Temperature dependence of thermal vibrations in cubic ZnS, a comparison of anharmonic models
Accurate integrated intensities for the Bragg reflection of neutrons from a ZnS single crystal have been measured at temperatures between 285 and 1173 K. After correction for thermal diffuse scattering and extinction effects the data were interpreted with different models that allow anharmonic contributions to the temperature factor. Both the cumulant expansion and the one-particle potential (OPP) model with quasi-harmonic temperature dependence describe the data satisfactorily, although the Gruneisen parameter obtained in the OPP analysis differs greatly from the value calculated from known thermodynamic quantities. Predictions based on Matsubara's anharmonic formalism are not in accord with the behavior observed at the highest temperatures
Anharmonic Vibrational Dynamics of DNA Oligomers
Kühn, O; Krishnan, G M; Fidder, H; Heyne, K
2008-01-01
Combining two-color infared pump-probe spectroscopy and anharmonic force field calculations we characterize the anharmonic coupling patterns between fingerprint modes and the hydrogen-bonded symmetric NH$_2$ stretching vibration in adenine-thymine dA$_{20}$-dT$_{20}$ DNA oligomers. Specifically, it is shown that the anharmonic coupling between the NH$_2$ bending and the CO stretching vibration, both absorbing around 1665 cm-1, can be used to assign the NH$_2$ fundamental transition at 3215 cm-1 despite the broad background absorption of water.
A local anharmonic treatment of vibrations of methane
Arias Carrasco, José Miguel; Pérez Bernal, Francisco; A. Frank; Lemus Casillas, Renato; Bijker, R.
1996-01-01
The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm$^{-1}$ (and a r.m.s. deviation of 1.16 cm$^{-1}$).
Anharmonic collective excitation in a solvable model
We apply the time-dependent variational principle, the nuclear field theory, and the boson expansion method to the Lipkin model to discuss anharmonicities of collective vibrational excitations. It is shown that all of these approaches lead to the same anharmonicity to leading order in the number of particles. Comparison with the exact solution of the Lipkin model shows that these theories reproduce quite well
Anharmonic Decay of Vibrational States in Amorphous Silicon
Fabian, Jaroslav; Allen, Philip B.
1996-01-01
Anharmonic decay rates are calculated for a realistic atomic model of amorphous silicon. The results show that the vibrational states decay on picosecond timescales and follow the two-mode density of states, similar to crystalline silicon, but somewhat faster. Surprisingly little change occurs for localized states. These results disagree with a recent experiment.
Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials
Gottwald, Fabian; Kühn, Oliver
2016-01-01
The Caldeira-Leggett (CL) model, which describes a system bi-linearly coupled to a harmonic bath, has enjoyed popularity in condensed phase spectroscopy owing to its utmost simplicity. However, the applicability of the model to cases with anharmonic system potentials, as it is required for the description of realistic systems in solution, is questionable due to the presence of the invertibility problem [J. Phys. Chem. Lett., \\textbf{6}, 2722 (2015)] unless the system itself resembles the CL model form. This might well be the case at surfaces or in the solid regime, which we here confirm for a particular example of an iodine molecule in the atomic argon environment under high pressure. For this purpose we extend the recently proposed Fourier method for parameterizing linear generalized Langevin dynamics[J. Chem. Phys., \\textbf{142}, 244110 (2015)] to the non-linear case based on the CL model and perform an extensive error analysis. In order to judge on the applicability of this model in advance, we give handy ...
Anharmonicities in vibrational spectra of deformed nuclei discussed in a simple model
Some microscopic treatments of the nuclear vibrational spectra are analyzed in terms of a model allowing an exact solution for a many-body nucleon system interacting via pairing plus quadrupole force. The multi-phonon approach -exact diagonalization in the restricted space of 1, 2, 3, .. collective phonons- appears satisfactory for the few lowest lying vibrational Ksup(π)=0+ states in deformed nuclei. The non conservation of the number of particles and coupling between collective and non collective states seem to be main sources of the discrepancies, that occur for the higher states. On the other hand, the lowest order contributions suggested by nuclear field theory lead to serious disagreement as compared with the exact solutions
Effective harmonic oscillator description of anharmonic molecular vibrations
Tapta Kanchan Roy; M Durga Prasad
2009-09-01
The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
Analytic calculations of anharmonic infrared and Raman vibrational spectra.
Cornaton, Yann; Ringholm, Magnus; Louant, Orian; Ruud, Kenneth
2016-02-01
Using a recently developed recursive scheme for the calculation of high-order geometric derivatives of frequency-dependent molecular properties [Ringholm et al., J. Comp. Chem., 2014, 35, 622], we present the first analytic calculations of anharmonic infrared (IR) and Raman spectra including anharmonicity both in the vibrational frequencies and in the IR and Raman intensities. In the case of anharmonic corrections to the Raman intensities, this involves the calculation of fifth-order energy derivatives-that is, the third-order geometric derivatives of the frequency-dependent polarizability. The approach is applicable to both Hartree-Fock and Kohn-Sham density functional theory. Using generalized vibrational perturbation theory to second order, we have calculated the anharmonic infrared and Raman spectra of the non- and partially deuterated isotopomers of nitromethane, where the inclusion of anharmonic effects introduces combination and overtone bands that are observed in the experimental spectra. For the major features of the spectra, the inclusion of anharmonicities in the calculation of the vibrational frequencies is more important than anharmonic effects in the calculated infrared and Raman intensities. Using methanimine as a trial system, we demonstrate that the analytic approach avoids errors in the calculated spectra that may arise if numerical differentiation schemes are used. PMID:26784673
Solvent effect on the anharmonic vibrational frequencies in guanine-cytosine base pair
Bende, A.; Muntean, C. M.
2012-02-01
We present an ab initio study of the vibrational properties of cytosine and guanine in the Watson-Crick and Hoogsteen base pair configurations. The results are obtained by considering the DFT method together with the Polarizable Continuum Model (PCM) using PBE and B3PW91 exchange-correlation functionals and triple-ζ valence basis set. We investigate the importance of anharmonic corrections for the vibrational modes taking into account the solvent effect of the water environment. In particular, the unusual anharmonic effect of the H+ vibration in the case of the Hoogsteen base pair configuration is discussed.
Vibrational Spectra of the Azabenzenes Revisited: Anharmonic Force Fields
Boese, A D; Martin, Jan M.L.
2003-01-01
Anharmonic force fields and vibrational spectra of the azabenzene series (pyridine, pyridazine, pyrimidine, pyrazine, s-triazine, 1,2,3-triazine, 1,2,4-triazine and s-tetrazine) and benzene are obtained using density functional theory (DFT) with the B97-1 exchange-correlation functional and a triple-zeta plus double polarization (TZ2P) basis set. Overall, the fundamental frequencies computed by second-order rovibrational perturbation theory are in excellent agreement with experiment. The resolution of the presently calculated anharmonic spectra is such that they represent an extremely useful tool for the assignment and interpretation of the experimental spectra, especially where resonances are involved.
Probing anharmonic properties of nuclear surface vibration by heavy-ion fusion reactions
Takigawa, N.; Hagino, K.; Kuyucak, S
1997-01-01
Describing fusion reactions between ^{16}O and ^{154}Dy and, between ^{16}O and ^{144}Sm by the $sd-$ and $sdf-$ interacting boson model, we show that heavy-ion fusion reactions are strongly affected by anharmonic properties of nuclear surface vibrations and nuclear shape, and thus provide a powerful method to study details of nuclear structure and dynamics.
Mckenzie, R. L.
1976-01-01
A semiclassical model of the inelastic collision between a vibrationally excited anharmonic oscillator and a structureless atom is used to predict the variation of thermally averaged vibrational-translational rate coefficients with temperature and initial-state quantum number. Multiple oscillator states are included in a numerical solution for collinear encounters. The results are compared with CO-He experimental values for both ground and excited initial states using several simplified forms of the interaction potential. The numerical model is also used as a basis for evaluating several less complete, but analytic, models. Two computationally simple analytic approximations are found that successfully reproduce the numerical rate coefficients for a wide range of molecular properties and collision partners. Their limitations are identified, and the relative rates of multiple-quantum transitions from excited states are evaluated for several molecular types.
Mckenzie, R. L.
1975-01-01
A semiclassical model of the inelastic collision between a vibrationally excited anharmonic oscillator and a structureless atom was used to predict the variation of thermally averaged vibration-translation rate coefficients with temperature and initial-state quantum number. Multiple oscillator states were included in a numerical solution for collinear encounters. The results are compared with CO-He experimental values for both ground and excited initial states using several simplified forms of the interaction potential. The numerical model was also used as a basis for evaluating several less complete but analytic models. Two computationally simple analytic approximations were found that successfully reproduced the numerical rate coefficients for a wide range of molecular properties and collision partners. Their limitations were also identified. The relative rates of multiple-quantum transitions from excited states were evaluated for several molecular types.
Anharmonic thermal vibrations of be metal found in the MEM nuclear density map
A direct observation of the thermal vibrations of Be metal was performed by the Maximum Entropy Method (MEM) using neutron single crystal data. In the previous study, the existence of the small but significant cubic anharmonicity of Be has been found by the conventional least squares refinement of the observed structure factors [Larsen, Lehmann and Merisalo (1980) Acta Cryst. A36, 159-163]. In the present study, the same data were used for the MEM analysis which are comprised of 48 reflections up to sinθ/λ = 1.41A-1 in order to obtain the high resolution nuclear density of Be without using any thermal vibrational model. It was directly visible in the MEM map that not only the cubic terms but also quartic anharmonicities exist in the thermal vibrations of Be nuclei. In order to evaluate thermal parameters of Be including anharmonic terms quantitatively, the least squares refinement of the effective one-particle potential (OPP) parameters up to quartic term was carried out by using the MEM nuclear densities around atomic sites as the data set to be fitted. It was found that the present treatment has a great advantage to decide the most appropriate model of OPP by visually comparing the model with MEM density map. As a result of the least squares refinement, the anharmonic thermal parameters are obtained as α33 = -0.340(5)[eV/A3], α40 = 0, β20 = 9.89(1)[eV/A4] and γ00 = 0. No other anharmonic term was significant. (author)
On the benefits of localized modes in anharmonic vibrational calculations for small molecules.
Panek, Paweł T; Jacob, Christoph R
2016-04-28
Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challenges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field and L-VCI calculations [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the n-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the n-mode expansion of the potential energy surface or to approximate higher-order contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules and provides a possible avenue for enabling such accurate calculations also for larger molecules. PMID:27131535
On the benefits of localized modes in anharmonic vibrational calculations for small molecules
Panek, Paweł T.; Jacob, Christoph R.
2016-04-01
Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challenges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field and L-VCI calculations [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the n-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the n-mode expansion of the potential energy surface or to approximate higher-order contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules and provides a possible avenue for enabling such accurate calculations also for larger molecules.
Bloino, Julien; Biczysko, Malgorzata; Barone, Vincenzo
2015-12-10
The aim of this paper is 2-fold. First, we want to report the extension of our virtual multifrequency spectrometer (VMS) to anharmonic intensities for Raman optical activity (ROA) with the full inclusion of first- and second-order resonances for both frequencies and intensities in the framework of the generalized second-order vibrational perturbation theory (GVPT2) for all kinds of vibrational spectroscopies. Then, from a more general point of view, we want to present and validate the performance of VMS for the parallel analysis of different vibrational spectra for medium-sized molecules (IR, Raman, VCD, ROA) including both mechanical and electric/magnetic anharmonicity. For the well-known methyloxirane benchmark, careful selection of density functional, basis set, and resonance thresholds permitted us to reach qualitative and quantitative agreement between experimental and computed band positions and shapes. Next, the whole series of halogenated azetidinones is analyzed, showing that it is now possible to interpret different spectra in terms of mass, electronegativity, polarizability, and hindrance variation between closely related substituents, chiral spectroscopies being particular effective in this connection. PMID:26580121
Anharmonic contributions to the inversion vibration in 2-aminopyrimidine
McCarthy, W. J.; Lapinski, L.; Nowak, M. J.; Adamowicz, L.
1995-07-01
The out-of-plane vibrations of the amino group in 2-aminopyrimidine have large amplitudes, and cannot be properly described within the harmonic approximation. The normal mode analysis carried out at this level of approximation at the restricted Hartree-Fock level and at the second-order Møller-Plesset perturbation theory level failed to match the experimental transition frequency of ν≊200 cm-1 of the inversion vibration in this compound. In an effort to better understand this vibration motion, we went beyond the harmonic approximation. The inversion vibration was treated as being uncoupled from all other nuclear degrees of freedom. An internal coordinate (ω) was chosen whose displacement mimicked the out-of-plane distortion of the amino group during the inversion vibration. Electronic energy was calculated at the second-order Møller-Plesset perturbation theory level at selected values of ω to form a double-well curve describing a model potential within which the nuclei move during the vibration. This potential was incorporated into a one-dimensional Hamiltonian, and vibrational energy expectation values were variationally determined by utilizing the harmonic wavefunctions as the basis set. Two sets of calculations were performed: one in which the mirror plane of symmetry was preserved throughout the vibrational deformation limiting the internal coordinates to 17, and another in which the symmetry was unconstrained permitting description by 3N-6=30 internal coordinates. These calculations resulted in prediction of the v=0→v=1 transition energy of ν=130.1 cm-1 and ν=206.7 cm-1, respectively, reasonably matching the experimental value of ≊200 cm-1.
