reduced or expanded in order to illustrate various non-linear effects. An original result is given with the automated parameter identification. It is fully implemented in Matlab. Such identified rheological models are intended for subsequent implementation in a multi-body model. This allows a significant enhancement of the overall model quality.

Nonlinear dynamical system identification using unscented Kalman filter

Science.gov (United States)

Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan

2016-11-01

Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.

Non-Linear Dynamics and Fundamental Interactions

CERN Document Server

Khanna, Faqir

2006-01-01

The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives

International Nuclear Information System (INIS)

Faybishenko, Boris

2002-01-01

The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences

Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives

Energy Technology Data Exchange (ETDEWEB)

Faybishenko, Boris

2002-11-27

The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.

Nonlinear dynamical triggering of slow slip

Energy Technology Data Exchange (ETDEWEB)

Johnson, Paul A [Los Alamos National Laboratory; Knuth, Matthew W [WISCONSIN; Kaproth, Bryan M [PENN STATE; Carpenter, Brett [PENN STATE; Guyer, Robert A [Los Alamos National Laboratory; Le Bas, Pierre - Yves [Los Alamos National Laboratory; Daub, Eric G [Los Alamos National Laboratory; Marone, Chris [PENN STATE

2010-12-10

Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred

Nonlinear dynamics and plasma transport

International Nuclear Information System (INIS)

Antonsen, T.M. Jr.; Drake, J.F.; Finn, J.M.; Guzdar, P.N.; Hassam, A.B.; Sagdeev, R.Z.

1992-01-01

In this paper we summarize the progress made over the last year in three different areas of research: (a) shear flow generation and reduced transport in fluids and plasma, (b) nonlinear dynamics and visualization of 3D flows, and (c) application of wavelet analysis to the study of fractal dimensions in experimental and numerical data

Leveraging Chaos in Continuous Thrust Trajectory Design

Data.gov (United States)

National Aeronautics and Space Administration — A trajectory design tool is sought to leverage chaos and nonlinear dynamics present in multi-body gravitational fields to design ultra-low energy transfer...

The nonlinear dynamics of a coupled fission system

International Nuclear Information System (INIS)

Bilanovic, Z.; Harms, A.A.

1993-01-01

The dynamic properties of a nonlinear and in situ vibrationally perturbed nuclear-to-thermal coupled neutron multiplying medium are examined. Some unique self-organizational temporal patterns appear in such fission systems and suggest a complex underlying dynamic. (Author)

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

Science.gov (United States)

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

Science.gov (United States)

Zhang, Yu; Jiang, Jack J.

2008-09-01

Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

Estimation of dynamic reactivity using an H∞ optimal filter with a nonlinear term

International Nuclear Information System (INIS)

Suzuki, Katsuo; Watanabe, Koiti

1996-01-01

A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of a linear H ∞ optimal filter with a nonlinear feedback loop added. The linear filter is designed on the basis of a linearized dynamical system model that consists of linearized point reactor kinetic equations and a reactivity state equation driven by a fictitious signal. The latter is artificially introduced to deal with the reactivity as a state variable. The results of the computer simulation show that the nonlinear filtering algorithm can be applied to estimate the dynamic reactivity of the nonlinear reactor system, even under relatively large reactivity disturbances

Nonlinear dynamics of biomimetic micro air vehicles

Energy Technology Data Exchange (ETDEWEB)

Hou, Y; Kong, J [College of Mechanical Automation, Wuhan University of Science and Technology, Wuhan, 430081 (China)], E-mail: fly_houyu@163.com.cn

2008-02-15

Flapping-wing micro air vehicles (FMAV) are new conceptual air vehicles that mimic the flying modes of birds and insects. They surpass the research fields of traditional airplane design and aerodynamics on application technologies, and initiate the applications of MEMS technologies on aviation fields. This paper studies a micro flapping mechanism that based upon insect thorax and actuated by electrostatic force. Because there are strong nonlinear coupling between the two physical domains, electrical and mechanical, the static and dynamic characteristics of this system are very complicated. Firstly, the nonlinear dynamic model of the electromechanical coupling system is set up according to the physical model of the flapping mechanism. The dynamic response of the system in constant voltage is studied by numerical method. Then the effect of damping and initial condition on dynamic characteristics of the system is analyzed in phase space. In addition, the dynamic responses of the system in sine voltage excitation are discussed. The results of research are helpful to the design, fabrication and application of the micro flapping mechanism of FMAV, and also to other micro electromechanical system that actuated by electrostatic force.

Nonlinear dynamic analysis of hydrodynamically-coupled stainless steel structures

International Nuclear Information System (INIS)

Zhao, Y.

1996-01-01

Spent nuclear fuel is usually stored temporarily on the site of nuclear power plants. The spent fuel storage racks are nuclear-safety-related stainless steel structures required to be analyzed for seismic loads. When the storage pool is subjected to three-dimensional (3-D) floor seismic excitations, rack modules, stored fuel bundles, adjacent racks and pool walls, and surrounding water are hydrodynamically coupled. Hydrodynamic coupling (HC) significantly affects the dynamic responses of the racks that are free-standing and submerged in water within the pool. A nonlinear time-history dynamic analysis is usually needed to describe the motion behavior of the racks that are both geometrically nonlinear and material nonlinear in nature. The nonlinearities include the friction resistance between the rack supporting legs and the pool floor, and various potential impacts of fuel-rack, rack-rack, and rack-pool wall. The HC induced should be included in the nonlinear dynamic analysis using the added-hydrodynamic-mass concept based on potential theory per the US Nuclear Regulatory Commission (USNRC) acceptance criteria. To this end, a finite element analysis constitutes a feasible and effective tool. However, most people perform somewhat simplified 1-D, or 2-D, or 3-D single rack and 2-D multiple rack analyses. These analyses are incomplete because a 3-D single rack model behaves quite differently from a 2-D mode. Furthermore, a 3-D whole pool multi-rack model behaves differently than a 3-D single rack model, especially when the strong HC effects are unsymmetrical. In this paper 3-D nonlinear dynamic time-history analyses were performed in a more quantitative manner using sophisticated finite element models developed for a single rack as well as all twelve racks in the whole-pool. Typical response results due to different HC effects are determined and discussed

Nonlinear dynamics of semiconductors in strong THz electric fields

DEFF Research Database (Denmark)

Tarekegne, Abebe Tilahun

In this thesis, we investigate nonlinear interactions of an intense terahertz (THz) field with semiconductors, in particular the technologically relevant materials silicon and silicon carbide. We reveal the time-resolved dynamics of the nonlinear processes by pump-probe experiments that involve...

Non-Linear Dynamics of Saturn's Rings

Science.gov (United States)

Esposito, L. W.

2016-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries

Dynamic interaction between rotor and axially-magnetized passive magnetic bearing considering magnetic eccentricity

DEFF Research Database (Denmark)

Enemark, Søren; Santos, Ilmar

2014-01-01

with a multibody system composed of rigid rotor and flexible foundation. The magnetic eccentricities of the shaft magnets are modelled using the distances (amplitudes) and directions (phase angles) between the shaft axis and the centre of the magnetic fields generated. A perturbation method, i.e. harmonic......-linear stiffness. In this investigation passive magnetic bearings using axially- aligned neodymium cylinder magnets are investigated. The cylinder magnets are axially magnetised for rotor as well as bearings. Compared to bearings with radial magnetisation, the magnetic stiffness of axially-aligned bearings...... is considerably lower, nevertheless they allow for asymmetric stiffness mounting, and it could be beneficial for rotor stabilization. A theoretical model is proposed to describe the non-linear rotor-bearing dynamics. It takes into account non-linear behaviour of the magnetic forces and their interaction...

Dynamics of electron wave packet in a disordered chain with delayed nonlinear response

International Nuclear Information System (INIS)

Zhu Hongjun; Xiong Shijie

2010-01-01

We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron-phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schroedinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.

Dynamic nonlinear analysis of shells of revolution

International Nuclear Information System (INIS)

Riesemann, W.A. von; Stricklin, J.A.; Haisler, W.E.

1975-01-01

Over the past few years a series of finite element computer programs have been developed at Texas A and M University for the static and dynamic nonlinear analysis of shells of revolution. This paper discusses one of these, DYNAPLAS, which is a program for the transient response of ring stiffened shells of revolution subjected to either asymmetric initial velocities or to asymmetric pressure loadings. Both material and geometric nonlinearities may be considered. (Auth.)

Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying

Directory of Open Access Journals (Sweden)

Inseok Yang

2014-01-01

Full Text Available The robust nonlinear dynamic inversion (RNDI control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI. NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC. SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.

Non-linear wave packet dynamics of coherent states

Indian Academy of Sciences (India)

In recent years, the non-linear quantum dynamics of these states have revealed some striking features. It was found that under the action of a Hamil- tonian which is a non-linear function of the photon operator(s) only, an initial coherent state loses its coherent structure quickly due to quantum dephasing induced by the non-.

Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

Directory of Open Access Journals (Sweden)

Nicolás Peréz Alvarez

2015-11-01

Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

Nonlinear dynamics and quantum chaos an introduction

CERN Document Server

Wimberger, Sandro

2014-01-01

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Lifespan Differences in Nonlinear Dynamics during Rest and Auditory Oddball Performance

Science.gov (United States)

Muller, Viktor; Lindenberger, Ulman

2012-01-01

Electroencephalographic recordings (EEG) were used to assess age-associated differences in nonlinear brain dynamics during both rest and auditory oddball performance in children aged 9.0-12.8 years, younger adults, and older adults. We computed nonlinear coupling dynamics and dimensional complexity, and also determined spectral alpha power as an…

Schemes for applying active lubrication to main engine bearings

DEFF Research Database (Denmark)

Estupinan, Edgar Alberto; Santos, Ilmar

2009-01-01

-difference method. The computed bearing fluid film forces are coupled to the set of nonlinear equations that describes the dynamics of the reciprocating engine, obtained with the help of multibody dynamics (rigid components) and finite elements method (flexible components). The main equations that govern...

Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin

International Nuclear Information System (INIS)

Yang, Ciann-Dong; Weng, Hung-Jen

2012-01-01

Highlights: ► This paper reveals the internal nonlinear dynamics embedded in a molecular quantum state. ► Analyze quantum molecular dynamics in a deterministic way, while preserving the consistency with probability interpretation. ► Molecular vibration–rotation interaction and spin–orbital coupling are considered simultaneously. ► Spin is just the remnant angular motion when orbital angular momentum is zero. ► Spin is the “zero dynamics” of nonlinear quantum dynamics. - Abstract: For a given molecular wavefunction Ψ, the probability density function Ψ ∗ Ψ is not the only information that can be extracted from Ψ. We point out in this paper that nonlinear quantum dynamics of a diatomic molecule, completely consistent with the probability prediction of quantum mechanics, does exist and can be derived from the quantum Hamilton equations of motion determined by Ψ. It can be said that the probability density function Ψ ∗ Ψ is an external representation of the quantum state Ψ, while the related Hamilton dynamics is an internal representation of Ψ, which reveals the internal mechanism underlying the externally observed random events. The proposed internal representation of Ψ establishes a bridge between nonlinear dynamics and quantum mechanics, which allows the methods and tools already developed by the former to be applied to the latter. Based on the quantum Hamilton equations of motion derived from Ψ, vibration, rotation and spin motions of a diatomic molecule and the interactions between them can be analyzed simultaneously. The resulting dynamic analysis of molecular motion is compared with the conventional probability analysis and the consistency between them is demonstrated.

Selected Problems in Nonlinear Dynamics and Sociophysics

Science.gov (United States)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

Laser acceleration and nonlinear beam dynamics

International Nuclear Information System (INIS)

Pellegrini, C.

1991-01-01

This research contract covers the period April 1990, September 1991. The work to be done under the contract was theoretical research in the areas of nonlinear beam dynamics and laser acceleration. In this final report we will discuss the motivation for this work and the results obtained

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

Science.gov (United States)

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Global investigation of the nonlinear dynamics of carbon nanotubes

KAUST Repository

Xu, Tiantian

2016-11-17

Understanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.

Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports

Science.gov (United States)

Wang, Hong; Han, Qinkai; Luo, Ruizhi; Qing, Tao

2017-10-01

Moment wheel assemblies (MWA) have been widely used in spacecraft attitude control and large angle slewing maneuvers over the years. Understanding and controlling vibration of MWAs is a crucial factor to achieving the desired level of payload performance. Dynamic modeling of a MWA with nonlinear rolling bearing supports is conducted. An improved load distribution analysis is proposed to more accurately obtain the contact deformations and angles between the rolling balls and raceways. Then, the bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. The effects of preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication could all be reflected in the nonlinear bearing forces. Considering the mass imbalances of the flywheel, flexibility of supporting structures and rolling bearing nonlinearity, the dynamic model of a typical MWA is established based upon the energy theorem. Dynamic tests are conducted to verify the nonlinear dynamic model. The influences of flywheel mass eccentricity and inner/outer waviness amplitudes on the dynamic responses are discussed in detail. The obtained results would be useful for the design and vibration control of the MWA system.

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

DEFF Research Database (Denmark)

Sun, Jialiang; Tian, Qiang; Hu, Haiyan

2018-01-01

Recent years have witnessed the application of topology optimization to flexible multibody systems (FMBS) so as to enhance their dynamic performances. In this study, an explicit topology optimization approach is proposed for an FMBS with variable-length bodies via the moving morphable components...... (MMC). Using the arbitrary Lagrangian–Eulerian (ALE) formulation, the thin plate elements of the absolute nodal coordinate formulation (ANCF) are used to describe the platelike bodies with variable length. For the thin plate element of ALE–ANCF, the elastic force and additional inertial force, as well...

Stability and nonlinear dynamics of gyrotrons at cyclotron harmonics

International Nuclear Information System (INIS)

Saraph, G.P.; Nusinovich, G.S.; Antonsen, T.M. Jr.; Levush, B.

1992-01-01

Gyrotrons operating at higher harmonics of the cyclotron frequency can overcome the frequency limitations caused by achievable strength of the magnetic field. However, the excitation of modes at the fundamental frequency exhibit a major problem for stable operation of harmonic gyrotron at high power with high efficiency. Therefore the issues of stability of gyrotron operation at the cyclotron harmonics and nonlinear dynamics of mode interaction are of great importance. The results of the authors stability analysis and multimode simulation are presented here. A detailed nonlinear theory of steady state single mode operation at cyclotron harmonics has been presented previously, taking into account beam-wave coupling and nonlinear gain function at cyclotron harmonics. A set of equations describing low gain regime interaction of modes resonant at different cyclotron harmonics was studied before. The multifrequency time-dependent nonlinear analysis presented here is based on previous gyrotron studies and beam-wave interaction at cyclotron harmonics. The authors have determined the parameter space for stable single mode operation at the second harmonic. The nonlinear dynamics of mode evolution and mode interaction for a harmonic gyrotron is presented. A new nonlinear effect in which the parasite at the fundamental harmonic helps excite the operating mode at the second harmonic has been demonstrated

Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

Science.gov (United States)

Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

The coupled nonlinear dynamics of a lift system

Energy Technology Data Exchange (ETDEWEB)

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.

Nonlinear and Stochastic Dynamics in the Heart

Science.gov (United States)

Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

2014-01-01

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872

Nonlinear and stochastic dynamics in the heart

Energy Technology Data Exchange (ETDEWEB)

Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)

2014-10-10

In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Nonlinear and stochastic dynamics in the heart

International Nuclear Information System (INIS)

Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

2014-01-01

In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems

Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

Directory of Open Access Journals (Sweden)

Qilin Huang

2013-01-01

Full Text Available A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM. Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

Science.gov (United States)

Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

2017-12-01

We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

Topics in Nonlinear Dynamics

DEFF Research Database (Denmark)

Mosekilde, Erik

Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...... food-web systems, nephron pressure and flow regulation, pulsatile secretion of hormones, thermostatically controlled radiator systems, post-stall maneuvering of aircrafts, transfer electron devices for microwave generation, economic long waves, human decision making behavior, and pattern formation...... in chemical reaction-diffusion systems....

Nonlinear dynamic effects in a two-wave CO2 laser

International Nuclear Information System (INIS)

Gorobets, V A; Kozlov, K V; Kuntsevich, B F; Petukhov, V O

1999-01-01

Theoretical and experimental investigations were made of nonlinear dynamic regimes of the operation of a two-wave CO 2 laser with cw excitation in an electric discharge and loss modulation in one of the channels. Nonlinear amplitude - frequency characteristics of each of the laser channels have two low-frequency resonance spikes, associated with forced linear oscillations of two coupled oscillators, and high-frequency spikes, corresponding to doubling of the period of the output radiation oscillations. At low loss-modulation frequencies the intensity oscillations of the output radiation in the coupled channels are in antiphase, whereas at high modulation frequencies the dynamics is cophasal. Nonlinear dynamic effects, such as doubling of the period and of the repetition frequency of the pulses and chaotic oscillations of the output radiation intensity, are observed for certain system parameters. (control of laser radiation parameters)

Machine learning control taming nonlinear dynamics and turbulence

CERN Document Server

Duriez, Thomas; Noack, Bernd R

2017-01-01

This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...

Integrating Multibody Simulation and CFD: toward Complex Multidisciplinary Design Optimization

Science.gov (United States)

Pieri, Stefano; Poloni, Carlo; Mühlmeier, Martin

This paper describes the use of integrated multidisciplinary analysis and optimization of a race car model on a predefined circuit. The objective is the definition of the most efficient geometric configuration that can guarantee the lowest lap time. In order to carry out this study it has been necessary to interface the design optimization software modeFRONTIER with the following softwares: CATIA v5, a three dimensional CAD software, used for the definition of the parametric geometry; A.D.A.M.S./Motorsport, a multi-body dynamic simulation software; IcemCFD, a mesh generator, for the automatic generation of the CFD grid; CFX, a Navier-Stokes code, for the fluid-dynamic forces prediction. The process integration gives the possibility to compute, for each geometrical configuration, a set of aerodynamic coefficients that are then used in the multiboby simulation for the computation of the lap time. Finally an automatic optimization procedure is started and the lap-time minimized. The whole process is executed on a Linux cluster running CFD simulations in parallel.

Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

Directory of Open Access Journals (Sweden)

Geoff Boeing

2016-11-01

Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.

Planar reorientation maneuvers of space multibody systems using internal controls

Science.gov (United States)

Reyhanoglu, Mahmut; Mcclamroch, N. H.

1992-01-01

In this paper a reorientation maneuvering strategy for an interconnection of planar rigid bodies in space is developed. It is assumed that there are no exogeneous torques, and torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero in this paper. The maneuver strategy uses the nonintegrability of the expression for the angular momentum. We demonstrate that large-angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is briefly summarized. Specifications and computer simulations of a specific reorientation maneuver, and the corresponding control strategies, are described.

A Volterra series approach to the approximation of stochastic nonlinear dynamics

NARCIS (Netherlands)

Wouw, van de N.; Nijmeijer, H.; Campen, van D.H.

2002-01-01

A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

Science.gov (United States)

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

NONLINEAR FILTER METHOD OF GPS DYNAMIC POSITIONING BASED ON BANCROFT ALGORITHM

Institute of Scientific and Technical Information of China (English)

ZHANGQin; TAOBen-zao; ZHAOChao-ying; WANGLi

2005-01-01

Because of the ignored items after linearization, the extended Kalman filter (EKF) becomes a form of suboptimal gradient descent algorithm. The emanative tendency exists in GPS solution when the filter equations are ill-posed. The deviation in the estimation cannot be avoided. Furthermore, the true solution may be lost in pseudorange positioning because the linearized pseudorange equations are partial solutions. To solve the above problems in GPS dynamic positioning by using EKF, a closed-form Kalman filter method called the two-stage algorithm is presented for the nonlinear algebraic solution of GPS dynamic positioning based on the global nonlinear least squares closed algorithm--Bancroft numerical algorithm of American. The method separates the spatial parts from temporal parts during processing the GPS filter problems, and solves the nonlinear GPS dynamic positioning, thus getting stable and reliable dynamic positioning solutions.