Anharmonic contributions to the inversion vibration in 2-aminopyrimidine
McCarthy, W.J. [Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States); Lapinski, L.; Nowak, M.J. [Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668, Warsaw (Poland); Adamowicz, L. [Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States)
1995-07-08
The out-of-plane vibrations of the amino group in 2-aminopyrimidine have large amplitudes, and cannot be properly described within the harmonic approximation. The normal mode analysis carried out at this level of approximation at the restricted Hartree--Fock level and at the second-order Moller--Plesset perturbation theory level failed to match the experimental transition frequency of {nu}{approx}200 cm{sup {minus}1} of the inversion vibration in this compound. In an effort to better understand this vibration motion, we went beyond the harmonic approximation. The inversion vibration was treated as being uncoupled from all other nuclear degrees of freedom. An internal coordinate ({omega}) was chosen whose displacement mimicked the out-of-plane distortion of the amino group during the inversion vibration. Electronic energy was calculated at the second-order Moller--Plesset perturbation theory level at selected values of {omega} to form a double-well curve describing a model potential within which the nuclei move during the vibration. This potential was incorporated into a one-dimensional Hamiltonian, and vibrational energy expectation values were variationally determined by utilizing the harmonic wavefunctions as the basis set. Two sets of calculations were performed: one in which the mirror plane of symmetry was preserved throughout the vibrational deformation limiting the internal coordinates to 17, and another in which the symmetry was unconstrained permitting description by 3{ital N}{minus}6=30 internal coordinates. These calculations resulted in prediction of the {ital v}=0{r_arrow}{ital v}=1 transition energy of {nu}=130.1 cm{sup {minus}1} and {nu}=206.7 cm{sup {minus}1}, respectively, reasonably matching the experimental value of {approx}200 cm{sup {minus}1}. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
A study of anharmonic al and nonlinear behaviours of vibrations of atomic nuclei
Double Giant Resonances, vibrational states in which a Giant Resonance is excited on top of another Giant Resonance, have been in the last years the object of many theories and studies. Whereas the measured energies and widths of these states agree with a theoretical predictions, the measured excitation cross sections on the other hand are almost always larger than the calculated ones. The standard theoretical approaches are based both on a harmonic approximation for the collective motion on the nucleus and on its linear response to an external field. In this work the influence of anharmonicities and non-linearities in the external field on the excitation of Double Giant Resonances are studied. First, an oscillator model and an extension of the Lipkin-Meshkow-Glick model are used to study the effects of anharmonicities and non-linearities on the excitation probabilities. The results show that these terms can influence the excitation probability of the second excited state in a significant way. Secondly, these exactly soluble schematic models are used to study some of the approximations made in microscopic calculations based on boson expansion methods and also some aspects on the time-dependent mean field approach. Finally, a microscopic calculation of the Coulomb excitation cross sections of Double Giant Resonances is presented for several nuclei. It is found that, for 208 Pb, the inclusion of anharmonicities and non-linearities and the consideration of many states that play a role in the excitation process give a satisfactory agreement between calculated and observed cross sections. (author)
The vibrational transition probability expressions for the forced Morse oscillator have been derived using the commutation relations of the anharmonic Boson operators. The formulation is based on the collinear collision model with the exponential repulsive potential in the framework of semiclassical collision dynamics. The sample calculation results for H2 + He collision system, where the anharmonicity is large, are in excellent agreement with those from an exact, numerical quantum mechanical study by Clark and Dickinson, using the reactance matrix. Our results,however, are markedly different from those of Ree, Kim, and Shin's in which they approximate the commutation operator Io as unity, the harmonic oscillator limit. We have concluded that the quantum number dependence in Io must be retained to get accurate vibrational transition probabilities for the Morse oscillator
Anharmonic calculation of vibration characteristics of the [F(HF)2]''- complex
Anharmonic vibrations of the [F(HF)2]- complex were calculated using second-order perturbation theory and the variational method. The interaction of the stretching vibrations of HF molecular fragments and stretching vibrations of the hydrogen bond, as well as the interaction between stretching and bending vibrations of HF was considered in the second method. A more accurate description of the high-frequency of stretching vibration of the HF molecules for the [F(HF)2]- system with a strong hydrogen bond is obtained by the variational method. (authors)
Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules
Rodriguez-Garcia, Valerie; Yagi, Kiyoshi; Hirao, Kimihiko; Iwata, Suehiro; Hirata, So
2006-07-01
Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X˜B12 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X˜B22 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.
Adiabatic coherent control in the anharmonic ion trap: Proposal for the vibrational two-qubit system
A method for encoding a multiqubit system into the quantized motional states of ion string in an anharmonic linear trap is proposed. Control over this system is achieved by applying oscillatory electric fields (rf) shaped optimally for desired state-to-state transitions. Anharmonicity of the vibrational spectrum of the system plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. The anharmonic trap architecture proposed earlier [Phys. Rev. A 83, 022305 (2011)] is explored here and the optimal control theory is used to derive pulses for a set of universal quantum gates. An accurate choice of pulse parameters allows deriving gates that are both accurate and simple. A practical realization of this approach seems to be within the reach of today's technology.
Brauer, B.; Gerber, R. B.; Kabeláč, Martin; Hobza, Pavel; Bakker, J. M.; Abo-Riziq, A.; Vries de, M. S.
2005-01-01
Roč. 109, - (2005), s. 6974-6984. ISSN 1089-5639 Grant ostatní: NSF(US) CHE-0244341 Institutional research plan: CEZ:AV0Z40550506 Keywords : nucleic acids base s * vibrational spectrum * frequencies anharmonicity Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.898, year: 2005
Anharmonic apical oxygen vibration in high-Tc superconductors
Using time-independent perturbation theory, a theoretical calculation has been performed for the transition temperatures for various high-Tc oxide compounds. It has been assumed that, three electrons are responsible for the superconducting current. Whereas two of these electrons form an exotic bound pair, the third electron causes perturbation H' = βx3 + γx4 with respect to apical oxygen vibrations. From the calculations, the transition temperatures are found to be realistic and comparable with experimental results. (author)
Structure, Anharmonic Vibrational Frequencies, and Intensities of NNHNN(+).
Yu, Qi; Bowman, Joel M; Fortenberry, Ryan C; Mancini, John S; Lee, Timothy J; Crawford, T Daniel; Klemperer, William; Francisco, Joseph S
2015-11-25
A semiglobal potential energy surface (PES) and quartic force field (QFF) based on fitting high-level electronic structure energies are presented to describe the structures and spectroscopic properties of NNHNN(+). The equilibrium structure of NNHNN(+) is linear with the proton equidistant between the two nitrogen groups and thus of D(∞h) symmetry. Vibrational second-order perturbation theory (VPT2) calculations based on the QFF fails to describe the proton "rattle" motion, i.e., the antisymmetric proton stretch, due to the very flat nature of PES around the global minimum but performs properly for other modes with sharper potential wells. Vibrational self-consistent field/virtual state configuration interaction (VSCF/VCI) calculations using a version of MULTIMODE without angular momentum terms successfully describe this motion and predict the fundamental to be at 759 cm(-1). This is in good agreement with the value of 746 cm(-1) from a fixed-node diffusion Monte Carlo calculation and the experimental Ar-tagged result of 743 cm(-1). Other VSCF/VCI energies are in good agreement with other experimentally reported ones. Both double-harmonic intensity and rigorous MULTIMODE intensity calculations show the proton-transfer fundamental has strong intensity. PMID:26529262
On the benefits of localized modes in anharmonic vibrational calculations for small molecules
Panek, Pawel T
2016-01-01
Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challanges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field (L-VSCF) and L-VCI calculations [P. T. Panek, Ch. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the $n$-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the $n$-mode expansion of the potential energy surface or to approximate ...
Jacobian elliptic wave solutions in an anharmonic molecular crystal model
Explicit Jacobian elliptic wave solutions are found in the anharmonic molecular crystal model for both the continuum limit and discrete modes. This class of wave solutions include the famous pulse-like and kink-like solitary modes. We would also like to report on the existence of some highly discrete staggered solitary wave modes not found in the continuum limit. (author). 9 refs, 1 fig
Anharmonicities and coherent vibrational dynamics of phosphate ions in bulk H2O.
Costard, Rene; Tyborski, Tobias; Fingerhut, Benjamin P
2015-11-28
Phosphates feature prominently in the energetics of metabolism and are important solvation sites of DNA and phospholipids. Here we investigate the ion H2PO4(-) in aqueous solution combining 2D IR spectroscopy of phosphate stretching vibrations in the range from 900-1300 cm(-1) with ab initio calculations and hybrid quantum-classical molecular dynamics based simulations of the non-linear signal. While the line shapes of diagonal peaks reveal ultrafast frequency fluctuations on a sub-100 fs timescale caused by the fluctuating hydration shell, an analysis of the diagonal and cross-peak frequency positions allows for extracting inter-mode couplings and anharmonicities of 5-10 cm(-1). The excitation with spectrally broad pulses generates a coherent superposition of symmetric and asymmetric PO2(-) stretching modes resulting in the observation of a quantum beat in aqueous solution. We follow its time evolution through the time-dependent amplitude and the shape of the cross peaks. The results provide a complete characterization of the H2PO4(-) vibrational Hamiltonian including fluctuations induced by the native water environment. PMID:26488541
Alparone, Andrea
2014-01-01
Infrared, Raman and electronic absorption spectra, electronic and vibrational (hyper)polarizabilities, of barbituric, 2-thiobarbituric and 2-selenobarbituric acids were studied in gas using ab initio and density functional theory levels. The vibrational spectra were computed using harmonic and anharmonic methods. Anharmonic contributions improve the agreement between calculated and available experimental wavenumbers, especially in the highest-energy spectral region (wavenumbers >1700 cm-1). Vibrational and electronic transitions potentially useful to identify the investigated compounds were explored. The electronic and vibrational hyperpolarizabilities for the IDRI nonlinear optical (NLO) process at the λ value of 790 nm were computed. Supported by spectroscopic results, electronic and vibrational polarizabilities and second-order hyperpolarizabilities increase progressively in the order barbituric acid acid acid. The seleno-derivative is predicted to be ca. three/four times more hyperpolarizable than the barbituric acid. The Se → O or Se → S substitutions can be practical strategies to enhances the NLO properties of barbituric and thiobarbituric acid-based materials.
Thermoelectric materials: The anharmonicity blacksmith
Heremans, Joseph P.
2015-12-01
Anharmonicity is a property of lattice vibrations governing how they interact and how well they conduct heat. Experiments on tin selenide, the most efficient thermoelectric material known, now provide a link between anharmonicity and electronic orbitals.
Krasnoshchekov, Sergey V; Craig, Norman C; Boopalachandran, Praveenkumar; Laane, Jaan; Stepanov, Nikolay F
2015-10-29
A quantum-mechanical (hybrid MP2/cc-pVTZ and CCSD(T)/cc-pVTZ) full quartic potential energy surface (PES) in rectilinear normal coordinates and the second-order operator canonical Van Vleck perturbation theory (CVPT2) are employed to predict the anharmonic vibrational spectra of s-trans- and s-gauche-butadiene (BDE). These predictions are used to interpret their infrared and Raman scattering spectra. New high-temperature Raman spectra in the gas phase are presented in support of assignments for the gauche conformer. The CVPT2 solution is based on a PES and electro-optical properties (EOP; dipole moment and polarizability) expanded in Taylor series. Higher terms than those routinely available from Gaussian09 software were calculated by numerical differentiation of quadratic force fields and EOP using the MP2/cc-pVTZ model. The integer coefficients of the polyad quantum numbers were derived for both conformers of BDE. Replacement of harmonic frequencies by their counterparts from the CCSD(T)/cc-pVTZ model significantly improved the agreement with experimental data for s-trans-BDE (root-mean-square deviation ≈ 5.5 cm(-1)). The accuracy in predicting the rather well-studied spectrum of fundamentals of s-trans-BDE assures good predictions of the spectrum of s-gauche-BDE. A nearly complete assignment of fundamentals was obtained for the gauche conformer. Many nonfundamental transitions of the BDE conformers were interpreted as well. The predictions of multiple Fermi resonances in the complex CH-stretching region correlate well with experiment. It is shown that solving a vibrational anharmonic problem through a numerical-analytic implementation of CVPT2 is a straightforward and computationally advantageous approach for medium-size molecules in comparison with the standard second-order vibrational perturbation theory (VPT2) based on analytic expressions. PMID:26437183
Tasinato, Nicola; Regini, Giorgia; Stoppa, Paolo; Pietropolli Charmet, Andrea; Gambi, Alberto
2012-06-01
Difluoromethane (CH(2)F(2), HFC-32) is a molecule used in refrigerant mixtures as a replacement of the more environmentally hazardous, ozone depleting, chlorofluorocarbons. On the other hand, presenting strong vibration-rotation bands in the 9 μm atmospheric window, it is a greenhouse gas which contributes to global warming. In the present work, the vibrational and ro-vibrational properties of CH(2)F(2), providing basic data for its atmospheric modeling, are studied in detail by coupling medium resolution Fourier transform infrared spectroscopy to high-level electronic structure ab initio calculations. Experimentally a full quantum assignment and accurate integrated absorption cross sections are obtained up to 5000 cm(-1). Ab initio calculations are carried out by using CCSD(T) theory and large basis sets of either the correlation consistent or atomic natural orbital hierarchies. By using vibrational perturbation theory to second order a complete set of vibrational and ro-vibrational parameters is derived from the ab initio quartic anharmonic force fields, which well compares with the spectroscopic constants retrieved experimentally. An excellent agreement between theory and experiment is achieved for vibrational energy levels and integrated absorption cross sections: transition frequencies up to four quanta of vibrational excitation are reproduced with a root mean square deviation (RMSD) of 7 cm(-1) while intensities are predicted within few km mol(-1) from the experiment. Basis set performances and core correlation effects are discussed throughout the paper. Particular attention is focused in the understanding of the anharmonic couplings which rule the vibrational dynamics of the |ν(1)>, |2ν(8)>, |2ν(2)> three levels interacting system. The reliability of the potential energy and dipole moment surfaces in reproducing the vibrational eigenvalues and intensities as well as in modeling the vibrational and ro-vibrational mixings over the whole 400-5000 cm(-1
Highlights: ► Halon 1113, potential ozone depleting gas, vibrational eigenstates and intensity. ► FT-IR experimental and theoretical study of chlorotrifluoroethene. ► Ab initio calculations at MP2 and CCSD(T) levels with cc-pVTZ and ANO basis sets. ► Equilibrium geometry and harmonic force field. ► Full CCSD(T) and hybrid anharmonic force fields. - Abstract: Halon 1113 (chlorotrifluoroethene), used in the synthesis of fluorocarbon-based polymers, has been recently detected in the atmosphere and it is a potential source of chlorine atoms. In this work, the vibrational properties of chlorotrifluoroethene are studied in the 125–5000 cm−1 region by coupling Fourier-transform infrared spectroscopy and high-level ab initio calculations. The vibrational analysis is performed over the whole spectral range and band intensities are obtained in the range 400–3100 cm−1. Ab initio calculations of the anharmonic force field are performed at the coupled cluster level of theory employing either cc-pVTZ or ANO basis sets. Vibration perturbation theory is applied to obtain spectroscopic parameters from the computed anharmonic force fields. The present results provide a solid interpretation of chlorotrifluoroethene vibrational spectrum, and they represent a significant reference for future studies on this molecule, being also the first published data on absorption cross sections and ab initio calculations.