Nonlinear Dynamics of Electrostatically Actuated MEMS Arches

KAUST Repository

Al Hennawi, Qais M.

2015-01-01

In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using

Nonlinear Dynamics of a Diffusing Interface

Science.gov (United States)

Duval, Walter M. B.

2001-01-01

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Nonlinear analysis and dynamic structure in the energy market

Science.gov (United States)

Aghababa, Hajar

This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non

Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference.

Science.gov (United States)

Venkataraman, Vinay; Turaga, Pavan

2016-12-01

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.

Dynamics of metastable breathers in nonlinear chains in acoustic vacuum

Science.gov (United States)

Sen, Surajit; Mohan, T. R. Krishna

2009-03-01

The study of the dynamics of one-dimensional chains with both harmonic and nonlinear interactions, as in the Fermi-Pasta-Ulam and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Nevertheless, little is known about the dynamical behavior of purely nonlinear chains where there is a complete absence of the harmonic term, and hence sound propagation is not admissible, i.e., under conditions of “acoustic vacuum.” Here we study the dynamics of highly localized excitations, or breathers, which are known to be initiated by the quasistatic stretching of the bonds between adjacent particles. We show via detailed particle-dynamics-based studies that many low-energy pulses also form in the vicinity of the perturbation, and the breathers that form are “fragile” in the sense that they can be easily delocalized by scattering events in the system. We show that the localized excitations eventually disperse, allowing the system to attain an equilibrium-like state that is realizable in acoustic vacuum. We conclude with a discussion of how the dynamics is affected by the presence of acoustic oscillations.

Nonlinear dynamics in psychology

Directory of Open Access Journals (Sweden)

Stephen J. Guastello

2001-01-01

Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.

Dynamic nonlinear elasticity in geo materials

International Nuclear Information System (INIS)

Ostrovsky, L.A.; Johnson, P.A.

2001-01-01

The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics

Nonlinear dynamics of cortical responses to color in the human cVEP.

Science.gov (United States)

Nunez, Valerie; Shapley, Robert M; Gordon, James

2017-09-01

The main finding of this paper is that the human visual cortex responds in a very nonlinear manner to the color contrast of pure color patterns. We examined human cortical responses to color checkerboard patterns at many color contrasts, measuring the chromatic visual evoked potential (cVEP) with a dense electrode array. Cortical topography of the cVEPs showed that they were localized near the posterior electrode at position Oz, indicating that the primary cortex (V1) was the major source of responses. The choice of fine spatial patterns as stimuli caused the cVEP response to be driven by double-opponent neurons in V1. The cVEP waveform revealed nonlinear color signal processing in the V1 cortex. The cVEP time-to-peak decreased and the waveform's shape was markedly narrower with increasing cone contrast. Comparison of the linear dynamics of retinal and lateral geniculate nucleus responses with the nonlinear dynamics of the cortical cVEP indicated that the nonlinear dynamics originated in the V1 cortex. The nature of the nonlinearity is a kind of automatic gain control that adjusts cortical dynamics to be faster when color contrast is greater.

Nonlinear dynamics and control of a vibrating rectangular plate

Science.gov (United States)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics

Science.gov (United States)

Kashima, Kenji

2016-01-01

Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics. PMID:27264780

Model reduction tools for nonlinear structural dynamics

NARCIS (Netherlands)

Slaats, P.M.A.; Jongh, de J.; Sauren, A.A.H.J.

1995-01-01

Three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes. Tangent modes are obtained from an eigenvalue problem with a momentary tangent stiffness matrix. Their

Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers

DEFF Research Database (Denmark)

Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.

Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio...... the evolution of the fiber output beam in the few micro or milliseconds after the beam is turned on. The characterization of the temporal behavior of the thermal nonlinear response provides important information about the nonlocality associated with heat diffusion inside the fiber, thus enabling studies of long...... and technological potential of liquid-infiltrated PCFs it is important to understand the temporal dynamics of nonlinear beam propagation in such structures. In this work we consider thermally induced spatial nonlinear effects in infiltrated photonic crystal fibers. We experimentally study the temporal dynamics...

Nonlinear dynamics of charged particles in the magnetotail

Science.gov (United States)

Chen, James

1992-01-01

An important region of the earth's magnetosphere is the nightside magnetotail, which is believed to play a significant role in energy storage and release associated with substorms. The magnetotail contains a current sheet which separates regions of oppositely directed magnetic field. Particle motion in the collisionless magnetotail has been a long-standing problem. Recent research from the dynamical point of view has yielded considerable new insights into the fundamental properties of orbits and of particle distribution functions. A new framework of understanding magnetospheric plasma properties is emerging. Some novel predictions based directly on nonlinear dynamics have proved to be robust and in apparent good agreement with observation. The earth's magnetotail may serve as a paradigm, one accessible by in situ observation, of a broad class of boundary regions with embedded current sheets. This article reviews the nonlinear dynamics of charged particles in the magnetotail configuration. The emphasis is on the relationships between the dynamics and physical observables. At the end of the introduction, sections containing basic material are indicated.

Nonlinear soil parameter effects on dynamic embedment of offshore pipeline on soft clay

Directory of Open Access Journals (Sweden)

Su Young Yu

2015-03-01

Full Text Available In this paper, the effects of nonlinear soft clay on dynamic embedment of offshore pipeline were investigated. Seabed embedment by pipe-soil interactions has impacts on the structural boundary conditions for various subsea structures such as pipeline, riser, pile, and many other systems. A number of studies have been performed to estimate real soil behavior, but their estimation of seabed embedment has not been fully identified and there are still many uncertainties. In this regards, comparison of embedment between field survey and existing empirical models has been performed to identify uncertainties and investigate the effect of nonlinear soil parameter on dynamic embedment. From the comparison, it is found that the dynamic embedment with installation effects based on nonlinear soil model have an influence on seabed embedment. Therefore, the pipe embedment under dynamic condition by nonlinear para- meters of soil models was investigated by Dynamic Embedment Factor (DEF concept, which is defined as the ratio of the dynamic and static embedment of pipeline, in order to overcome the gap between field embedment and currently used empirical and numerical formula. Although DEF through various researches is suggested, its range is too wide and it does not consider dynamic laying effect. It is difficult to find critical parameters that are affecting to the embedment result. Therefore, the study on dynamic embedment factor by soft clay parameters of nonlinear soil model was conducted and the sensitivity analyses about parameters of nonlinear soil model were performed as well. The tendency on dynamic embedment factor was found by conducting numerical analyses using OrcaFlex software. It is found that DEF was influenced by shear strength gradient than other factors. The obtained results will be useful to understand the pipe embedment on soft clay seabed for applying offshore pipeline designs such as on-bottom stability and free span analyses.

Discretization model for nonlinear dynamic analysis of three dimensional structures

International Nuclear Information System (INIS)

Hayashi, Y.

1982-12-01

A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt

Non-Linear Dynamics of Saturn’s Rings

Science.gov (United States)

Esposito, Larry W.

2015-11-01

Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects

Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

International Nuclear Information System (INIS)

Liu Chunliang; Xie Xi; Chen Yinbao

1991-01-01

The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

Mixed Finite Element Method for Static and Dynamic Contact Problems with Friction and Initial Gaps

Directory of Open Access Journals (Sweden)

Lanhao Zhao

2014-01-01

Full Text Available A novel mixed finite element method is proposed for static and dynamic contact problems with friction and initial gaps. Based on the characteristic of local nonlinearity for the problem, the system of forces acting on the contactor is divided into two parts: external forces and contact forces. The displacement of structure is chosen as the basic variable and the nodal contact force in contact region under local coordinate system is selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. In this way, the sophisticated contact nonlinearity is revealed by the variety of the contact forces which are determined by the external load and the contact state stick, slip, or separation. Moreover, in the case of multibody contact problem, the flexibility matrix is symmetric and sparse; thus, the iterative procedure becomes easily carried out and much more economical. In the paper, both the finite element formulations and the iteration process are given in detail for static and dynamic contact problems. Four examples are included to demonstrate the accuracy and applicability of the presented method.

Nonlinear dynamics new directions theoretical aspects

CERN Document Server

Ugalde, Edgardo

2015-01-01

This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: ·         Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics ·         Features recent developments on...

Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model

Directory of Open Access Journals (Sweden)

Yacouba Simporé

2016-01-01

Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.

Nonlinear Dynamic Buckling of Damaged Composite Cylindrical Shells

Institute of Scientific and Technical Information of China (English)

WANG Tian-lin; TANG Wen-yong; ZHANG Sheng-kun

2007-01-01

Based on the first order shear deformation theory(FSDT), the nonlinear dynamic equations involving transverse shear deformation and initial geometric imperfections were obtained by Hamilton's philosophy. Geometric deformation of the composite cylindrical shell was treated as the initial geometric imperfection in the dynamic equations, which were solved by the semi-analytical method in this paper. Stiffness reduction was employed for the damaged sub-layer, and the equivalent stiffness matrix was obtained for the delaminated area. By circumferential Fourier series expansions for shell displacements and loads and by using Galerkin technique, the nonlinear partial differential equations were transformed to ordinary differential equations which were finally solved by the finite difference method. The buckling was judged from shell responses by B-R criteria, and critical loads were then determined. The effect of the initial geometric deformation on the dynamic response and buckling of composite cylindrical shell was also discussed, as well as the effects of concomitant delamination and sub-layer matrix damages.

Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.

Science.gov (United States)

Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

2014-03-10

We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

Null Space Integration Method for Constrained Multibody Systems with No Constraint Violation

International Nuclear Information System (INIS)

Terze, Zdravko; Lefeber, Dirk; Muftic, Osman

2001-01-01

A method for integrating equations of motion of constrained multibody systems with no constraint violation is presented. A mathematical model, shaped as a differential-algebraic system of index 1, is transformed into a system of ordinary differential equations using the null-space projection method. Equations of motion are set in a non-minimal form. During integration, violations of constraints are corrected by solving constraint equations at the position and velocity level, utilizing the metric of the system's configuration space, and projective criterion to the coordinate partitioning method. The method is applied to dynamic simulation of 3D constrained biomechanical system. The simulation results are evaluated by comparing them to the values of characteristic parameters obtained by kinematics analysis of analyzed motion based unmeasured kinematics data

Heat flux expressions that satisfy the conservation laws in atomistic system involving multibody potentials

Energy Technology Data Exchange (ETDEWEB)

Fu, Yao, E-mail: Yao.Fu@colorado.edu; Song, Jeong-Hoon, E-mail: JH.Song@colorado.edu

2015-08-01

Heat flux expressions are derived for multibody potential systems by extending the original Hardy's methodology and modifying Admal & Tadmor's formulas. The continuum thermomechanical quantities obtained from these two approaches are easy to compute from molecular dynamics (MD) results, and have been tested for a constant heat flux model in two distinctive systems: crystalline iron and polyethylene (PE) polymer. The convergence criteria and affecting parameters, i.e. spatial and temporal window size, and specific forms of localization function are found to be different between the two systems. The conservation of mass, momentum, and energy are discussed and validated within this atomistic–continuum bridging.

Heat flux expressions that satisfy the conservation laws in atomistic system involving multibody potentials

International Nuclear Information System (INIS)

Fu, Yao; Song, Jeong-Hoon

2015-01-01

Heat flux expressions are derived for multibody potential systems by extending the original Hardy's methodology and modifying Admal & Tadmor's formulas. The continuum thermomechanical quantities obtained from these two approaches are easy to compute from molecular dynamics (MD) results, and have been tested for a constant heat flux model in two distinctive systems: crystalline iron and polyethylene (PE) polymer. The convergence criteria and affecting parameters, i.e. spatial and temporal window size, and specific forms of localization function are found to be different between the two systems. The conservation of mass, momentum, and energy are discussed and validated within this atomistic–continuum bridging

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ-Expansion Method Implementation

Directory of Open Access Journals (Sweden)

Nur Alam

2016-02-01

Full Text Available In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs describing microtubules, by implementing the exp(−Φ(ξ-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ-Expansion Method not disappointing in the least, is found and declared highly efficient.

The nonlinear response of the complex structural system in nuclear reactors using dynamic substructure method

International Nuclear Information System (INIS)

Zheng, Z.C.; Xie, G.; Du, Q.H.

1987-01-01

Because of the existence of nonlinear characteristics in practical engineering structures, such as large steam turbine-foundation system and offshore platform, it is necessary to predict nonlinear dynamic responses for these very large and complex structural systems subjected extreme load. Due to the limited storage and high executing cost of computers, there are still some difficulties in the analysis for such systems although the traditional finite element methods provide basic available methods to the problems. The dynamic substructure methods, which were developed as a branch of general structural dynamics in the past more than 20 years and have been widely used from aircraft, space vehicles to other mechanical and civil engineering structures, present a powerful method to the analysis of very large structural systems. The key to success is due to the considerable reduction in the number of degrees of freedom while not changing the physical essence of the problems investigated. The dynamic substructure method has been extended to nonlinear system and applicated to the analysis of nonlinear dynamic response of an offshore platform by Z.C. Zheng, et al. (1983, 1985a, b, c). In this paper, the method is presented to analyze dynamic responses of the systems contained intrinsic nonlinearities and with nonlinear attachments and nonlinear supports of nuclear structural systems. The efficiency of the method becomes more clear for nonlinear dynamic problems due to the adoption of iterating processes. For simplicity, the analysis procedure is demonstrated briefly. The generalized substructure method of nonlinear systems is similar to linear systems, only the nonlinear terms are treated as pseudo-forces. Interface coordinates are classified into two categories, the connecting interface coordinates which connect with each other directly in the global system and the linking interface coordinates which link to each other through attachments. (orig./GL)

Parametric Identification of Nonlinear Dynamical Systems

Science.gov (United States)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory

International Nuclear Information System (INIS)

Qian, Hong

2011-01-01

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)

Nonlinear modal analysis in NPP dynamics: a proposal

International Nuclear Information System (INIS)

Suarez Antola, R.

2005-07-01

We propose and briefly suggest how to apply the analytical tools of nonlinear modal analysis (NMA) to problems of nuclear reactor kinetics, NPP dynamics, and NPP instrumentation and control. The proposed method is closely related with recent approaches by modal analysis using the reactivity matrix with feedbacks to couple neutron kinetics with thermal hydraulics in the reactors core. A nonlinear system of ordinary differential equations for mode amplitudes is obtained, projecting the dynamic equations of a model of NPP onto the eigenfunctions of a suitable adjoint operator. A steady state solution of the equations is taken as a reference, and the behaviour of transient solutions in some neighbourhood of the steady state solution is studied by an extension of Liapunov's First Method that enables to cope directly with the non-linear terms in the dynamics. In NPP dynamics these differential equations for the mode amplitudes are of polynomial type of low degree A few dominant modes can usually be identified. These mode amplitudes evolve almost independently of the other modes, more slowly and tending to slave the other mode amplitudes. Using asymptotic methods, it is possible to calculate a closed form analytical approximation to the response to finite amplitude perturbations from the given steady spatial pattern (the origin of the space of mode amplitudes).When there is finite amplitude instability, the method allows us to calculate the threshold amplitude as a well defined function of system's parameters. This is a most significant accomplishment that the other methods cannot afford

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

Dynamic Flight Simulation Utilizing High Fidelity CFD-Based Nonlinear Reduced Order Model, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — The Nonlinear Dynamic Flight Simulation (NL-DFS) system will be developed in the Phase II project by combining the classical nonlinear rigid-body flight dynamics...

Analysis of the Nonlinear Static and Dynamic Behavior of Offshore Structures

KAUST Repository

Alfosail, Feras

2015-01-01

Understanding static and dynamic nonlinear behavior of pipes and risers is crucial for the design aspects in offshore engineering fields. In this work, we examine two nonlinear problems in offshore engineering field: vortex Induced vibration

Summary report of the group on single-particle nonlinear dynamics

International Nuclear Information System (INIS)

Axinescu, S.; Bartolini, R.; Bazzani, A.

1996-10-01

This report summarizes the research on single-particle nonlinear beam dynamics. It discusses the following topics: analytical and semi-analytical tools; early prediction of the dynamic aperture; how the results are commonly presented; Is the mechanism of the dynamic aperture understand; ripple effects; and beam-beam effects

Nonlinear dynamics in cardiac conduction

Science.gov (United States)

Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.

1988-01-01

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

Nonlinear Relaxation in Population Dynamics

Science.gov (United States)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

Creation of 3D Multi-Body Orthodontic Models by Using Independent Imaging Sensors

Directory of Open Access Journals (Sweden)

Armando Viviano Razionale

2013-02-01

Full Text Available In the field of dental health care, plaster models combined with 2D radiographs are widely used in clinical practice for orthodontic diagnoses. However, complex malocclusions can be better analyzed by exploiting 3D digital dental models, which allow virtual simulations and treatment planning processes. In this paper, dental data captured by independent imaging sensors are fused to create multi-body orthodontic models composed of teeth, oral soft tissues and alveolar bone structures. The methodology is based on integrating Cone-Beam Computed Tomography (CBCT and surface structured light scanning. The optical scanner is used to reconstruct tooth crowns and soft tissues (visible surfaces through the digitalization of both patients’ mouth impressions and plaster casts. These data are also used to guide the segmentation of internal dental tissues by processing CBCT data sets. The 3D individual dental tissues obtained by the optical scanner and the CBCT sensor are fused within multi-body orthodontic models without human supervisions to identify target anatomical structures. The final multi-body models represent valuable virtual platforms to clinical diagnostic and treatment planning.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Nonlinear dynamical modes of climate variability: from curves to manifolds

Science.gov (United States)

Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

2016-04-01

The necessity of efficient dimensionality reduction methods capturing dynamical properties of the system from observed data is evident. Recent study shows that nonlinear dynamical mode (NDM) expansion is able to solve this problem and provide adequate phase variables in climate data analysis [1]. A single NDM is logical extension of linear spatio-temporal structure (like empirical orthogonal function pattern): it is constructed as nonlinear transformation of hidden scalar time series to the space of observed variables, i. e. projection of observed dataset onto a nonlinear curve. Both the hidden time series and the parameters of the curve are learned simultaneously using Bayesian approach. The only prior information about the hidden signal is the assumption of its smoothness. The optimal nonlinearity degree and smoothness are found using Bayesian evidence technique. In this work we do further extension and look for vector hidden signals instead of scalar with the same smoothness restriction. As a result we resolve multidimensional manifolds instead of sum of curves. The dimension of the hidden manifold is optimized using also Bayesian evidence. The efficiency of the extension is demonstrated on model examples. Results of application to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

Science.gov (United States)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

Polarization dynamics in nonlinear anisotropic fibers

International Nuclear Information System (INIS)

Komarov, Andrey; Komarov, Konstantin; Meshcheriakov, Dmitry; Amrani, Foued; Sanchez, Francois

2010-01-01

We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincare sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincare sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.

Nonlinear Dynamics and the Growth of Literature.

Science.gov (United States)

Tabah, Albert N.