Inclusion of the anharmonicity normal mode vibrations [i.e., the third and fourth (and higher) derivatives of a molecular Born-Oppenheimer potential energy surface] is necessary in order to theoretically reproduce experimental fundamental vibrational frequencies of a molecule. Although ab initio determinations of harmonic vibrational frequencies may give errors of only a few percent by the inclusion of electron correlation within a large basis set for small molecules, in general, molecular fundamental vibrational frequencies are more often available from high resolution vibration-rotation spectra. Recently developed analytic third derivatives methods for self-consistent-field (SCF) wavefunctions have made it possible to examine with previously unavailable accuracy and computational efficiency the anharmonic force fields of small molecules
The interesting features of phase transition in Rochelle Salt (RS) or C4H4O6NaK.4(H2O) i.e. the appearance of two Curie points Tsub(c1) (255 K) and Tsub(c2) (297 K) and large isotope effect on Tsub(c) are studied. On deuteration the lower Curie point shifts towards lower temperature and the upper Curie point towards the higher temperature, showing evidently the important role played by the hydrogen atoms in the ferroelectric behaviour of RS. A conclusion has finally been drawn from the present and previous investigations that both proton-lattice and phonon-phonon interactions play a vital role in the phase transition in hydrogen bonded ferroelectrics including KDP family and the present Rochelle Salt group. An estimation of the anharmonic contribution in the dynamic and static properties has also been found out for these crystals. (K.B.)
Highlights: ► UV, IR and hole-burning spectra of a tri-peptide Z-PLG-NH2 were measured in a jet. ► The laser desorption technique was used to evaporate the peptide. ► The conformers were detected but the population is mainly distributed to a single conformation. ► MD simulations and DFT calculations reproduced the IR spectrum except for NH stretch. ► Anharmonic vibrational analysis VQDPT reproduced the splitting of the NH stretch. - Abstract: The electronic excitation and infrared (IR) spectra of a capped tri-peptide, Z-PLG-NH2 (Z = benzyloxycarbonyl, P = Pro, L = Leu, G = Gly), were measured in the gas phase by using the laser desorption supersonic jet technique. By measuring an ultraviolet–ultraviolet hole burning spectrum, it was found that Z-PLG-NH2 has the maximum three conformers in the gas phase, but that the population is mainly distributed to a single conformation. Molecular dynamics simulations and density functional theory calculations well-reproduced the observed IR spectrum, except for splitting of the NH stretching bands by a β-turn structure that corresponds to a global minimum structure. Anharmonic vibrational analysis by vibrational quasi-degenerate perturbation theory (VQDPT) successfully reproduced the anharmonic splitting, and confirmed the assignments
Graphical abstract: The spectrum of the water dimer trapped in neon has been recorded and analysed up to 14,000 cm-1. Highlights: → Observation of the vibrational spectrum of the water dimer from the far infrared to the visible. → Assignment based on 18O/16O shift and on approximate values of anharmonicity coefficients. → Calculations in the framework of the second-order perturbation - resonance theory. - Abstract: The infrared spectrum of the water dimer trapped in solid neon has been recorded up to the visible by improving significantly the experimental technique used in a previous paper [Y. Bouteiller, J.P. Perchard, Chem. Phys. 305 (2004) 1]. A total of 22 intramolecular transitions of the proton donor (PD) and 23 of the proton acceptor (PA) are now identified and assigned on the basis of 16O/18O isotopic shifts and of realistic anharmonicity corrections. From an ab initio determination of the potential energy a perturbation-resonance treatment has been carried out for each polyad Pn, n = 2-8. Finally combinations of intra + intermolecular transitions were identified and assigned on the basis of calculated anharmonicity coefficients.
Reynolds, Anthony
Proton-coupled electron transfer model systems (PCET) are examined using polarization selective femtosecond infrared pump-probe spectroscopy to determine how the structural modes are coupled to the OH/OD stretching vibrational mode by monitoring low frequency oscillations in the OH/OD vibrational mode using pump-probe techniques. For all of the systems discussed in this dissertation, low frequency modes are anharmonically coupled to the OH/OD stretching vibration. The OH/OD stretching vibration discussed in this dissertation have complex and broad lineshapes in the infrared region (IR) that are difficult to decipher. A broadband IR (BBIR) source, when used as part of a third order nonlinear infrared pump-probe spectroscopy, gains access into the electronic ground state potential energy surface. This information reveals the molecular dynamics that give rise to the complex structure in an IR spectra. The BBIR used for these experiments is generated by focusing 800 nm/400 nm pulses into compressed air and is tunable from 2 -- 5 microns with a FWHM greater than 1200 wavenumbers. The BBIR is a crucial mid-IR source in subsequent chapters for examining the broad lineshapes of the OH/OD stretching mode, which often exceeds 200 wavenumbers. The coupling of low frequency structural modulations to hydrogen bonding dynamics in PCET systems is explored by using the OH/OD stretching vibration in CCl4 or CHCl3. Third order nonlinear ultrafast infrared pump-probe spectroscopy is used to gather information on the high frequency OH/OD stretching vibrational modes in the ground state such as vibrational relaxation time and anharmonic vibrational coupling to low frequency structural modulations. At least one anharmonically coupled low frequency mode between 120 and 250 wavenumbers has been observed in all systems. To better understand and visualize how the low frequency mode may contribute to the PCET chemistry, we calculated the fundamental frequencies and third order coupling
Anharmonic vibrations around a triaxial nuclear deformation “frozen” to γ = 30°
Buganu, Petrica, E-mail: buganu@theory.nipne.ro; Budaca, Radu [Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Str. Reactorului 30, RO-077125, POB-MG6, Bucharest-Magurele (Romania)
2015-12-07
The Davydov-Chaban Hamiltonian with a sextic oscillator potential for the variable β and γ fixed to 30° is exactly solved for the ground and β bands and approximately for the γ band. The model is called Z(4)-Sextic in connection with the already established Z(4) solution. The energy spectra, normalized to the energy of the first excited state, and several B(E2) transition probabilities, normalized to the B(E2) transition from the first excited state to the ground state, depend on a single parameter α. By varying α within a sufficiently large interval, a shape phase transition from an approximately spherical shape to a deformed one is evidenced.
Low-temperature vibrational anharmonicity of 151Eu in EuBa2Cu3O7-δ
The angular averaged mean-square displacement of 151Eu in EuBa2Cu3O7-δ was measured as a function of temperature by Moessbauer spectroscopy using the absorption area method. Large low-temperature anharmonicity was found; i.e. the adiabatic potential experienced by Eu3+ ions presents a 'wine-bottle bottom' shape with a flat region about 0.1 AA wide. Comparisons with other experimental results are made. (author)
Alcohol dimers - how much diagonal OH anharmonicity?
Kollipost, Franz; Papendorf, Kim; Lee, Yu-Fang; Lee, Yuan-Pern; Suhm, Martin A
2014-01-01
The OH bond of methanol, ethanol and t-butyl alcohol becomes more anharmonic upon hydrogen bonding and the infrared intensity ratio between the overtone and the fundamental transition of the bridging OH stretching mode decreases drastically. FTIR spectroscopy of supersonic slit jet expansions allows to quantify these effects for isolated alcohol dimers, enabling a direct comparison to anharmonic vibrational predictions. The diagonal anharmonicity increase amounts to 15-18%, growing with incre...
Kesharwani, Manoj K; Brauer, Brina; Martin, Jan M L
2015-03-01
We have obtained uniform frequency scaling factors λ(harm) (for harmonic frequencies), λ(fund) (for fundamentals), and λ(ZPVE) (for zero-point vibrational energies (ZPVEs)) for the Weigend-Ahlrichs and other selected basis sets for MP2, SCS-MP2, and a variety of DFT functionals including double hybrids. For selected levels of theory, we have also obtained scaling factors for true anharmonic fundamentals and ZPVEs obtained from quartic force fields. For harmonic frequencies, the double hybrids B2PLYP, B2GP-PLYP, and DSD-PBEP86 clearly yield the best performance at RMSD = 10-12 cm(-1) for def2-TZVP and larger basis sets, compared to 5 cm(-1) at the CCSD(T) basis set limit. For ZPVEs, again, the double hybrids are the best performers, reaching root-mean-square deviations (RMSDs) as low as 0.05 kcal/mol, but even mainstream functionals like B3LYP can get down to 0.10 kcal/mol. Explicitly anharmonic ZPVEs only are marginally more accurate. For fundamentals, however, simple uniform scaling is clearly inadequate. PMID:25296165
Exact solutions for anharmonic oscillators
Rigorous solutions for the one-dimensional quantum mechanical doubly anharmonic oscillator in the form of definite integrals, already presented (Flessas. Phys. Lett. 81 A: 17 (1981)), are here generalised to anharmonic interactions and their interest for models of the charmonium system considered. (U.K.)
Generation of discrete superpositions of coherent states in the anharmonic oscillator model
Miranowicz, A; Kielich, S; 10.1088/0954-8998/2/3/006
2011-01-01
The problem of generating discrete superpositions of coherent states in the process of light propagation through a nonlinear Kerr medium, which is modelled by the anharmonic oscillator, is discussed. It is shown that under an appropriate choice of the length (time) of the medium the superpositions with both even and odd numbers of coherent states can appear. Analytical formulae for such superpositions with a few components are given explicitly. General rules governing the process of generating discrete superpositions of coherent states are also given. The maximum number of well distinguished states that can be obtained for a given number of initial photons is estimated. The quasiprobability distribution $Q(\\alpha,\\alpha^*,t)$ representing the superposition states is illustrated graphically, showing regular structures when the component states are well separated.
The vibration states of the Skyrme model
In the paper an algebraic method for the construction of the collective Hamiltonian of the Skyrme model is treated. The Skyrme model has some phenomenological success in describing the static properties of nucleon and their interactions. The vibration spectra in the framework of the subgroup SU(5) have been discussed. Exploiting the related symmetry group it is possible to obtain the simple analytic expressions for the eigenvalues of boson Hamiltonian and for intraband transition matrix elements as well as for side feeding from one band to the other. Back-bending occurs naturally as the crossing of two bands and it can be predicted from the relative spacing of the low excited states. The algebraic properties of collective variables lead to a new quantum number N which implies in the boson representation the maximum number of phonons contained in vibrational states. Because the boson-boson interaction in SU(5) invariant Hamiltonian splits the degeneracy of the multiplets, this limits describes an anharmonic vibrator. It should be noted, we describe finite dimensional system in contrast with the geometrical description in which N→∞. It is worth noting that the knowledge of the invariance properties of Hamiltonian provides directly a solution to the eigenvalue problem. The transformation into intrinsic frame of reference has been performed explicitly. Thus, the formulae for the potential energy, the quadrupole moments are obtained as well as the spectroscopic factors for 0+ state excitation in the two nucleon transfer reactions. The proposed collective Hamiltonian is applied to the transformational nuclei Sm, Gd and Dy. The agreement between the experimental data and the theoretical description is good
Model Indepedent Vibration Control
Yuan, Jing
2010-01-01
A NMIFC system is proposed for broadband vibration control. It has two important features. Feature F1 is that the NMIFC is stable without introducing any invasive effects, such as probing signals or controller perturbations, into the vibration system; feature F2 is
Energy localization in an anharmonic twist-opening model of DNA dynamics.
Tabi, Conrad Bertrand
2010-10-20
Energy localization is investigated in the framework of the anharmonic twist-opening model proposed by Cocco and Monasson. This model includes the coupling between opening and twist that result from the helicoidal geometry of B-DNA. I first reduce the corresponding two-component model to its amplitude equations, which have the form of coupled discrete nonlinear Schrödinger (DNLS) equations, and I perform the linear stability analysis of the plane waves, solutions of the coupled DNLS equations. It is shown that the stability criterion deeply depends on the stiffness of the molecule. Numerical simulations are carried out in order to verify analytical predictions. It results that increasing the value of the molecule stiffness makes the energy patterns long-lived and highly localized. This can be used to explain the way enzymes concentrate energy on specific sequences of DNA for the base-pairs to be broken. The role of those enzymes could therefore be to increase the stiffness of closed regions of DNA at the boundaries of an open state. PMID:21386590
Anharmonic modeling of the conformation-specific IR spectra of ethyl, n-propyl, and n-butylbenzene
Tabor, Daniel P.; Hewett, Daniel M.; Bocklitz, Sebastian; Korn, Joseph A.; Tomaine, Anthony J.; Ghosh, Arun K.; Zwier, Timothy S.; Sibert, Edwin L.