1992-01-01

Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…

Influences of the Control on the Nonlinear Vibrations of a Variable Compression Ratio Mechanism

Directory of Open Access Journals (Sweden)

Mănescu Bogdan

2018-01-01

Full Text Available For the mechanism described in references the study of the nonlinear vibrations is performed considering a multibody approach for the elements of the mechanism and different laws of motion for the control element. A great attention is paid to the equilibrium of the motion. The influence of different parameters of control is highlighted in the paper. The results are numerically validated.

Nonlinear laser dynamics from quantum dots to cryptography

CERN Document Server

Lüdge, Kathy

2012-01-01

A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research.By presenting both experimental and theoretical results, the distinguished authors consider solitary lase

Dynamic nonlinear thermal optical effects in coupled ring resonators

Directory of Open Access Journals (Sweden)

Chenguang Huang

2012-09-01

Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.

Nonlinearly coupled dynamics of irregularities in the equatorial electrojet

Energy Technology Data Exchange (ETDEWEB)

Atul, J.K., E-mail: jkatulphysics@gmail.com [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India); Sarkar, S. [FCIPT, Institute for Plasma Research, Gandhinagar 382428 (India); Singh, S.K. [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India)

2016-04-01

Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed. - Highlights: • Nonlinear influence of Farley Buneman mode on the Gradient drift mode, is investigated. • Electron collision frequency and density gradient scale length get modified. • A new quasimode gets excited due to the competition between these modes. • It seems to be important for modelling of Equatorial Electrojet current system.

Nonlinearly coupled dynamics of irregularities in the equatorial electrojet

International Nuclear Information System (INIS)

Atul, J.K.; Sarkar, S.; Singh, S.K.

2016-01-01

Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed. - Highlights: • Nonlinear influence of Farley Buneman mode on the Gradient drift mode, is investigated. • Electron collision frequency and density gradient scale length get modified. • A new quasimode gets excited due to the competition between these modes. • It seems to be important for modelling of Equatorial Electrojet current system.

An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

KAUST Repository

Xu, Tiantian

2014-08-17

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

Dynamic beam cleaning by a nonlinear resonance

Energy Technology Data Exchange (ETDEWEB)

Chao, A W; Month, M [Brookhaven National Lab., Upton, N.Y. (USA)

1976-03-15

The general framework for the dynamic cleaning of a stored proton beam by passing the beam through a nonlinear resonance is developed. The limitations and advantages of this technique are discussed. The method is contrasted with physical beam scraping, which is currently in use at the CERN ISR.

Nonlinear dynamics and predictability in the atmospheric sciences

Science.gov (United States)

Ghil, M.; Kimoto, M.; Neelin, J. D.

1991-01-01

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Reconstructing a nonlinear dynamical framework for testing quantum mechanics

International Nuclear Information System (INIS)

Jordan, T.F.

1993-01-01

The nonlinear generalization of quantum dynamics constructed by Weinberg as a basis for experimental tests is reconstructed in terms of density-matrix elements to allow independent dynamics for subsystems. Dynamics is generated with a Lie bracket and a nonlinear Hamiltonian function. It takes density matrices to density matrices and pure states to pure states. Each density matrix has a Hamiltonian operator that makes its evolution for an infinitesimal time, but the Hamiltonian operator may be different for different density matrices and may change in time as the density matrix changes. A Hamiltonian function for a subsystem serves also for the entire system. Independence of separate subsystems is confirmed by seeing that brackets are zero for functions from different subsystems and by looking at the Hamiltonian operator for each density matrix. Scaling properties of Hamiltonian functions are found to be important in connection with locality. An example of all this is obtained from every one of the local nonlinear Schroedinger equations described by Bialynicki-Birula and Mycielski. Examples are worked out for spins coupled together or to fields, demonstrating Hamiltonian functions and equations of motion written directly in terms of physical mean values. Observables and states are taken to be the same as in ordinary quantum mechanics. An attempt to find nonlinear representations of observables by characterizing propositions as functions equal to their squares yields a negative result. Sharper interpretation of mixed states is proposed. In a mixture of parts that are prepared separately, time dependence must be calculated separately for each part so different mixtures that yield the same density matrix can be distinguished. No criticism has shown that a consistent interpretation cannot be made this way. Thus, nonlinearity remains a viable hypothesis for experimental tests. 16 refs

Design and Dynamics Analysis of a Bio-Inspired Intermittent Hopping Robot for Planetary Surface Exploration

Directory of Open Access Journals (Sweden)

Long Bai

2012-10-01

Full Text Available A small, bio-inspired and minimally actuated intermittent hopping robot for planetary surface exploration is proposed in this paper. The robot uses a combined-geared six-bar linkage/spring mechanism, which has a possible rich trajectory and metamorphic characteristics and, due to this, the robot is able to recharge, lock/release and jump by using just a micro-power motor as the actuator. Since the robotic system has a closed-chain structure and employs underactuated redundant motion, the constrained multi-body dynamics are derived with time-varying driving parameters and ground unilateral constraint both taken into consideration. In addition, the established dynamics equations, mixed of higher order differential and algebraic expressions, are solved by the immediate integration algorithm. A prototype is implemented and experiments are carried out. The results show that the robot, using a micro-power motor as the actuator and solar cells as the power supply, can achieve a biomimetic multi-body hopping stance and a nonlinearly increasing driving force. Typically, the robot can jump a horizontal distance of about 1 m and a vertical height of about 0.3 m, with its trunk and foot moving stably during takeoff. In addition, the computational and experimental results are consistent as regards the hopping performance of the robot, which suggests that the proposed dynamics model and its solution have general applicability to motion prediction and the performance analysis of intermittent hopping robots.

Application of homotopy-perturbation method to nonlinear population dynamics models

International Nuclear Information System (INIS)

Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.

2007-01-01

In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

Science.gov (United States)

Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John

1988-01-01

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

Dynamics and genetic fuzzy neural network vibration control design of a smart flexible four-bar linkage mechanism

International Nuclear Information System (INIS)

Rong Bao; Rui Xiaoting; Tao Ling

2012-01-01

In this paper, a dynamic modeling method and an active vibration control scheme for a smart flexible four-bar linkage mechanism featuring piezoelectric actuators and strain gauge sensors are presented. The dynamics of this smart mechanism is described by the Discrete Time Transfer Matrix Method of Multibody System (MS-DTTMM). Then a nonlinear fuzzy neural network control is employed to suppress the vibration of this smart mechanism. For improving the dynamic performance of the fuzzy neural network, a genetic algorithm based on the MS-DTTMM is designed offline to tune the initial parameters of the fuzzy neural network. The MS-DTTMM avoids the global dynamics equations of the system, which results in the matrices involved are always very small, so the computational efficiency of the dynamic analysis and control system optimization can be greatly improved. Formulations of the method as well as a numerical simulation are given to demonstrate the proposed dynamic method and control scheme.

Hierarchical nonlinear dynamics of human attention.

Science.gov (United States)

Rabinovich, Mikhail I; Tristan, Irma; Varona, Pablo

2015-08-01

Attention is the process of focusing mental resources on a specific cognitive/behavioral task. Such brain dynamics involves different partially overlapping brain functional networks whose interconnections change in time according to the performance stage, and can be stimulus-driven or induced by an intrinsically generated goal. The corresponding activity can be described by different families of spatiotemporal discrete patterns or sequential dynamic modes. Since mental resources are finite, attention modalities compete with each other at all levels of the hierarchy, from perception to decision making and behavior. Cognitive activity is a dynamical process and attention possesses some universal dynamical characteristics. Thus, it is time to apply nonlinear dynamical theory for the description and prediction of hierarchical attentional tasks. Such theory has to include the analyses of attentional control stability, the time cost of attention switching, the finite capacity of informational resources in the brain, and the normal and pathological bifurcations of attention sequential dynamics. In this paper we have integrated today's knowledge, models and results in these directions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Nonlinear dynamics of semiclassical coherent states in periodic potentials

International Nuclear Information System (INIS)

Carles, Rémi; Sparber, Christof

2012-01-01

We consider nonlinear Schrödinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding semiclassical scaling regime, we construct asymptotic solutions, which are concentrated both in space and in frequency around the effective semiclassical phase-space flow induced by Bloch’s spectral problem. The dynamics of these generalized coherent states is governed by a nonlinear Schrödinger model with effective mass. In the case of nonlocal nonlinearities, we establish a novel averaging-type result in the critical case. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Modelling Hermetic Compressors Using Different Constraint Equations to Accommodate Multibody Dynamics and Hydrodynamic Lubrication

DEFF Research Database (Denmark)

Estupinan, Edgar Alberto; Santos, Ilmar

2009-01-01

elements are supported by fluid film bearings, where the hydrodynamic interaction forces are described by the Reynolds equation. The system of nonlinear equations is numerically solved for three different restrictive conditions of the motion of the crank, where the third case takes into account lateral...... and tilting oscillations of the extremity of the crankshaft. The numerical results of the behaviour of the journal bearings for each case are presented giving some insights into design parameters such as, maximum oil film pressure, minimum oil film thickness, maximum vibration levels and dynamic reaction...

Some Nonlinear Dynamic Inequalities on Time Scales

Indian Academy of Sciences (India)

The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential ...

A probabilistic analysis of the dynamic response of monopile foundations: Soil variability and its consequences

DEFF Research Database (Denmark)

Damgaard, M.; Andersen, L.V.; Ibsen, L.B.

2015-01-01

The reliability of offshore wind turbines is highly influenced by the uncertainties related to the subsoil conditions. Traditionally, the evaluation of the dynamic structural behaviour is based on a computational model with deterministic soil properties. Using this approach, however, provides...... on a Monte Carlo method facilitating the derivation of the probability densities of the modal properties and the fatigue loading. The main conclusion of the presented work is that the dynamic structural behaviour of the wind turbine and its support structure is strongly affected by the stochastic soil......-analytical impedance functions of a monopile embedded in a stochastic linear viscoelastic soil layer, fully coupled aero-hydro-elastic simulations are conducted in the nonlinear multi-body code Hawc2. The probabilistic analysis accounts for the uncertainty of soil properties (e.g. damping and stiffness) and relies...

Nonlinear dynamic analysis and state space representation of a manipulator under viscoelastic material conditions

Directory of Open Access Journals (Sweden)

Esfandiar, H.

2013-05-01

Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.

Collective Dynamics of Nonlinear and Disordered Systems

CERN Document Server

Radons, G; Just, W

2005-01-01

Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

Science.gov (United States)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

Dissipative quantum dynamics and nonlinear sigma-model

International Nuclear Information System (INIS)

Tarasov, V.E.

1992-01-01

Sedov variational principle which is the generalization of the least action principle for the dissipative and irreversible processes and the classical dissipative mechanics in the phase space is considered. Quantum dynamics for the dissipative and irreversible processes is constructed. As an example of the dissipative quantum theory the nonlinear two-dimensional sigma-model is considered. The conformal anomaly of the energy momentum tensor trace for closed bosonic string on the affine-metric manifold is investigated. The two-loop metric beta-function for nonlinear dissipative sigma-model was calculated. The results are compared with the ultraviolet two-loop conterterms for affine-metric sigma model. 71 refs

Econometric testing on linear and nonlinear dynamic relation between stock prices and macroeconomy in China

Science.gov (United States)

Borjigin, Sumuya; Yang, Yating; Yang, Xiaoguang; Sun, Leilei

2018-03-01

Many researchers have realized that there is a strong correlation between stock prices and macroeconomy. In order to make this relationship clear, a lot of studies have been done. However, the causal relationship between stock prices and macroeconomy has still not been well explained. A key point is that, most of the existing research adopts linear and stable models to investigate the correlation of stock prices and macroeconomy, while the real causality of that may be nonlinear and dynamic. To fill this research gap, we investigate the nonlinear and dynamic causal relationships between stock prices and macroeconomy. Based on the case of China's stock prices and acroeconomy measures from January 1992 to March 2017, we compare the linear Granger causality test models with nonlinear ones. Results demonstrate that the nonlinear dynamic Granger causality is much stronger than linear Granger causality. From the perspective of nonlinear dynamic Granger causality, China's stock prices can be viewed as "national economic barometer". On the one hand, this study will encourage researchers to take nonlinearity and dynamics into account when they investigate the correlation of stock prices and macroeconomy; on the other hand, our research can guide regulators and investors to make better decisions.

Chaotic dynamics with high complexity in a simplified new nonautonomous nonlinear electronic circuit

International Nuclear Information System (INIS)

Arulgnanam, A.; Thamilmaran, K.; Daniel, M.

2009-01-01

A two dimensional nonautonomous dissipative forced series LCR circuit with a simple nonlinear element exhibiting an immense variety of dynamical features is proposed for the first time. Unlike the usual cases of nonlinear element, the nonlinear element used here possesses three segment piecewise linear character with one positive and one negative slope. This nonlinearity is verified to be sufficient to produce chaos with high complexity in many established nonautonomous nonlinear circuits, such as MLC, MLCV, driven Chua, etc., thus indicating an universal behavior similar to the familiar Chua's diode. The dynamics of the proposed circuit is studied experimentally, confirmed numerically, simulated through PSPICE and proved mathematically. An important feature of the circuit is its ability to show dual chaotic behavior.

A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

Science.gov (United States)

Shi, H.; Yang, B.; Thomson, M.; Fang, H.

2011-01-01

This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

On non-linear dynamics of a coupled electro-mechanical system

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2012-01-01

Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...

IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

CERN Document Server

Rega, Giuseppe

2013-01-01

Nonlinear dynamics has been enjoying a vast development for nearly four decades resulting in a range of well established theory, with the potential to significantly enhance performance, effectiveness, reliability and safety of physical systems as well as offering novel technologies and designs. By critically appraising the state-of-the-art, it is now time to develop design criteria and technology for new generation products/processes operating on principles of nonlinear interaction and in the nonlinear regime, leading to more effective, sensitive, accurate, and durable methods than what is currently available. This new approach is expected to radically influence the design, control and exploitation paradigms, in a magnitude of contexts. With a strong emphasis on experimentally calibrated and validated models, contributions by top-level international experts will foster future directions for the development of engineering technologies and design using robust nonlinear dynamics modelling and analysis.  

Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

Science.gov (United States)

Agarwal, S.; Wettlaufer, J. S.

2014-12-01

We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations.

Science.gov (United States)

Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

Science.gov (United States)

Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

2013-05-10

We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.

1996-01-01

Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...

Semiconductor Nonlinear Dynamics Study by Broadband Terahertz Spectroscopy

Science.gov (United States)

Ho, I.-Chen

Semiconductor nonlinearity in the terahertz (THz) frequency range has been attracting considerable attention due to the recent development of high-power semiconductor-based nanodevices. However, the underlying physics concerning carrier dynamics in the presence of high-field THz transients is still obscure. This thesis introduces an ultrafast, time-resolved THz pump/THz probe approach to the study of semiconductor properties in the nonlinear regime. The carrier dynamics regarding two mechanisms, intervalley scattering and impact ionization, is observed for doped InAs on a sub-picosecond time scale. In addition, polaron modulation driven by intense THz pulses is experimentally and theoretically investigated. The observed polaron dynamics verifies the interaction between energetic electrons and a phonon field. In contrast to previous work which reports optical phonon responses, acoustic phonon modulations are addressed in this study. A further understanding of the intense field interacting with solid materials will accelerate the development of semiconductor devices. This thesis starts with the design and performance of a table-top THz spectrometer which has the advantages of ultra-broad bandwidth (one order higher bandwidth compared to a conventional ZnTe sensor) and high electric field strength (>100 kV/cm). Unlike the conventional THz time-domain spectroscopy, the spectrometer integrates a novel THz air-biased-coherent-detection (THz-ABCD) technique and utilizes selected gases as THz emitters and sensors. In comparison with commonly used electro-optic (EO) crystals or photoconductive (PC) dipole antennas, the gases have the benefits of no phonon absorption as existing in EO crystals and no carrier life time limitation as observed in PC dipole antennas. The newly development THz-ABCD spectrometer with a strong THz field strength capability provides a platform for various research topics especially on the nonlinear carrier dynamics of semiconductors. Two mechanisms

Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings

Science.gov (United States)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

In current bearing dynamic models, the displacement coordinate relations are usually utilized to approximately obtain the contact deformations between the rolling element and raceways, and then the nonlinear restoring forces of the rolling bearing could be calculated accordingly. Although the calculation efficiency is relatively higher, the accuracy is lower as the contact deformations should be solved through iterative analysis. Thus, an improved nonlinear dynamic model is presented in this paper. Considering the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, load distribution analysis is solved iteratively to more accurately obtain the contact deformations and angles between the rolling balls and raceways. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests upon a typical rotor system supported by two angular contact ball bearings are conducted to verify the model. Through comparisons, the differences between the nonlinear dynamic model and current models are also pointed out. The effects of axial preload, rotor eccentricity and inner/outer waviness amplitudes on the dynamic response are discussed in detail.

Molecular dynamics simulation of nonlinear spectroscopies of intermolecular motions in liquid water.

Science.gov (United States)

Yagasaki, Takuma; Saito, Shinji

2009-09-15

Water is the most extensively studied of liquids because of both its ubiquity and its anomalous thermodynamic and dynamic properties. The properties of water are dominated by hydrogen bonds and hydrogen bond network rearrangements. Fundamental information on the dynamics of liquid water has been provided by linear infrared (IR), Raman, and neutron-scattering experiments; molecular dynamics simulations have also provided insights. Recently developed higher-order nonlinear spectroscopies open new windows into the study of the hydrogen bond dynamics of liquid water. For example, the vibrational lifetimes of stretches and a bend, intramolecular features of water dynamics, can be accurately measured and are found to be on the femtosecond time scale at room temperature. Higher-order nonlinear spectroscopy is expressed by a multitime correlation function, whereas traditional linear spectroscopy is given by a one-time correlation function. Thus, nonlinear spectroscopy yields more detailed information on the dynamics of condensed media than linear spectroscopy. In this Account, we describe the theoretical background and methods for calculating higher order nonlinear spectroscopy; equilibrium and nonequilibrium molecular dynamics simulations, and a combination of both, are used. We also present the intermolecular dynamics of liquid water revealed by fifth-order two-dimensional (2D) Raman spectroscopy and third-order IR spectroscopy. 2D Raman spectroscopy is sensitive to couplings between modes; the calculated 2D Raman signal of liquid water shows large anharmonicity in the translational motion and strong coupling between the translational and librational motions. Third-order IR spectroscopy makes it possible to examine the time-dependent couplings. The 2D IR spectra and three-pulse photon echo peak shift show the fast frequency modulation of the librational motion. A significant effect of the translational motion on the fast frequency modulation of the librational motion is

Nonlinear chaos-dynamical approach to analysis of atmospheric ...

Indian Academy of Sciences (India)

false nearest neighbors, Lyapunov's exponents, surrogate data, nonlinear prediction ... Chaotic dynamics; time series of the 222Rn concentration; universal complex ... tems is due to a number of applications, including the ..... Computer Engineering. ... Ternovsky,Quantum Systems in Physics, Chemistry, and. Biology, pp.

The periodic structure of the natural record, and nonlinear dynamics.

Science.gov (United States)

Shaw, H.R.

1987-01-01

This paper addresses how nonlinear dynamics can contribute to interpretations of the geologic record and evolutionary processes. Background is given to explain why nonlinear concepts are important. A resume of personal research is offered to illustrate why I think nonlinear processes fit with observations on geological and cosmological time series data. The fabric of universal periodicity arrays generated by nonlinear processes is illustrated by means of a simple computer mode. I conclude with implications concerning patterns of evolution, stratigraphic boundary events, and close correlations of major geologically instantaneous events (such as impacts or massive volcanic episodes) with any sharply defined boundary in the geologic column. - from Author

Parameter and state estimation in nonlinear dynamical systems

Science.gov (United States)

Creveling, Daniel R.