2016-06-01
Conformation-specific UV-IR double resonance spectra are presented for ethyl, n-propyl, and n-butylbenzene. With the aid of a local mode Hamiltonian that includes the effects of stretch-scissor Fermi resonance, the spectra can be accurately modeled for specific conformers. These molecules allow for further development of a first principles method for calculating alkyl stretch spectra. Across all chain lengths, certain dihedral patterns impart particular spectral motifs at the quadratic level. However, the anharmonic contributions are consistent from molecule to molecule and conformer to conformer. This transferability of anharmonicities allows for the Hamiltonian to be constructed from only a harmonic frequency calculation, reducing the cost of the model. The phenyl ring alters the frequencies of the CH2 stretches by about 15 cm-1 compared to their n-alkane counterparts in trans configurations. Conformational changes in the chain can lead to shifts in frequency of up to 30 cm-1.
Are giant resonances harmonic vibrations?
Giant resonances are understood as the first quantum of collective vibrations. The non-linear response of a quantum anharmonic oscillator is investigated as a model for the excitation of giant resonances in heavy ion collisions. It is shown that the introduction of small anharmonicities and non-linearities can double the predicted cross section for the excitation of the two-phonon states. (R.P.)
Langevin model of the temperature and hydration dependence of protein vibrational dynamics.
Moritsugu, Kei; Smith, Jeremy C
2005-06-23
The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes. PMID:16852503
Spontaneous and stimulated Raman studies of vibrational dephasing in condensed phases
Vibrational dephasing in condensed phases is studied from both a theoretical and experimental standpoint. A theory is presented which describes the dynamics of motional or exchange processes in weakly perturbed systems. This general formalism, which has been previously used to describe motional narrowing in magnetic resonance, is applied to vibrational spectroscopy. The model treats the case of a high frequency vibration anharmonically coupled to a low-frequency vibration. Intermolecular exchange of low frequency vibrational quanta results in a temperature dependent broadening and frequency shift of the high frequency vibration. Analysis of experimental data by this model yields both the exchange rates and the anharmonic couplings
Vibration absorber modeling for handheld machine tool
Abdullah, Mohd Azman; Mustafa, Mohd Muhyiddin; Jamil, Jazli Firdaus; Salim, Mohd Azli; Ramli, Faiz Redza
2015-05-01
Handheld machine tools produce continuous vibration to the users during operation. This vibration causes harmful effects to the health of users for repeated operations in a long period of time. In this paper, a dynamic vibration absorber (DVA) is designed and modeled to reduce the vibration generated by the handheld machine tool. Several designs and models of vibration absorbers with various stiffness properties are simulated, tested and optimized in order to diminish the vibration. Ordinary differential equation is used to derive and formulate the vibration phenomena in the machine tool with and without the DVA. The final transfer function of the DVA is later analyzed using commercial available mathematical software. The DVA with optimum properties of mass and stiffness is developed and applied on the actual handheld machine tool. The performance of the DVA is experimentally tested and validated by the final result of vibration reduction.
Anharmonicity and hydrogen bonding in electrooptic sucrose crystal
Szostak, M. M.; Giermańska, J.
1990-03-01
The polarized absorption spectra of the sucrose crystal in the 5300 - 7300 cm -1 region have been measured. The assignments of all the eight OH stretching overtones are proposed and their mechanical anharmonicities are estimated. The discrepancies from the oriented gas model (OGM) in the observed relative band intensities, especially of the -CH vibrations, are assumed to be connected with vibronic couplings enhanced by the helical arrangement of molecules joined by hydrogen bondings. It seems that this kind of interactions might be important for the second harmonic generation (SHG) by the sucrose crystal.
Quantum and anharmonic effects are investigated in H2-Li+-benzene, a model for hydrogen adsorption in metal-organic frameworks and carbon-based materials. Three- and 8-dimensional quantum diffusion Monte Carlo (QDMC) and rigid-body diffusion Monte Carlo (RBDMC) simulations are performed on potential energy surfaces interpolated from electronic structure calculations at the M05-2X/6-31+G(d,p) and M05-2X/6-311+G(2df,p) levels of theory using a three-dimensional spline or a modified Shepard interpolation. These calculations investigate the intermolecular interactions in this system, with three- and 8-dimensional 0 K H2 binding enthalpy estimates, ΔHbind (0 K), being 16.5 kJ mol−1 and 12.4 kJ mol−1, respectively: 0.1 and 0.6 kJ mol−1 higher than harmonic values. Zero-point energy effects are 35% of the value of ΔHbind (0 K) at M05-2X/6-311+G(2df,p) and cannot be neglected; uncorrected electronic binding energies overestimate ΔHbind (0 K) by at least 6 kJ mol−1. Harmonic intermolecular binding enthalpies can be corrected by treating the H2 “helicopter” and “ferris wheel” rotations as free and hindered rotations, respectively. These simple corrections yield results within 2% of the 8-dimensional anharmonic calculations. Nuclear ground state probability density histograms obtained from the QDMC and RBDMC simulations indicate the H2 molecule is delocalized above the Li+-benzene system at 0 K
We investigate a chain of oscillators with anharmonic on-site potentials, with long range interparticle interactions, and coupled both to external and internal stochastic thermal reservoirs of Ornstein–Uhlenbeck type. We develop an integral representation, a' la Feynman–Kac, for the correlations and the heat current. We assume the approximation of discrete times in the integral formalism (together with a simplification in a subdominant part of the harmonic interaction) and develop a suitable polymer expansion for the model. In the regime of strong anharmonicity, strong harmonic pinning, and for the interparticle interaction with integrable polynomial decay, we prove the convergence of the polymer expansion uniformly in volume (number of sites and time). We also show that the two-point correlation decays in space such as the interparticle interaction. The existence of a convergent polymer expansion is of practical interest: it establishes a rigorous support for a perturbative analysis of the heat flow problem and for the computation of the thermal conductivity in related anharmonic crystals, including those with inhomogeneous potentials and long range interparticle interactions. To show the usefulness and trustworthiness of our approach, we compute the thermal conductivity of a specific anharmonic chain, and make a comparison with related numerical results presented in the literature. (paper)
Kabeláč, Martin; Hobza, Pavel; Špirko, Vladimír
2009-01-01
Roč. 11, č. 20 (2009), s. 3921-3926. ISSN 1463-9076 R&D Projects: GA AV ČR IAA400550511; GA AV ČR IAA400550808; GA ČR GA203/06/0420; GA MŠk LC512 Grant ostatní: GA ČR(CZ) GA203/06/0738 Institutional research plan: CEZ:AV0Z40550506 Keywords : tryptophan * anharmonicity * harmonic frequencies * ab initio Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 4.116, year: 2009
In this work the mass spectra for some of the baryon resonances of the particle data group with three and four star status are obtained, and a unified description of the ground states and excitation spectra of baryons are provided in the framework of a non-relativistic potential model. For this goal we have analytically solved the radial Schroedinger equation for three identical interacting particles with the anharmonic potential by using the Ansatz method and then we have calculated the baryon resonances spectrum by using the Goursey Radicati mass formula (GR) and with generalized Goursey Radicati mass formula (GGR). The results of our model show that the calculated masses of baryon resonances by using the generalized Goursey Radicati mass formula are found to be in good agreement with the tabulations of the Particle Data Group. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiples up to 3 GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon. (authors)
Zaleśny, Robert; Góra, Robert W; Luis, Josep M; Bartkowiak, Wojciech
2015-09-14
The influence of the spatial confinement on the electronic and vibrational contributions to longitudinal electric-dipole properties of model linear molecules including HCN, HCCH and CO2 is discussed. The effect of confinement is represented by two-dimensional harmonic oscillator potential of cylindrical symmetry, which mimics the key features of various types of trapping environments like, for instance, nanotubes or quantum well wires. Our results indicate that in general both (electronic and vibrational) contributions to (hyper)polarizabilities diminish upon spatial confinement. However, since the electronic term is particularly affected, the relative importance of vibrational contributions is larger for confined species. This effect increases also with the degree of anharmonicity of vibrational motion. PMID:26247540
An overview is given on anharmonic lattice vibrations originating from structural instabilities. The transverse vibrations of the chain oxygens in YBa2Cu3O7 are found to be only moderately anharmonic. Measurements of the phonon linewidths in the Cu-O bond stretching vibrations strongly support recent calculations of the electron-phonon coupling. Results are presented on superconductivity-induced frequency shifts at short wavelengths. 20 refs., 15 figs
Anharmonic force fields and thermodynamic functions using density functional theory
Boese, A. Daniel; Klopper, Wim; Martin, Jan M. L.
2004-01-01
The very good performance of modern density functional theory for molecular geometries and harmonic vibrational frequencies has been well established. We investigate the performance of density functional theory (DFT) for quartic force fields, vibrational anharmonicity and rotation-vibration coupling constants, and thermodynamic functions beyond the RRHO (rigid rotor-harmonic oscillator) approximation of a number of small polyatomic molecules. Convergence in terms of basis set, integration gri...
Vibrational Spectroscopy of Methyl benzoate
Maiti, Kiran Sankar
2014-01-01
Methyl benzoate (MB) is studied as a model compound for the development of new IR pulse schemes with possible applicability to biomolecules. Anharmonic vibrational modes of MB are calculated on different level (MP2, SCS, CCSD(T) with varying basis sets) ab-initio PESs using the vibrational self-consistent field (VSCF) method and its correlation corrected extensions. Dual level schemes, combining different quantum chemical methods for diagonal and coupling potentials, are systematically studied and applied successfully to reduce the computational cost. Isotopic substitution of {\\beta}-hydrogen by deuterium is studied to obtain a better understanding of the molecular vibrational coupling topology.
Anomalous dynamical scaling in anharmonic chains and plasma models with multi-particle collisions
Di Cintio, Pierfrancesco; Bufferand, Hugo; Ciraolo, Guido; Lepri, Stefano; Straka, Mika J
2015-01-01
We study the anomalous dynamical scaling of equilibrium correlations in one dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through the Multi-Particle Collision dynamics. For both models -that admit three conservation laws- by means of detailed numerical simulations we verify the predictions of Nonlinear Fluctuating Hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite of this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.
Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions
Di Cintio, Pierfrancesco; Livi, Roberto; Bufferand, Hugo; Ciraolo, Guido; Lepri, Stefano; Straka, Mika J.
2015-12-01
We study the anomalous dynamical scaling of equilibrium correlations in one-dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through multiparticle collision dynamics. For both models—that admit three conservation laws—by means of detailed numerical simulations we verify the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.
The origin of phonon anharmonicity in MgB{sub 2} and related compounds
Boeri, L [INFM Center for Statistical Mechanics and Complexity and Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale A. Moro 2, 00185 Rome (Italy); Bachelet, G B [INFM Center for Statistical Mechanics and Complexity and Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale A. Moro 2, 00185 Rome (Italy); Cappelluti, E [INFM Center for Statistical Mechanics and Complexity and Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale A. Moro 2, 00185 Rome (Italy); Pietronero, L [INFM Center for Statistical Mechanics and Complexity and Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale A. Moro 2, 00185 Rome (Italy)
2003-02-01
The recent discovery of a superconducting transition at 39 K in MgB{sub 2} - made of alternating Mg and graphene-like B planes - has raised great interest, for both its technological and theoretical implications. It was clear since the very beginning that the properties of this material are related to an anomalous coupling between the charge carriers in the {sigma} bands - due to in-plane bonds between Boron atoms - and the phonon mode (E{sub 2g}) which involves in-plane vibrations of the B ions. Theoretical studies have thus been focused on the search for possible anomalies in the e-ph coupling: one of the first results was the discovery that the E{sub 2g} phonon is highly anharmonic, but the connection between anharmonicity and T{sub c} in this material is still a controversial point. We first present a detailed first-principles study of the E{sub 2g} phonon anharmonicity in MgB{sub 2} and analogous compounds which are not superconducting, AlB{sub 2} and graphite, and in a hypothetical hole-doped graphite (C{sup 2+}{sub 2}); we then introduce an analytical model which allows us to relate the onset of anharmonicity with the small Fermi energy of the carriers in {sigma} bands. Our study suggests a possible relation between anharmonicity and non-adiabaticity; non-adiabatic effects, which can lead to a sensible increase of T{sub c} with respect to values predicted by conventional theory, become in fact relevant when phonon frequencies are comparable to electronic energy scales.
E x circle ε Jahn-Teller anharmonic coupling for an octahedral system
The coupling between doubly degenerate electronic states and doubly degenerate vibrations is analyzed for an octahedral system on the basis of the introduction of an anharmonic Morse potential for the vibronic part. The vibrations are described by anharmonic coherent states and their linear coupling with the electronic states is considered. The matrix elements of the vibronic interaction are built and the energy levels corresponding to the interaction Hamiltonian are derived. (authors)
Modelling chaotic vibrations using NASTRAN
Sheerer, T. J.
1993-09-01
Due to the unavailability and, later, prohibitive cost of the computational power required, many phenomena in nonlinear dynamic systems have in the past been addressed in terms of linear systems. Linear systems respond to periodic inputs with periodic outputs, and may be characterized in the time domain or in the frequency domain as convenient. Reduction to the frequency domain is frequently desireable to reduce the amount of computation required for solution. Nonlinear systems are only soluble in the time domain, and may exhibit a time history which is extremely sensitive to initial conditions. Such systems are termed chaotic. Dynamic buckling, aeroelasticity, fatigue analysis, control systems and electromechanical actuators are among the areas where chaotic vibrations have been observed. Direct transient analysis over a long time period presents a ready means of simulating the behavior of self-excited or externally excited nonlinear systems for a range of experimental parameters, either to characterize chaotic behavior for development of load spectra, or to define its envelope and preclude its occurrence.
Stoppa, Paolo; Tasinato, Nicola; Baldacci, Agostino; Pietropolli Charmet, Andrea; Giorgianni, Santi; Tamassia, Filippo; Cané, Elisabetta; Villa, Mattia
2016-05-01
The FTIR spectra of CH2F2 have been investigated in a region of atmospheric interest (1000-1300 cm-1) where four fundamentals ν3, ν5, ν7 and ν9 occur. These vibrations perturb each other by different Coriolis interactions and the forbidden ν5 borrows intensity from the neighboring levels. Furthermore, the v4=2 state has been found to interact with the v3=1 and v9=1 states by anharmonic and c-type Coriolis resonances, respectively. The spectral analysis resulted in the assignment of about 7500 rovibrational transitions which have been simultaneously fitted, together with microwave data available in literature (Hirota E. J Mol Spectrosc 1978; 69: 409-420) [15] using the Watson's A-reduction Hamiltonian in the Ir representation and the relevant perturbation operators. The model employed includes eight types of resonances within the pentad ν3/ν5/ν7/ν9/2ν4. A set of spectroscopic constants for the four fundamentals as well as parameters for the v4=2 state and eighteen coupling terms have been determined. The simulations performed in different spectral regions well reproduce the experimental data.
Morgan, Sarah E; Chin, Alex W
2016-01-01
Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.
Information criteria and selection of vibration models.
Ruzek, Michal; Guyader, Jean-Louis; Pézerat, Charles
2014-12-01
This paper presents a method of determining an appropriate equation of motion of two-dimensional plane structures like membranes and plates from vibration response measurements. The local steady-state vibration field is used as input for the inverse problem that approximately determines the dispersion curve of the structure. This dispersion curve is then statistically treated with Akaike information criterion (AIC), which compares the experimentally measured curve to several candidate models (equations of motion). The model with the lowest AIC value is then chosen, and the utility of other models can also be assessed. This method is applied to three experimental case studies: A red cedar wood plate for musical instruments, a thick paper subjected to unknown membrane tension, and a thick composite sandwich panel. These three cases give three different situations of a model selection. PMID:25480053
Graphical abstract: Schematic diagram of a bent triatomic molecule, depicting the atom numbering, and molecular axis system. An algebraic approach to perform global rovibrational analysis is presented. Highlights: ► Novel approach for a global rovibrational analysis of polyatomic molecules spectra. ► One-dimensional vibron model limit combined with rotational degrees of freedom. ► Phase space Hamiltonian written in terms of anharmonic ladder operators. ► Algebraic calculations performed with a symmetry-adapted rovibrational basis. ► Description of the rovibrational spectrum of H2Se in the ground electronic state. - Abstract: An algebraic approach to perform global rovibrational analysis of molecular spectra is presented. The approach combines the one-dimensional limit of the vibron model with rotational degrees of freedom. The model is based on the expression of the phase space Hamiltonian in terms of anharmonic ladder operators and the use of a symmetry-adapted basis set given by the linear combination of products of local vibrational and rotational wavefunctions. As an example we model the rovibrational spectra of a bent triatomic molecule, providing a global analysis for vibrational bands up to polyad 12 and Jmax = 5 of Hydrogen Selenide (H2Se). Satisfactory fits of vibrational and rovibrational energies are obtained. A prediction of 2579 rovibrational energies up to J ⩽ 5 and polyad 12 for the 140 lowest vibrational bands is also obtained. A possible extension of the model to reach spectroscopic quality results in larger molecular systems is also given.
Monitoring Vibration of A Model of Rotating Machine
Arko Djajadi
2012-03-01
Full Text Available Mechanical movement or motion of a rotating machine normally causes additional vibration. A vibration sensing device must be added to constantly monitor vibration level of the system having a rotating machine, since the vibration frequency and amplitude cannot be measured quantitatively by only sight or touch. If the vibration signals from the machine have a lot of noise, there are possibilities that the rotating machine has defects that can lead to failure. In this experimental research project, a vibration structure is constructed in a scaled model to simulate vibration and to monitor system performance in term of vibration level in case of rotation with balanced and unbalanced condition. In this scaled model, the output signal of the vibration sensor is processed in a microcontroller and then transferred to a computer via a serial communication medium, and plotted on the screen with data plotter software developed using C language. The signal waveform of the vibration is displayed to allow further analysis of the vibration. Vibration level monitor can be set in the microcontroller to allow shutdown of the rotating machine in case of excessive vibration to protect the rotating machine from further damage. Experiment results show the agreement with theory that unbalance condition on a rotating machine can lead to larger vibration amplitude compared to balance condition. Adding and reducing the mass for balancing can be performed to obtain lower vibration level.
Global modeling of vibration-rotation spectra of the acetylene molecule
Lyulin, O. M.; Perevalov, V. I.
2016-07-01
The global modeling of both line positions and intensities of the acetylene molecule in the 50-9900 cm-1 region has been performed using the effective operators approach. The parameters of the polyad model of effective Hamiltonian have been fitted to the line positions collected from the literature. The used polyad model of effective Hamiltonian takes into account the centrifugal distortion, rotational and vibrational ℓ-doubling terms and both anharmonic and Coriolis resonance interaction operators arising due to the approximate relations between the harmonic frequencies: ω1≈ω3≈5ω4≈5ω5 and ω2≈3ω4≈3ω5. The dimensionless weighted standard deviation of the fit is 2.8. The fitted set of 237 effective Hamiltonian parameters allowed reproducing 24,991 measured line positions of 494 bands with a root mean squares deviation 0.0037 cm-1. The eigenfunctions of the effective Hamiltonian corresponding to the fitted set of parameters were used to fit the observed line intensities collected from the literature for 15 series of transitions: ΔP = 0-13,15, where P=5V1+5V3 +3V2+V4+V5 is the polyad number (Vi are the principal vibrational quantum numbers). The fitted sets of the effective dipole moment parameters reproduce the observed line intensities within their experimental uncertainties 2-20%.
Jacobs, M. H.; Van Den Berg, A. P.
2013-12-01
Thermodynamic databases are indispensable tools in materials science and mineral physics to derive thermodynamic properties in regions of pressure-temperature-composition space for which experimental data are not available or scant. Because the amount of phases and substances in a database is arbitrarily large, thermodynamic formalisms coupled to these databases are often kept as simple as possible to sustain computational efficiency. Although formalisms based on parameterizations of 1 bar thermodynamic data, commonly used in Calphad methodology, meet this requirement, physically unrealistic behavior in properties hamper the application in the pressure regime prevailing in the Earth's lower mantle. The application becomes especially cumbersome when they are applied to planetary mantles of massive super earth exoplanets or in the development of pressure scales, where Hugoniot data at extreme conditions are involved. Methods based on the Mie-Grüneisen-Debye formalism have the advantage that physically unrealistic behavior in thermodynamic properties is absent, but due to the simple construction of the vibrational density of states (VDoS), they lack engineering precision in the low-pressure regime, especially at 1 bar pressure, hampering application of databases incorporating such formalism to industrial processes. To obtain a method that is generally applicable in the complete stability range of a material, we developed a method based on an alternative use of Kieffer's lattice vibrational formalism. The method requires experimental data to constrain the model parameters and is therefore semi-empirical. It has the advantage that microscopic properties for substances, such as the VDoS, Grüneisen parameters and electronic and static lattice properties resulting from present-day ab-initio methods can be incorporated to constrain a thermodynamic analysis of experimental data. It produces results free from physically unrealistic behavior at high pressure and temperature
Takács, Gergely
2012-01-01
Real-time model predictive controller (MPC) implementation in active vibration control (AVC) is often rendered difficult by fast sampling speeds and extensive actuator-deformation asymmetry. If the control of lightly damped mechanical structures is assumed, the region of attraction containing the set of allowable initial conditions requires a large prediction horizon, making the already computationally demanding on-line process even more complex. Model Predictive Vibration Control provides insight into the predictive control of lightly damped vibrating structures by exploring computationally efficient algorithms which are capable of low frequency vibration control with guaranteed stability and constraint feasibility. In addition to a theoretical primer on active vibration damping and model predictive control, Model Predictive Vibration Control provides a guide through the necessary steps in understanding the founding ideas of predictive control applied in AVC such as: · the implementation of ...
Nonlinear (Anharmonic Casimir Oscillator
Habibollah Razmi
2011-01-01
Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.
Studying and Modeling Vibration Transducers and Accelerometers
Katalin Ágoston
2010-12-01
Full Text Available This paper presents types and operating mode of vibration sensors. Piezoelectric sensing elements are often used in accelerometers. It will be investigate the structure and transfer function of the seismic mass type sensing element. The article presents how the piezoelectric sensing element works and how can be modeled with an electronic circuit. The transfer functions of the electronic circuit models are studied in Matlab and the results are presented. It will be presented the influence of the seismic mass on the accelerometer’s working frequency domain.
Modelling the vibration of tyre sidewalls
Graham, W. R.
2013-10-01
The dynamical behaviour of the sidewall has an important influence on tyre vibration characteristics. Nonetheless, it remains crudely represented in many existing models. The current work considers a geometrically accurate, two-dimensional, sidewall description, with a view to identifying potential shortcomings in the approximate formulations and identifying the physical characteristics that must be accounted for. First, the mean stress state under pressurisation and centrifugal loading is investigated. Finite-Element calculations show that, while the loaded sidewall shape remains close to a toroid, its in-plane tensions differ appreciably from the associated analytical solution. This is largely due to the inability of the anisotropic sidewall material to sustain significant azimuthal stress. An approximate analysis, based on the meridional tension alone, is therefore developed, and shown to yield accurate predictions. In conjunction with a set of formulae for the ‘engineering constants’ of the sidewall material, the approximate solutions provide a straightforward and efficient means of determining the base state for the vibration analysis. The latter is implemented via a ‘waveguide’ discretisation of a variational formulation. Its results show that, while the full geometrical description is necessary for a complete and reliable characterisation of the sidewall's vibrational properties, a one-dimensional approximation will often be satisfactory in practice. Meridional thickness variations only become important at higher frequencies (above 500 Hz for the example considered here), and rotational inertia effects appear to be minor at practical vehicle speeds.
Ceausu-Velcescu, A.; Pracna, Petr
2012-01-01
Roč. 275, č. 276 (2012), s. 41-47. ISSN 0022-2852 Institutional support: RVO:61388955 Keywords : deuterated fluoroform * anharmonic * coriolis Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.670, year: 2012
A shell model for tyre belt vibrations
Lecomte, C.; Graham, W. R.; Dale, M.
2010-05-01
We present a new formulation for the prediction of tyre belt vibrations in the frequency range 0-500 Hz. Our representation includes the effects of belt width, curvature and anisotropy, and also explicitly models the tyre sidewalls. Many of the associated numerical parameters are fixed by physical considerations; the remainder require empirical input. A systematic and general approach to this problem is developed, and illustrated for the specific example of a Goodyear Wrangler tyre. The resulting predictions for the radial response to radial forcing show good correspondence with experiment up to 300 Hz, and satisfactory agreement up to 1 kHz.
A quantum model of a heterogeneous system consisting of a mixture of isotopes adsorbed on a solid surface and subjected to laser radiation is presented. The model system is described by a total Hamiltonian including direct and indirect (surface-phonon-mediated) couplings. The equations of motion are derived in the Heisenberg--Markovian picture in which the many-body effects of the surface phonon modes and the adspecies are reduced to an overall broadening (damping factor) given by the sum of the energy (T1) and phase (T 2) relaxations. The effects of the dephasing and anharmonicity on the average excitation are investigated. The ''bistability'' feature with a red-shifted optimal detuning is discussed in terms of the solution of a cubic equation. A diagonalization procedure is presented in a new basis which reveals the effects of the coupling strength, the frequency difference, and the level width of the isotopes on the total steady-state excitation, which in turn reflects the surface spectrum of the model system. Finally, the isotope selectivity given by the numerical results of the time-integrated excitation is discussed. It is shown that the optimal detuning for a weak coupling strength is further red-shifted for a strong isotopic coupling strength. Finally, energy feedback effects of the bath modes on the excitations of the active modes are investigated by combining a quantum excitation equation and a classical heat diffusion equation
Fermi resonance-algebraic model for molecular vibrational spectra
侯喜文; 董世海; 谢汨; 马中骐
1999-01-01
A Fermi resonance-algebraic model is proposed for molecular vibrations, where a U(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent molecule XY2 and a molecule XY3 is successfully applied to fitting the recently observed vibrational spectrum of the water molecule and arsine (AsH3), respectively, and the results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method to describe molecular vibrations with small standard deviations.
Low Dimensional Models of Shell Vibrations. Parametrically Excited Vibrations of Cylinder Shells
Popov, A. A.; Thompson, J. M. T.; McRobie, F. A.
1998-01-01
Vibrations of cylindrical shells parametrically excited by axial forcing are considered. The governing system of two coupled non-linear partial differential equations is discretized by using Lagrange equations. The computation is simplified significantly by the application of computer algebra and as a result low dimensional models of shell vibrations are readily obtained. After applying numerical continuation techniques and ideas from dynamical systems theory, complete bifurcation diagrams are constructed. The principal aim is to investigate the interaction between different modes of shell vibration. Results for system models with two of the lowest modes are discussed.
A vibration model for centrifugal contactors
Leonard, R.A.; Wasserman, M.O.; Wygmans, D.G.