This thesis is concerned with the problem of state and parameter estimation in nonlinear systems. The need to evaluate unknown parameters in models of nonlinear physical, biophysical and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. When verifying and validating these models, it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, this thesis develops a framework for presenting data to a candidate model of a physical process in a way that makes efficient use of the measured data while allowing for estimation of the unknown parameters in the model. The approach presented here builds on existing work that uses synchronization as a tool for parameter estimation. Some critical issues of stability in that work are addressed and a practical framework is developed for overcoming these difficulties. The central issue is the choice of coupling strength between the model and data. If the coupling is too strong, the model will reproduce the measured data regardless of the adequacy of the model or correctness of the parameters. If the coupling is too weak, nonlinearities in the dynamics could lead to complex dynamics rendering any cost function comparing the model to the data inadequate for the determination of model parameters. Two methods are introduced which seek to balance the need for coupling with the desire to allow the model to evolve in its natural manner without coupling. One method, 'balanced' synchronization, adds to the synchronization cost function a requirement that the conditional Lyapunov exponents of the model system, conditioned on being driven by the data, remain negative but small in magnitude. Another method allows the coupling between the data and the model to vary in time according to a specific form of differential equation. The coupling dynamics is damped to allow for a tendency toward zero coupling

Design of advanced materials for linear and nonlinear dynamics

DEFF Research Database (Denmark)

Frandsen, Niels Morten Marslev

to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple......The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... but general model of inhomogeneous structural materials with nonlinear material characteristics. The second material system is an “engineered” material in the sense that a classical structural element, a linear elastic and homogeneous rod, is “enhanced” by applying a mechanism on its surface, amplifying...

Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

Science.gov (United States)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

2017-04-01

Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

Attitude and Configuration Control of Flexible Multi-Body Spacecraft

Science.gov (United States)

Cho, Sung-Ki; Cochran, John E., Jr.

2002-06-01

Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems addressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

Attitude and Configuration Control of Flexible Multi-Body Spacecraft

Directory of Open Access Journals (Sweden)

Sungki Cho

2002-06-01

Full Text Available Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems addressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

Instantaneous nonlinear assessment of complex cardiovascular dynamics by Laguerre-Volterra point process models.

Science.gov (United States)

Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo

2013-01-01

We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.

Nonlinear dynamic analysis using Petrov-Galerkin natural element method

International Nuclear Information System (INIS)

Lee, Hong Woo; Cho, Jin Rae

2004-01-01

According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem

Soliton dynamics in periodic system with different nonlinear media

International Nuclear Information System (INIS)

Zabolotskij, A.A.

2001-01-01

To analyze pulse dynamics in the optical system consisting of periodic sequence of nonlinear media one uses a composition model covering a model of resonance interaction of light ultrashort pulse with energy transition of medium with regard to pumping of the upper level and quasi-integrable model describing propagation of light field in another medium with cubic nonlinearity and dispersion. One additionally takes account of losses and other types of interaction in the from of perturbation members. On the basis of the method of scattering back problem and perturbation theory one developed a simple method to study peculiarities of soliton evolution in such periodic system. Due to its application one managed to describe different modes of soliton evolution in such a system including chaotic dynamics [ru

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

CERN Document Server

Wu, Shen R

2012-01-01

A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress.

Science.gov (United States)

Dakos, Vasilis; Glaser, Sarah M; Hsieh, Chih-Hao; Sugihara, George

2017-03-01

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom-bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress. © 2017 The Author(s).

Bubble and Drop Nonlinear Dynamics (BDND)

Science.gov (United States)

Trinh, E. H.; Leal, L. Gary; Thomas, D. A.; Crouch, R. K.

1998-01-01

Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.

Nonlinear dynamical systems for theory and research in ergonomics.

Science.gov (United States)

Guastello, Stephen J

2017-02-01

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

Multibody neutrino exchange in a neutron star neutrino sea and border effects

CERN Document Server

Abada, A; Rodríguez-Quintero, J; Abada, As

1998-01-01

The interaction due to the exchange of massless neutrinos between neutrons is a long-range force. Border effects on this multibody exchange inside a dense core are studied and computed analytically in 1 + 1 dimensions. We demonstrate in this work that a proper treatment of the star's border effect automatically incorporates the condensate contribution as a consequence of the appropriate boundary conditions for the neutrino Feynman propagator inside the star. The total multibody exchange contribution is infrared-safe and vanishes exactly in 1 + 1 dimensions. The general conclusion of this work is that the border effect does not modify the result that neutrino exchange is infrared-safe. This toy model prepares the ground and gives the tools for the study of the realistic 3 + 1 star.

The landscape of nonlinear structural dynamics: an introduction.

Science.gov (United States)

Butlin, T; Woodhouse, J; Champneys, A R

2015-09-28

Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape. © 2015 The Authors.

Modified dynamic Stark shift and depopulation rate of an atom inside a Kerr nonlinear blackbody

International Nuclear Information System (INIS)

Yin Miao; Cheng Ze

2009-01-01

We investigate the dynamic Stark shift and atomic depopulation rate induced by real photons in a Kerr nonlinear blackbody. We found that the dynamic Stark shift and atomic depopulation rate are equally modified by a nonlinear contribution factor and a linear contribution factor under a transition temperature T c . The nonlinear contribution factor depends on the Kerr nonlinear coefficient as well as the absolute temperature. Below T c , the absolute values of the dynamic Stark shift and depopulation rate of a single atomic state (not the ground state) are correspondingly larger than those in a normal blackbody whose interior is filled with a nonabsorbing linear medium. Above T c , the dynamic Stark shift and atomic depopulation rate are correspondingly equal to those in a normal blackbody with a nonabsorbing linear medium in its interior.

Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.

Science.gov (United States)

Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal

2017-08-18

The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.

Short- and long-term variations in non-linear dynamics of heart rate variability

DEFF Research Database (Denmark)

Kanters, J K; Højgaard, M V; Agner, E

1996-01-01

OBJECTIVES: The purpose of the study was to investigate the short- and long-term variations in the non-linear dynamics of heart rate variability, and to determine the relationships between conventional time and frequency domain methods and the newer non-linear methods of characterizing heart rate...... rate and describes mainly linear correlations. Non-linear predictability is correlated with heart rate variability measured as the standard deviation of the R-R intervals and the respiratory activity expressed as power of the high-frequency band. The dynamics of heart rate variability changes suddenly...

A Large-Scale Multibody Manipulator Soft Sensor Model and Experiment Validation

Directory of Open Access Journals (Sweden)

Wu Ren

2014-01-01

Full Text Available Stress signal is difficult to obtain in the health monitoring of multibody manipulator. In order to solve this problem, a soft sensor method is presented. In the method, stress signal is considered as dominant variable and angle signal is regarded as auxiliary variable. By establishing the mathematical relationship between them, a soft sensor model is proposed. In the model, the stress information can be deduced by angle information which can be easily measured for such structures by experiments. Finally, test of ground and wall working conditions is done on a multibody manipulator test rig. The results show that the stress calculated by the proposed method is closed to the test one. Thus, the stress signal is easier to get than the traditional method. All of these prove that the model is correct and the method is feasible.

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy

Science.gov (United States)

Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.

2018-01-01

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

Science.gov (United States)

Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.

2012-12-01

In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.

Use of the dynamic stiffness method to interpret experimental data from a nonlinear system

Science.gov (United States)

Tang, Bin; Brennan, M. J.; Gatti, G.

2018-05-01

The interpretation of experimental data from nonlinear structures is challenging, primarily because of dependency on types and levels of excitation, and coupling issues with test equipment. In this paper, the use of the dynamic stiffness method, which is commonly used in the analysis of linear systems, is used to interpret the data from a vibration test of a controllable compressed beam structure coupled to a test shaker. For a single mode of the system, this method facilitates the separation of mass, stiffness and damping effects, including nonlinear stiffness effects. It also allows the separation of the dynamics of the shaker from the structure under test. The approach needs to be used with care, and is only suitable if the nonlinear system has a response that is predominantly at the excitation frequency. For the structure under test, the raw experimental data revealed little about the underlying causes of the dynamic behaviour. However, the dynamic stiffness approach allowed the effects due to the nonlinear stiffness to be easily determined.

A data driven nonlinear stochastic model for blood glucose dynamics.

Science.gov (United States)

Zhang, Yan; Holt, Tim A; Khovanova, Natalia

2016-03-01

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

A comparative analysis of alternative approaches for quantifying nonlinear dynamics in cardiovascular system.

Science.gov (United States)

Chen, Yun; Yang, Hui

2013-01-01

Heart rate variability (HRV) analysis has emerged as an important research topic to evaluate autonomic cardiac function. However, traditional time and frequency-domain analysis characterizes and quantify only linear and stationary phenomena. In the present investigation, we made a comparative analysis of three alternative approaches (i.e., wavelet multifractal analysis, Lyapunov exponents and multiscale entropy analysis) for quantifying nonlinear dynamics in heart rate time series. Note that these extracted nonlinear features provide information about nonlinear scaling behaviors and the complexity of cardiac systems. To evaluate the performance, we used 24-hour HRV recordings from 54 healthy subjects and 29 heart failure patients, available in PhysioNet. Three nonlinear methods are evaluated not only individually but also in combination using three classification algorithms, i.e., linear discriminate analysis, quadratic discriminate analysis and k-nearest neighbors. Experimental results show that three nonlinear methods capture nonlinear dynamics from different perspectives and the combined feature set achieves the best performance, i.e., sensitivity 97.7% and specificity 91.5%. Collectively, nonlinear HRV features are shown to have the promise to identify the disorders in autonomic cardiovascular function.

Parallel processing for nonlinear dynamics simulations of structures including rotating bladed-disk assemblies

Science.gov (United States)

Hsieh, Shang-Hsien

1993-01-01

The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.