1992-11-01
Using the transfer matrix method, we created the Excel worksheet ``Beam`` for analyzing vibrations in centrifugal contactors. With this worksheet, a user can calculate the first natural frequency of the motor/rotor system for a centrifugal contactor. We determined a typical value for the bearing stiffness (k{sub B}) of a motor after measuring the k{sub B} value for three different motors. The k{sub B} value is an important parameter in this model, but it is not normally available for motors. The assumptions that we made in creating the Beam worksheet were verified by comparing the calculated results with those from a VAX computer program, BEAM IV. The Beam worksheet was applied to several contactor designs for which we have experimental data and found to work well.
A vibration model for centrifugal contactors
Using the transfer matrix method, we created the Excel worksheet ''Beam'' for analyzing vibrations in centrifugal contactors. With this worksheet, a user can calculate the first natural frequency of the motor/rotor system for a centrifugal contactor. We determined a typical value for the bearing stiffness (kB) of a motor after measuring the kB value for three different motors. The kB value is an important parameter in this model, but it is not normally available for motors. The assumptions that we made in creating the Beam worksheet were verified by comparing the calculated results with those from a VAX computer program, BEAM IV. The Beam worksheet was applied to several contactor designs for which we have experimental data and found to work well
Detecting anharmonicity at a glance
Harmonic motion is generally presented in such a way that most of the students believe that the small oscillations of a body are all harmonic. Since the situation is not actually so simple, and since the comprehension of harmonic motion is essential in many physical contexts, we present here some suggestions, addressed to undergraduate students and pre-service teachers, that allow one to find out at a glance the anharmonicity of a motion. Starting from a didactically motivated definition of harmonic motion, and stressing the importance of the interplay between mathematics and experiments, we give a four-point criterion for anharmonicity together with some emblematic examples. The role of linear damping is also analysed in relation to the gradual changing of harmonicity into anharmonicity when the ratio between the damping coefficient and the zero-friction angular frequency increases. (paper)
Detecting anharmonicity at a glance
Giliberti, M.; Stellato, M.; Barbieri, S.; Cavinato, M.; Rigon, E.; Tamborini, M.
2014-11-01
Harmonic motion is generally presented in such a way that most of the students believe that the small oscillations of a body are all harmonic. Since the situation is not actually so simple, and since the comprehension of harmonic motion is essential in many physical contexts, we present here some suggestions, addressed to undergraduate students and pre-service teachers, that allow one to find out at a glance the anharmonicity of a motion. Starting from a didactically motivated definition of harmonic motion, and stressing the importance of the interplay between mathematics and experiments, we give a four-point criterion for anharmonicity together with some emblematic examples. The role of linear damping is also analysed in relation to the gradual changing of harmonicity into anharmonicity when the ratio between the damping coefficient and the zero-friction angular frequency increases.
Anharmonic densities of states: A general dynamics-based solution
Jellinek, Julius; Aleinikava, Darya
2016-06-01
Density of states is a fundamental physical characteristic that lies at the foundation of statistical mechanics and theoretical constructs that derive from them (e.g., kinetic rate theories, phase diagrams, and others). Even though most real physical systems are anharmonic, the vibrational density of states is customarily treated within the harmonic approximation, or with some partial, often limited, account for anharmonicity. The reason for this is that the problem of anharmonic densities of states stubbornly resisted a general and exact, yet convenient and straightforward in applications, solution. Here we formulate such a solution within both classical and quantum mechanics. It is based on actual dynamical behavior of systems as a function of energy and as observed, or monitored, on a chosen time scale, short or long. As a consequence, the resulting anharmonic densities of states are fully dynamically informed and, in general, time-dependent. As such, they lay the ground for formulation of new statistical mechanical frameworks that incorporate time and are ergodic, by construction, with respect to actual dynamical behavior of systems.
Partial dynamical symmetry and anharmonicity in γ-soft nuclei
The concept of dynamical symmetry (DS) is now widely accepted to be of central importance in our understanding of many-body systems, such as nuclei. Its hallmarks are the solvability of the complete spectrum, and the existence of exact quantum numbers for all eigenstates. However, in most applications to realistic systems, the predictions of an exact DS are rarely fulfilled and one is compelled to break it. More often one finds that the assumed symmetry is not obeyed uniformly, i.e., is fulfilled by only some states but not by others. The need to address such situations has led to the introduction of partial dynamical symmetries (PDSs). The essential idea is to relax the stringent conditions of complete solvability, so that the DS is broken, but part of the eigen spectrum remains solvable with good symmetry. Various types of bosonic and fermionic PDS, have been shown to be relevant to nuclear spectroscopy [1-7] and to quantum phase transitions [8]. In the present contribution we extend the notion of PDS to encompass Hamiltonians with higher-order terms. We present a systematic procedure for constructing such PDS Hamiltonians and demonstrate their relevance to the anharmonicity of excited bands in the -soft nucleus 196Pt. The work, to be reported, was done in collaboration with J.E. Garcfa-Ramos (Huelva) and P. Van backer (GANIL) [9]. The SO(6)-DS limit of the interacting boson model (IBM) [10], provides a good description of the rotational spectrum and E2 rates for states in the ground band of 196Pt [11]. However, the resulting fit to energies of excited bands is quite poor. The empirical anharmonicity of excited vibrational bands is large and negative. On the other hand, in the SO(6)-DS limit, the calculated anharmonicity is fixed by the number of valence nucleons, and is found to be in marked disagreement with the empirical value. A detailed study of double-phonon excitations within the IBM, has concluded that large anharmonicities can be incorporated only by the
Molina, Andrew; Smereka, Peter; Zimmerman, Paul M.
2016-03-01
The use of alternate coordinate systems as a means to improve the efficiency and accuracy of anharmonic vibrational structure analysis has seen renewed interest in recent years. While normal modes (which diagonalize the mass-weighted Hessian matrix) are a typical choice, the delocalized nature of this basis makes it less optimal when anharmonicity is in play. When a set of modes is not designed to treat anharmonicity, anharmonic effects will contribute to inter-mode coupling in an uncontrolled fashion. These effects can be mitigated by introducing locality, but this comes at its own cost of potentially large second-order coupling terms. Herein, a method is described which partially localizes vibrations to connect the fully delocalized and fully localized limits. This allows a balance between the treatment of harmonic and anharmonic coupling, which minimizes the error that arises from neglected coupling terms. Partially localized modes are investigated for a range of model systems including a tetramer of hydrogen fluoride, water dimer, ethene, diphenylethane, and stilbene. Generally, partial localization reaches ˜75% of maximal locality while introducing less than ˜30% of the harmonic coupling of the fully localized system. Furthermore, partial localization produces mode pairs that are spatially separated and thus weakly coupled to one another. It is likely that this property can be exploited in the creation of model Hamiltonians that omit the coupling parameters of the distant (and therefore uncoupled) pairs.
陈恒杰; 方旺; 刘丰奎; 薛善增
2014-01-01
采用包含迭代三激发的耦合簇理论（ CC3和CCSDT-3），在aug-cc-pVTZ基组水平上对HOF分子几何构型进行优化。通过解析二阶导数结合有限差分技术获得HOF二阶、完全三阶和半对角四阶力场。通过非谐性分析，得到其基频、旋振相互作用常数、非谐性常数和离心畸变光谱常数。应用二阶振动微扰理论（VPT2）得到HOF多个泛频峰位置。目前计算值与实验及其它文献结果符合良好。%The molecular equilibrium structure of HOF has been optimized using iterative triplet coupled cluster approach (CC3 and CCSDT-3) together with aug-cc-pVTZ basis set.Quadratic, full cubic and semidiagonal part of the quartic force field have been obtained by the analytic second derivatives and finite difference techniques. Fundamental frequencies, vibration-rotation interaction constants, anharmonic constants and centrifugal distor-tion constants have been evaluated according to the anharmonic analytics.Several overtones have been expected by the vibrational second-order perturbation theory ( VPT2 ) .The present calculation values are in good agree-ment with others theoretical and experimental results.
Iyer, Srikanth S.; Candler, Robert N.
2016-03-01
In this work, we determine the intrinsic mechanical energy dissipation limit for single-crystal resonators due to anharmonic phonon-phonon scattering in the Akhiezer (Ω τ ≪1 ) regime. The energy loss is derived using perturbation theory and the linearized Boltzmann transport equation for phonons, and includes the direction- and polarization-dependent mode-Grüneisen parameters in order to capture the strain-induced anharmonicity among phonon branches. This expression reveals the fundamental differences among the internal friction limits for different types of bulk-mode elastic waves. For cubic crystals, 2D-extensional modes have increased dissipation compared to width-extensional modes because the biaxial deformation opposes the natural Poisson contraction of the solid. Additionally, we show that shear-mode vibrations, which preserve volume, have significantly reduced energy loss because dissipative phonon-phonon scattering is restricted to pure-shear phonon branches, indicating that Lamé- or wineglass-mode resonators will have the highest upper limit on mechanical efficiency. Finally, we employ key simplifications to evaluate the quality factor limits for common mode shapes in single-crystal silicon devices, explicitly including the correct effective elastic storage moduli for different vibration modes and crystal orientations. Our expression satisfies the pressing need for a reliable analytical model that can predict the phonon-phonon dissipation limits for modern resonant microelectromechanical systems, where precise manufacturing techniques and accurate finite-element methods can be used to select particular vibrational mode shapes and crystal orientations.
Vibration induced flow in hoppers: DEM 2D polygon model
无
2008-01-01
A two-dimensional discrete element model (DEM) simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle-particle interaction model used is based on a multi-contact principle.The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size (Be) to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that Be decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner.The second part of the study showed that vibration could enhance flow, effectively reducing Be. The model demonstrated the importance of vibrator location (height), consistent with previous continuum model results, and vibration amplitude in enhancing flow.
Maltseva, Elena; Candian, Alessandra; Mackie, Cameron J; Huang, Xinchuan; Lee, Timothy J; Tielens, Alexander G G M; Oomens, Jos; Buma, Wybren Jan
2015-01-01
We report on an experimental and theoretical investigation of the importance of anharmonicity in the 3 micron CH stretching region of Polycyclic Aromatic Hydrocarbon (PAH) molecules. We present mass-resolved, high-resolution spectra of the gas-phase cold (~4K) linear PAH molecules naphthalene, anthracene, and tetracene. The measured IR spectra show a surprisingly high number of strong vibrational bands. For naphthalene, the observed bands are well separated and limited by the rotational contour, revealing the band symmetries. Comparisons are made to the harmonic and anharmonic approaches of the widely used Gaussian software. We also present calculated spectra of these acenes using the computational program SPECTRO, providing anharmonic predictions enhanced with a Fermi-resonance treatment that utilises intensity redistribution. We demonstrate that the anharmonicity of the investigated acenes is strong, dominated by Fermi resonances between the fundamental and double combination modes, with triple combination ...
Positive Anharmonicities: The Oxonide Anion as an Example
Lee, Timothy J.; Arnold, James O. (Technical Monitor)
1997-01-01
An accurate ab initio quartic force field for the ozonide anion has been determined at the singles and doubles coupled-cluster level of theory that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), using the augmented valence triple-zeta correlation consistent one-particle basis set. Convergence of the harmonic frequencies with respect to the one-particle basis set has been demonstrated by computing quadratic force fields at the CCSD(T) level using augmented valence double-zeta and quadruple-zeta basis sets. Fundamental vibrational frequencies have been determined via second-order ro-vibrational perturbation theory and also using exact variational methods. Agreement is very good, and they both show that the antisymmetric O-O stretch, v 3, possesses a positive anharmonic correction (that is, the fundamental frequency is predicted to be higher in energy than the harmonic frequency). Comparison of the O_3 and O3 quartic force fields shows that the positive anharmonic correction is the result of a particularly large F3333 symmetry internal coordinate force constant. The reasonableness of this force constant has been tested by computing both F33 and F3333 at the CCSD, CCSD(T), and CASPT2 levels of theory. A discussion of known positive anharmonicities for stretching modes is presented.
THEORETICAL MODEL OF VIBRATING OBJECT TRANSMITTING NOISE TOWARDS EXTERNAL SOUND
姚志远
2002-01-01
On the basic theory of modal method, the coupling relation between the vibration of objects and external sound was analyzed, the theoretical model solving the vibration and noise was provided, the corresponding calculation formula was given. The calculating results show out that this calculation formula is correct.
The spectroscopic constants and anharmonic force field of AgSH: An ab initio study.
Zhao, Yanliang; Wang, Meishan; Yang, Chuanlu; Ma, Xiaoguang; Zhu, Ziliang
2016-07-01
The equilibrium structure, spectroscopy constants, and anharmonic force field of silver hydrosulfide (AgSH) have been calculated at B3P86, B3PW91 and MP2 methods employing two basis sets, TZP and QZP, respectively. The calculated geometries, ground state rotational constants, harmonic vibrational wave numbers, and quartic and sextic centrifugal distortion constants are compared with the available experimental and theoretical data. The equilibrium rotational constants, fundamental frequencies, anharmonic constants, and vibration-rotation interaction constants, Coriolis coupling constants, cubic and quartic force constants are predicted. The calculated results show that the MP2/TZP results are in good agreement with experiment observation and are also an advisable choice to study the anharmonic force field of AgSH. PMID:27085293
Bishop, David M.; Luis Luis, Josep Maria; Kirtman, Bernard
1998-01-01
Compact expressions, complete through second order in electrical and/or mechanical anharmonicity, are given for the dynamic dipole vibrational polarizability and dynamic first and second vibrational hyperpolarizabilities. Certain contributions not previously formulated are now included
Vibration Reduction Evaluation of an Isolated EDG Model
A vibration and noise are among one of the well known problems of a rotational machine. An Emergency Diesel Generator (EDG) is one of the safety related equipment of a Nuclear Power Plant. The EDG system also has a vibration problem. Kim, et al studied the operating vibration problem of the EDG system in Yonggwang 5, Ulchin 2 and 3 unit. Foundation systems of the Yongwang 5, Ulchin 2 and 3 unit EDG systems are an anchor bolt, coil spring with a seismic mass and a coil spring and viscous damper system, respectively. But in these cases it is impossible to evaluate the vibration reduction effect according to the spring system. So, in this study, a small scale EDG model and a spring-damper system were developed and a vibration was measured. For a producing a sine wave vibration, a vibration generator was produced. As a result, at least 80% of a vibration was decreased by using the coil spring and viscous damper system
Unexpected red shift of C-H vibrational band of Methyl benzoate
Maiti, Kiran Sankar; Scheurer, Christoph
2016-01-01
The C-H vibrational bands become more and more important in the structural determination of biological molecules with the development of CARS microscopy and 2DIR spectroscopy. Due to the congested pattern, near degeneracy, and strong anharmonicity of the C-H stretch vibrations, assignment of the C-H vibrational bands are often misleading. Anharmonic vibrational spectra calculation with multidimensional potential energy surface interprets the C-H vibrational spectra more accurately. In this article we have presented the importance of multidimensional potential energy surface in anharmonic vibrational spectra calculation and discuss the unexpected red shift of C-H vibrational band of Methyl benzoate.
Vibration Response of Multi Storey Building Using Finite Element Modelling
Chik, T. N. T.; Zakaria, M. F.; Remali, M. A.; Yusoff, N. A.
2016-07-01
Interaction between building, type of foundation and the geotechnical parameter of ground may trigger a significant effect on the building. In general, stiffer foundations resulted in higher natural frequencies of the building-soil system and higher input frequencies are often associated with other ground. Usually, vibrations transmitted to the buildings by ground borne are often noticeable and can be felt. It might affect the building and become worse if the vibration level is not controlled. UTHM building is prone to the ground borne vibration due to closed distance from the main road, and the construction activities adjacent to the buildings. This paper investigates the natural frequency and vibration mode of multi storey office building with the presence of foundation system and comparison between both systems. Finite element modelling (FEM) package software of LUSAS is used to perform the vibration analysis of the building. The building is modelled based on the original plan with the foundation system on the structure model. The FEM results indicated that the structure which modelled with rigid base have high natural frequency compare to the structure with foundation system. These maybe due to soil structure interaction and also the damping of the system which related to the amount of energy dissipated through the foundation soil. Thus, this paper suggested that modelling with soil is necessary to demonstrate the soil influence towards vibration response to the structure.
Origin of the large anharmonicity in the phonon modes of LiBH{sub 4}
Gremaud, R.; Züttel, A. [Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory 505 (Hydrogen and Energy), Überlandstrasse 129, CH-8600 Dübendorf (Switzerland); Borgschulte, A., E-mail: andreas.borgschulte@empa.ch [Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory 505 (Hydrogen and Energy), Überlandstrasse 129, CH-8600 Dübendorf (Switzerland); Ramirez-Cuesta, A.J.; Refson, K. [Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, PO Box 2008, MS 6473 Oak Ridge (United States); Colognesi, D. [Istituto dei Sistemi Complessi – sezione di Firenze, Consiglio Nazionale delle Ricerche, via Madonna del piano 10, 50019 Sesto Fiorentino (Italy)
2013-12-12
Highlights: • IR, Raman, and INS spectroscopy data and corresponding DFT-calculations on LiBH4. • Mismatch between experiment and theory are due to anharmonicity. • Strong anharmonic effects can be expected for vibrations with high H amplitude. - Abstract: The dynamics and bonding of the complex hydride LiBH{sub 4} have been investigated by vibrational spectroscopy and density functional theory (DFT). The combination of infrared, Raman, and inelastic neutron-scattering (INS) spectroscopies on hydrided and deuterated samples reveals a complete picture of the dynamics of the BH{sub 4}{sup −} ions as well as of the lattice. Particular emphasis is laid on a comparison between experiment and theory, revealing significant discrepancy between the two approaches for vibrations with high anharmonicity, which is related to large vibrational amplitudes. The latter is typical for librational modes in molecular crystals and pseudo-ionic crystals such as complex hydrides. The presented strategy for anharmonic frequency corrections might thus be generally applicable for this kind of materials.
Mathematical modeling of mechanical vibration assisted conductivity imaging
Ammari, Habib; Kwon, Hyeuknam; Seo, Jin Keun; Woo, Eung Je
2014-01-01
This paper aims at mathematically modeling a new multi-physics conductivity imaging system incorporating mechanical vibrations simultaneously applied to an imaging object together with current injections. We perturb the internal conductivity distribution by applying time-harmonic mechanical vibrations on the boundary. This enhances the effects of any conductivity discontinuity on the induced internal current density distribution. Unlike other conductivity contrast enhancing frameworks, it does not require a prior knowledge of a reference data. In this paper, we provide a mathematical framework for this novel imaging modality. As an application of the vibration-assisted impedance imaging framework, we propose a new breast image reconstruction method in electrical impedance tomography (EIT). As its another application, we investigate a conductivity anomaly detection problem and provide an efficient location search algorithm. We show both analytically and numerically that the applied mechanical vibration increas...
Modeling of Axial Spring Stiffness in Active Vibration Controlled Drilling
Pao William
2014-07-01
Full Text Available During drilling process, substantial amount of vibration and shock are induced to the drill string. Active vibration controlled drilling is introduced to reduce the vibration and increase the efficiency of drilling process. In this system, two main components that determine the damping coefficient are magnetorheological (MR damper and spring assembly. Performance of vibration damping system is depending on the viscosity of MR fluid in the damper and spring constant of spring assembly. One of the key issues that are unclear from the design is the correlation between the axial spring stiffness configuration and the damping force which needs to be tuned actively. There has been lack of studies on how the viscosity of MR fluid on the active vibration damper affects the damping stiffness of the whole system. The objective of the project is to extract the correlations for the viscous damping coefficient, equivalent spring stiffness and power input to the system. Simplified vibration model is thus created using Simulink, together with experimental data fed from APS Technology’s in-house team. Inputs of the simulation such as force exerted, mass of mandrel, spring constant and step time are based on the experimental data and can be adjusted to suit different experiments. By having the model, behavior of the system can be studied and analyzed. From the simulation, it is also observed that the relationship between damping coefficient and power input of the system is linear.
On the Applicability of the Caldeira-Leggett Model to Condensed Phase Vibrational Spectroscopy
Ivanov, Sergei D; Kühn, Oliver
2014-01-01
Formulating a rigorous system-bath partitioning approach remains an open issue. In this context the famous Caldeira-Leggett (CL) model that enables quantum and classical treatment of Brownian motion on equal footing has enjoyed popularity. Although this model is by any means a useful theoretical tool, its validity for describing anharmonic dynamics of real systems is often taken for granted. In this Letter we show that the model is not able to describe real systems unless the system part of the potential is taken effectively harmonic. We demonstrate that the deficiencies of the model are rooted in the anharmonicity. Further, we elaborate on the mathematical origin of the breakdown of the CL model.
Methyl group dynamics and the onset of anharmonicity in myoglobin
The role of methyl groups in the onset of low-temperature anharmonic dynamics in a crystalline protein at low temperature is investigated using atomistic molecular dynamics (MD) simulation. Anharmonicity appears at 150 ∼ K, far below the much-studied solvent-activated dynamical transition at ∼ 220 K. A significant fraction of methyl groups exhibit nanosecond time scale rotational jump diffusion at 150 K. The splitting and shift in peak position of both the librational band (around 100 cm-1) and the torsional band (around 270?300 cm-1) also differ significantly among methyl groups, depending on the local environment. The simulation results provide no evidence for a correlation between methyl dynamics and solvent exposure, consistent with the hydration-independence of the low-temperature anharmonic dynamics observed in neutron scattering experiments. The calculated proton mean-square fluctuation and methyl NMR order parameters show a systematic nonlinear dependence on the rotational barrier which can be described using model functions. The methyl groups that exhibit many rotational excitations are located near xenon cavities, suggesting that cavities in proteins act as activation centers of anharmonic dynamics. The dynamic heterogeneity and the environmental sensitivity of motional parameters and low-frequency spectral bands of CH3 groups found here suggest that methyl dynamics may be used as a probe to investigate the relation between low-energy structural fluctuations and packing defects in proteins
The Modeling of Vibration Damping in SMA Wires
Reynolds, D R; Kloucek, P; Seidman, T I
2003-09-16
Through a mathematical and computational model of the physical behavior of shape memory alloy wires, this study shows that localized heating and cooling of such materials provides an effective means of damping vibrational energy. The thermally induced pseudo-elastic behavior of a shape memory wire is modeled using a continuum thermodynamic model and solved computationally as described by the authors in [23]. Computational experiments confirm that up to 80% of an initial shock of vibrational energy can be eliminated at the onset of a thermally-induced phase transformation through the use of spatially-distributed transformation regions along the length of a shape memory alloy wire.
The multiphonon method, which is an exact diagonalization in the restricted space of collective phonons of different types, is tested in a simple two shell model allowing an exact solution for a many body system of fermions interacting via pairing plus quadrupole and octupole forces. It appears satisfactory for the description of the anharmonicities of the lowest-lying vibrational Ksup(π) = 0+ and 0- states in deformed nuclei. In particular, it allows electromagnetic transitions between the different one phonon states, which are completely forbidden in any harmonic treatment as TDA or RPA. It seems also that a restriction to the space spanned by the two lowest collective phonons of different type is sufficient for the description of the spectroscopic properties of the corresponding levels
Noise, vibration, harshness model of a rotating tyre
Bäcker, Manfred; Gallrein, Axel; Roller, Michael
2016-04-01
The tyre plays a fundamental role in the generation of acoustically perceptible driving noise and vibrations inside the vehicle. An essential part of these vibrations is induced by the road excitation and transferred via the tyre into the vehicle. There are two basic ways to study noise, vibration, harshness (NVH) behaviour: Simulations in time and frequency domains. Modelling the tyre transfer behaviour in frequency domain requires special attention to the rotation of the tyre. This paper shows the approach taken by the authors to include the transfer behaviour in the frequency range up to 250 Hz from geometric road excitations to resulting spindle forces in frequency domain. This paper validates the derived NVH tyre model by comparison with appropriate transient simulations of the base transient model.
Vibrational spectrum of CF4 isotopes in an algebraic model
Joydeep Choudhury; Srinivasa Rao Karumuri; Nirmal Kumar Sarkar; Ramendu Bhattacharjee
2009-11-01
n this paper the stretching vibrational modes of CF4 isotopes are calculated up to first overtone using the one-dimensional vibron model for the first time. The model Hamiltonian so constructed seems to describe the C–F stretching modes accurately using a relatively small set of well-defined parameters.
Lattice thermal conductivity of filled skutterudites: An anharmonicity perspective
We report a phenomenological model to calculate the high-temperature lattice thermal conductivity of filled skutterudite antimonides. The model needs no phonon resonant scattering terms. Instead, we assume that umklapp processes dominate the high-temperature phonon scattering. In order to represent the anharmonicity introduced by the filling atom, we introduce a Gaussian term into the relaxation time of the umklapp process. The developed model agrees remarkably well with the experimental results of REfCo4Sb12 and REfFe4Sb12 (RE = Yb, Ba, and Ca) alloys. To further test the validity of our model, we calculate the lattice thermal conductivity of nanostructured or multi-filled skutterudites. The calculation results are also in good agreement with experiment, increasing our confidence in the developed anharmonicity model.
Ground state properties of a Bose-Einstein condensate confined in an anharmonic external potential
Wang Deng-Long; Yan Xiao-Hong; Tang Yi
2004-01-01
In light of the interference experiment of Bose-Einstein condensates, we present an anharmonic external potential model to study ground state properties of Bose-Einstein condensates. The ground state energy and the chemical potential have been analytically obtained, which are lower than those in harmonic trap. Additionally, it is found that the anharmonic strength of the external potential has an important effect on density and velocity distributions of the ground state for the Thomas-Fermi model.
We show a first-principles approach for analyzing anharmonic properties of lattice vibrations in solids. We firstly extract harmonic and anharmonic force constants from accurate first-principles calculations based on the density functional theory. Using the many-body perturbation theory of phonons, we then estimate the phonon scattering probability due to anharmonic phonon-phonon interactions. We show the validity of the approach by computing the lattice thermal conductivity of Si, a typical covalent semiconductor, and selected thermoelectric materials PbTe and Bi2Te3 based on the Boltzmann transport equation. We also show that the phonon lifetime and the lattice thermal conductivity of the high-temperature phase of SrTiO3 can be estimated by employing the perturbation theory on top of the solution of the self-consistent phonon equation
Tadano, Terumasa [Department of Applied Physics, The University of Tokyo, Tokyo 113-8656 (Japan); Tsuneyuki, Shinji [Department of Physics, The University of Tokyo, Tokyo 113-0033 (Japan); Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581 (Japan)
2015-12-31
We show a first-principles approach for analyzing anharmonic properties of lattice vibrations in solids. We firstly extract harmonic and anharmonic force constants from accurate first-principles calculations based on the density functional theory. Using the many-body perturbation theory of phonons, we then estimate the phonon scattering probability due to anharmonic phonon-phonon interactions. We show the validity of the approach by computing the lattice thermal conductivity of Si, a typical covalent semiconductor, and selected thermoelectric materials PbTe and Bi{sub 2}Te{sub 3} based on the Boltzmann transport equation. We also show that the phonon lifetime and the lattice thermal conductivity of the high-temperature phase of SrTiO{sub 3} can be estimated by employing the perturbation theory on top of the solution of the self-consistent phonon equation.