Modelamento Multicorpo do Sistema Musculoesquelético/Multibody modeling of the Musculoskeletal System

Directory of Open Access Journals (Sweden)

José Elias Tomazini

2012-12-01

Full Text Available Vários sistemas podem ser tratados com formalismos multicorpos: mecanismos de máquinas em geral, robôs industriais e manipuladores, estruturas espaciais, motores e, ainda, sistemas biomecânicos. A locomoção ou marcha humana e animal podem ser estudadas através de formalismos multicorpos.Nos últimos anos, diversos trabalhos relacionados à biomecânica, e utilizando formalismos multicorpos, têm sido apresentados. Muitos estudos in vitro e in vivo têm sido realizados, objetivando descrever o potencial de sobrecarga nas articulações do corpo humano e de modelos animais. O objetivo desta revisão foi apresentar estudos envolvendo o modelamento matemático aplicado à bioengenharia, biomecânica e engenharia biomédica. Conclui-se que o modelamento matemático é uma ferramenta muito útil, barata e não invasiva que vem contribuir nos estudos envolvendo o sistema multicorpo mecânico e complexo, que é o corpo humano. Several systems can be treated with multibody formalisms: mechanisms of general machinery, industrial robots and manipulators, space structures, engines, and also biomechanical systems. The locomotion or human gait can be studied using multibody formalisms. Several studies related to biomechanics, and using multibody formalisms, have been presented in recent years. Many studies in vitro and in vivo have been carried out, aiming to describe the potential overload in the joints of the human body and animal models. The aim of this review was to present studies involving mathematical modeling applied to bioengineering, biomechanics and biomedical engineering. We have concluded that mathematical modeling is a useful, inexpensive and noninvasive tool which comes to contribute in studies involving the mechanical and complex multibody system which is the human body.

Dynamical soil-structure interactions: influence of soil behaviour nonlinearities

International Nuclear Information System (INIS)

Gandomzadeh, Ali

2011-01-01

The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in

Nonlinear dynamic analysis of piping systems using the pseudo force method

International Nuclear Information System (INIS)

Prachuktam, S.; Bezler, P.; Hartzman, M.

1979-01-01

Simple piping systems are composed of linear elastic elements and can be analyzed using conventional linear methods. The introduction of constraint springs separated from the pipe with clearance gaps to such systems to cope with the pipe whip or other extreme excitation conditions introduces nonlinearities to the system, the nonlinearities being associated with the gaps. Since these spring-damper constraints are usually limited in number, descretely located, and produce only weak nonlinearities, the analysis of linear systems including these nonlinearities can be carried out by using modified linear methods. In particular, the application of pseudo force methods wherein the nonlinearities are treated as displacement dependent forcing functions acting on the linear system were investigated. The nonlinearities induced by the constraints are taken into account as generalized pseudo forces on the right-hand side of the governing dynamic equilibrium equations. Then an existing linear elastic finite element piping code, EPIPE, was modified to permit application of the procedure. This option was inserted such that the analyses could be performed using either the direct integration method or via a modal superposition method, the Newmark-Beta integration procedure being employed in both methods. The modified code was proof tested against several problems taken from the literature or developed with the nonlinear dynamics code OSCIL. The problems included a simple pipe loop, cantilever beam, and lumped mass system subjected to pulsed and periodic forcing functions. The problems were selected to gage the overall accuracy of the method and to insure that it properly predicted the jump phenomena associated with nonlinear systems. (orig.)

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

Science.gov (United States)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

A nonlinear dynamics approach for incorporating wind-speed patterns into wind-power project evaluation.

Science.gov (United States)

Huffaker, Ray; Bittelli, Marco

2015-01-01

Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind-the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns.

Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

Science.gov (United States)

Ryzhov, Eugene A

2017-11-01

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

Nonlinear dynamics of tearing modes in the reversed field pinch

International Nuclear Information System (INIS)

Holmes, J.A.; Carreras, B.A.; Diamond, P.H.; Lynch, V.E.

1988-01-01

The results of investigations of nonlinear tearing-mode dynamics in reversed field pinch plasmas are described. The linear instabilities have poloidal mode number m = 1 and toroidal mode numbers 10approx. < napprox. <20, and the resonant surfaces are therefore in the plasma core. The nonlinear dynamics result in dual cascade processes. The first process is a rapid m = 1 spectral broadening toward high n, with a simultaneous spreading of magnetic turbulence radially outward toward the field-reversal surface. Global m = 0 perturbations, which are driven to large amplitudes by the m = 1 instabilities, in turn trigger the m = 1 spectral broadening by back coupling to the higher n. The second process is a cascade toward large m and is mediated by m = 2 modes. The m = 2 perturbations have the structure of localized, driven current sheets and nonlinearly stabilize the m = 1 modes by transferring m = 1 energy to small-scale dissipation. The calculated spectrum has many of the qualitative features observed in experiments

Photonic single nonlinear-delay dynamical node for information processing

Science.gov (United States)

Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

2012-06-01

An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

Nonlinear modeling and dynamic analysis of hydro-turbine governing system in the process of load rejection transient

International Nuclear Information System (INIS)

Zhang, Hao; Chen, Diyi; Xu, Beibei; Wang, Feifei

2015-01-01

Graphical abstract: Nonlinear dynamic transfer coefficients are introduced to the hydro-turbine governing system. In the process of load reject ion transient, the nonlinear dynamical behaviors of the system are studied in detail. - Highlights: • A novel mathematical model of a hydro-turbine governing system is established. • The process of load rejection transient is considered. • Nonlinear dynamic transfer coefficients are introduced to the system. • The bifurcation diagram with the variable t has better engineering significance. • The nonlinear dynamical behaviors of the system are studied in detail. - Abstract: This article pays attention to the mathematical modeling of a hydro-turbine governing system in the process of load rejection transient. As a pioneer work, the nonlinear dynamic transfer coefficients are introduced in a penstock system. Considering a generator system, a turbine system and a governor system, we present a novel nonlinear dynamical model of a hydro-turbine governing system. Fortunately, for the unchanged of PID parameters, we acquire the stable regions of the governing system in the process of load rejection transient by numerical simulations. Moreover, the nonlinear dynamic behaviors of the governing system are illustrated by bifurcation diagrams, Poincare maps, time waveforms and phase orbits. More importantly, these methods and analytic results will present theoretical groundwork for allowing a hydropower station in the process of load rejection transient

Numerical simulation of the nonlinear dynamics of packets of spiral density waves

International Nuclear Information System (INIS)

Korchagin, V.I.

1987-01-01

In a numerical experiment, the behavior of nonlinear packets of spiral density waves in a gas disk has been investigated for different initial wave amplitudes. If the amplitude of the density perturbations is small (<5%), the wave packet is drawn toward the center or toward the periphery of the disk in accordance with the linear theory. The behavior of linear packets of waves with wavelength comparable to the disk radius (R/sub d//lambda = 4) exhibits good agreement with the conclusions of the linear theory of tightly wound spiral waves. The dynamics of wave packets with initial density amplitudes 16, 30, 50% demonstrates the nonlinear nature of the behavior. THe behavior is governed by whether or not the nonlinear effects of higher than third order in the wave amplitude play a part. If the wave packet dynamics is determined by the cubic nonlinearity, the results of the numerical experiment are in qualitative and quantitative agreement with the nonlinear theory of short waves, although the characteristic scale of the packet and the wavelength are of the order of the disk radius. In the cases when the nonlinear effects of higher orders in the amplitude play an important part, the behavior of a packet does not differ qualitatively from the behavior predicted by the theory of cubic nonlinearity, but the nonlinear spreading of the packet takes place more rapidly

Global sensitivity analysis of the joint kinematics during gait to the parameters of a lower limb multi-body model.

Science.gov (United States)

El Habachi, Aimad; Moissenet, Florent; Duprey, Sonia; Cheze, Laurence; Dumas, Raphaël

2015-07-01

Sensitivity analysis is a typical part of biomechanical models evaluation. For lower limb multi-body models, sensitivity analyses have been mainly performed on musculoskeletal parameters, more rarely on the parameters of the joint models. This study deals with a global sensitivity analysis achieved on a lower limb multi-body model that introduces anatomical constraints at the ankle, tibiofemoral, and patellofemoral joints. The aim of the study was to take into account the uncertainty of parameters (e.g. 2.5 cm on the positions of the skin markers embedded in the segments, 5° on the orientation of hinge axis, 2.5 mm on the origin and insertion of ligaments) using statistical distributions and propagate it through a multi-body optimisation method used for the computation of joint kinematics from skin markers during gait. This will allow us to identify the most influential parameters on the minimum of the objective function of the multi-body optimisation (i.e. the sum of the squared distances between measured and model-determined skin marker positions) and on the joint angles and displacements. To quantify this influence, a Fourier-based algorithm of global sensitivity analysis coupled with a Latin hypercube sampling is used. This sensitivity analysis shows that some parameters of the motor constraints, that is to say the distances between measured and model-determined skin marker positions, and the kinematic constraints are highly influencing the joint kinematics obtained from the lower limb multi-body model, for example, positions of the skin markers embedded in the shank and pelvis, parameters of the patellofemoral hinge axis, and parameters of the ankle and tibiofemoral ligaments. The resulting standard deviations on the joint angles and displacements reach 36° and 12 mm. Therefore, personalisation, customisation or identification of these most sensitive parameters of the lower limb multi-body models may be considered as essential.

Data based identification and prediction of nonlinear and complex dynamical systems

Science.gov (United States)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical

Data based identification and prediction of nonlinear and complex dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Wen-Xu [School of Systems Science, Beijing Normal University, Beijing, 100875 (China); Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Lai, Ying-Cheng, E-mail: Ying-Cheng.Lai@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Grebogi, Celso [Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom)

2016-07-12

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear

Data based identification and prediction of nonlinear and complex dynamical systems

International Nuclear Information System (INIS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01