Scale modeling flow-induced vibrations of reactor components
Similitude relationships currently employed in the design of flow-induced vibration scale-model tests of nuclear reactor components are reviewed. Emphasis is given to understanding the origins of the similitude parameters as a basis for discussion of the inevitable distortions which occur in design verification testing of entire reactor systems and in feature testing of individual component designs for the existence of detrimental flow-induced vibration mechanisms. Distortions of similitude parameters made in current test practice are enumerated and selected example tests are described. Also, limitations in the use of specific distortions in model designs are evaluated based on the current understanding of flow-induced vibration mechanisms and structural response
The importance of anharmonicity in thermal transport across solid-solid interfaces
Understanding interfacial thermal transport is of great importance for applications like energy devices and thermal management of electronics. Despite the significant efforts in the past few decades, thermal transport across solid-solid interfaces is still not fully understood and cannot be accurately predicted. Anharmonicity is often ignored in many prediction models, such as the mismatch models, the wave-packet method, and the Atomic Green's function. In this paper, we use molecular dynamics to systematically study the role of anharmonicity in thermal transport across solid-solid interfaces. The interatomic interactions are modeled using force constants up to the third order. This model allows controlling the anharmonicity independently by tuning the cubic force constants. The interfacial thermal conductance as a function of anharmonicity inside the materials and that at the interface is studied. We found that the anharmonicity inside the materials plays an important role in the interfacial thermal transport by facilitating the energy communication between different phonon modes. The anharmonicity at the interface has much less impact on the interfacial thermal transport. These results are important to the modification of traditional models to improve their prediction power
Maltseva, Elena; Petrignani, Annemieke; Candian, Alessandra; Mackie, Cameron J.; Huang, Xinchuan; Lee, Timothy J.; Tielens, Alexander G. G. M.; Oomens, Jos; Buma, Wybren Jan
2016-01-01
We report on an experimental and theoretical investigation of the importance of anharmonicity in the 3 micrometers CH stretching region of Polycyclic Aromatic Hydrocarbon (PAH) molecules. We present mass-resolved, high-resolution spectra of the gas-phase cold ((is) approximately 4K) linear PAH molecules naphthalene, anthracene, and tetracene. The measured IR spectra show a surprisingly high number of strong vibrational bands. For naphthalene, the observed bands are well separated and limited by the rotational contour, revealing the band symmetries. Comparisons are made to the harmonic and anharmonic approaches of the widely used Gaussian software. We also present calculated spectra of these acenes using the computational program SPECTRO, providing anharmonic predictions enhanced with a Fermi-resonance treatment that utilizes intensity redistribution. We demonstrate that the anharmonicity of the investigated acenes is strong, dominated by Fermi resonances between the fundamental and double combination modes, with triple combination bands as possible candidates to resolve remaining discrepancies. The anharmonic spectra as calculated with SPECTRO lead to predictions of the main modes that fall within 0.5% of the experimental frequencies. The implications for the Aromatic Infrared Bands, specifically the 3-m band are discussed.
Modeling vibration response and damping of cables and cabled structures
Spak, Kaitlin S.; Agnes, Gregory S.; Inman, Daniel J.
2015-02-01
In an effort to model the vibration response of cabled structures, the distributed transfer function method is developed to model cables and a simple cabled structure. The model includes shear effects, tension, and hysteretic damping for modeling of helical stranded cables, and includes a method for modeling cable attachment points using both linear and rotational damping and stiffness. The damped cable model shows agreement with experimental data for four types of stranded cables, and the damped cabled beam model shows agreement with experimental data for the cables attached to a beam structure, as well as improvement over the distributed mass method for cabled structure modeling.
We clarify the role of the critical imidazolium C(2)H position (the central C between N atoms in the heterocycle) in the assembly motif of the [EMIM][BF4] ionic liquid by analyzing the vibrational spectra of the bare EMIM+ ion as well as that of the cationic [EMIM]2[BF4]+ (EMIM+ = 1-ethyl-3-methylimidazolium, C6H11N2+) cluster. Vibrational spectra of the cold, mass-selected ions are obtained using cryogenic ion vibrational predissociation of weakly bound D2 molecules formed in a 10 K ion trap. The C(2)H behavior is isolated by following the evolution of key vibrational features when the C(2) hydrogen, the proposed binding location of the anion to the imidazolium ring, is replaced by either deuterium or a methyl group (i.e., in the EMMIM+ analogue). Strong features in the ring CH stretching region of the bare ion are traced to Fermi resonances with overtones of lower frequency modes. Upon incorporation into the EMIM+ ⋅ ⋅ ⋅ BF4− ⋅ ⋅ ⋅ EMIM+ ternary complex, the C(2)H oscillator strength is dramatically increased, accounting for the much more complicated patterns derived from the EMIM+ ring CH stretches in the light isotopomer, which are strongly suppressed in the deuterated analogue. Further changes in the spectra that occur when the C(2)H is replaced by a methyl group are consistent with BF4− attachment directly to the imidazolium ring in an arrangement that maximizes the electrostatic interaction between the molecular ions
Dynamical response functions in models of vibrated granular media
Nicodemi, Mario
1998-01-01
In recently introduced schematic lattice gas models for vibrated dry granular media, we study the dynamical response of the system to small perturbations of shaking amplitudes and its relations with the characteristic fluctuations. Strong off equilibrium features appear and a generalized version of the fluctuation dissipation theorem is introduced. The relations with thermal glassy systems and the role of Edwards' compactivity are discussed.
Vibration testing of a 1/4-scale containment model
This paper presents programs for the validation of soil-structure interaction (SSI) analysis methods with data that include ground and structural response motions during natural earthquakes and structural response from low-level vibration tests. The primary source of the data is the 1/4-scale containment building situated in Lotung in a seismically active region of Taiwan. The analysis validation program involves blind predictions of site and structural response to the vibration test excitations and to a selected strong-motion seismic event, and the subsequent comparison of predictions with corresponding measurements. This paper focuses on the vibration testing of the model containment structure and the determination of its dynamic characteristics from the experimental data. The 1/4-scale reinforced concrete containment structure, built by EPRI in cooperation with Taiwan Power Company, is located within an array of strong-motion seismographs, known as the SMART-1 array
Anharmonic effects in the optical and acoustic bending modes of graphene
Ramírez, R.; Chacón, E.; Herrero, C. P.
2016-06-01
The out-of-plane fluctuations of carbon atoms in a graphene sheet have been studied by means of classical molecular dynamic simulations with an empirical force field as a function of temperature. The Fourier analysis of the out-of-plane fluctuations often applied to characterize the acoustic bending mode of graphene is extended to the optical branch, whose polarization vector is perpendicular to the graphene layer. This observable is inaccessible in a continuous elastic model of graphene but it is readily obtained by the atomistic treatment. Our results suggest that the long-wavelength limit of the acoustic out-of-plane fluctuations of a free layer without stress is qualitatively similar to that predicted by a harmonic model under a tensile stress. This conclusion is a consequence of the anharmonicity of both in-plane and out-of-plane vibrational modes of the lattice. The most striking anharmonic effect is the presence of a linear term, ωA=vAk , in the dispersion relation of the acoustic bending band of graphene at long wavelengths (k →0 ). This term implies a strong reduction of the amplitude of out-of-plane oscillations in comparison to a flexural mode with a k2 dependence in the long-wavelength limit. Our simulations show an increase of the sound velocity associated to the bending mode, as well as an increase of its bending constant, κ , as the temperature increases. Moreover, the frequency of the optical bending mode, ωO(Γ ), also increases with the temperature. Our results are in agreement with recent analytical studies of the bending modes of graphene using either perturbation theory or an adiabatic approximation in the framework of continuous layer models.
Modeling and vibration control of an active membrane mirror
Ruggiero, Eric J.; Inman, Daniel J.
2009-09-01
The future of space satellite technology lies in ultra-large mirrors and radar apertures for significant improvements in imaging and communication bandwidths. The availability of optical-quality membranes drives a parallel effort for structural models that can capture the dominant dynamics of large, ultra-flexible satellite payloads. Unfortunately, the inherent flexibility of membrane mirrors wreaks havoc with the payload's on-orbit stability and maneuverability. One possible means of controlling these undesirable dynamics is by embedding active piezoelectric ceramics near the boundary of the membrane mirror. In doing so, active feedback control can be used to eliminate detrimental vibration, perform static shape control, and evaluate the health of the structure. The overall motivation of the present work is to design a control system using distributed bimorph actuators to eliminate any detrimental vibration of the membrane mirror. As a basis for this study, a piezoceramic wafer was attached in a bimorph configuration near the boundary of a tensioned rectangular membrane sample. A finite element model of the system was developed to capture the relevant system dynamics from 0 to 300 Hz. The finite element model was compared against experimental results, and fair agreement found. Using the validated finite element models, structural control using linear quadratic regulator control techniques was then used to numerically demonstrate effective vibration control. Typical results show that less than 12 V of actuation voltage is required to eliminate detrimental vibration of the membrane samples in less than 15 ms. The functional gains of the active system are also derived and presented. These spatially descriptive control terms dictate favorable regions within the membrane domain for placing sensors and can be used as a design guideline for structural control applications. The results of the present work demonstrate that thin plate theory is an appropriate modeling
Insight into structural phase transitions from the decoupled anharmonic mode approximation.
Adams, Donat J; Passerone, Daniele
2016-08-01
We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T = 0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200-300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model. PMID:27269514
Insight into structural phase transitions from the decoupled anharmonic mode approximation
Adams, Donat J.; Passerone, Daniele
2016-08-01
We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T = 0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200–300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model.
The role of damping for the driven anharmonic quantum oscillator
Guo, Lingzhen; André, Stephan; Schön, Gerd
2011-01-01
For the model of a linearly driven quantum anharmonic oscillator, the role of damping is investigated. We compare the position of the stable points in phase space obtained from a classical analysis to the result of a quantum mechanical analysis. The solution of the full master equation shows that the stable points behave qualitatively similar to the classical solution but with small modifications. Both the quantum effects and additional effects of temperature can be described by renormalizing the damping.
Vibration signal models for fault diagnosis of planet bearings
Feng, Zhipeng; Ma, Haoqun; Zuo, Ming J.
2016-05-01
Rolling element bearings are key components of planetary gearboxes. Among them, the motion of planet bearings is very complex, encompassing spinning and revolution. Therefore, planet bearing vibrations are highly intricate and their fault characteristics are completely different from those of fixed-axis case, making planet bearing fault diagnosis a difficult topic. In order to address this issue, we derive the explicit equations for calculating the characteristic frequency of outer race, rolling element and inner race fault, considering the complex motion of planet bearings. We also develop the planet bearing vibration signal model for each fault case, considering the modulation effects of load zone passing, time-varying angle between the gear pair mesh and fault induced impact force, as well as the time-varying vibration transfer path. Based on the developed signal models, we derive the explicit equations of Fourier spectrum in each fault case, and summarize the vibration spectral characteristics respectively. The theoretical derivations are illustrated by numerical simulation, and further validated experimentally and all the three fault cases (i.e. outer race, rolling element and inner race localized fault) are diagnosed.
Nonlinear dynamic modeling and resonance tuning of Galfenol vibration absorbers
This paper investigates the semi-active control of a magnetically-tunable vibration absorber’s resonance frequency. The vibration absorber that is considered is a metal-matrix composite containing the magnetostrictive material Galfenol (FeGa). A single degree of freedom model for the nonlinear vibration of the absorber is presented. The model is valid under arbitrary stress and magnetic field, and incorporates the variation in Galfenol’s elastic modulus throughout the composite as well as Galfenol’s asymmetric tension–compression behavior. Two boundary conditions—cantilevered and clamped–clamped—are imposed on the composite. The frequency response of the absorber to harmonic base excitation is calculated as a function of the operating conditions to determine the composite’s capacity for resonance tuning. The results show that nearly uniform controllability of the vibration absorber’s resonance frequency is possible below a threshold of the input power amplitude using weak magnetic fields of 0–8 kA m−1. Parametric studies are presented to characterize the effect on resonance tunability of Galfenol volume fraction and Galfenol location within the composite. The applicability of the results to composites of varying geometry and containing different Galfenol materials is discussed. (paper)
Modeling nonlinear random vibration: Implication of the energy conservation law
Sun, Xu; Duan, Jinqiao; Li, Xiaofan
2012-01-01
Nonlinear random vibration under excitations of both Gaussian and Poisson white noises is considered. The model is based on stochastic differential equations, and the corresponding stochastic integrals are defined in such a way that the energy conservation law is satisfied. It is shown that Stratonovich integral and Di Paola-Falsone integral should be used for excitations of Gaussian and Poisson white noises, respectively, in order for the model to satisfy the underlining physical laws (e.g.,...
Anharmonic resonances with recursive delay feedback
Goldobin, Denis S.
2011-01-01
We consider application of the multiple time delayed feedback for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, the multiple one exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators. Highlights: > We construct general theory of ...
Anharmonicity effects in the frictionlike mode of graphite
Menéndez, C.; Lobato, A.; Abbasi-Pérez, D.; Fernández-Núñez, J.; Baonza, V. G.; Recio, J. M.
2016-04-01
Graphite is a prototypical solid lubricant demanding a thorough understanding of its low-friction behavior. The E2 g(1) Raman active vibrational mode of graphite is associated with the rigid-layer relative movement of its graphene sheets. Thus, this mode can provide a good means of exploring the low resistance of graphene layers to slip with respect to each other. To take advantage of this fact, the anharmonicity of the E2 g(1) mode has to be carefully characterized and evaluated since the atomic arrangement of carbon atoms in the ambient condition ABA stacking of graphite evidences potential asymmetry. The calculated one-dimensional energetic profile of the E2 g(1) mode reveals this local anisotropy around the energy minima and can be microscopically interpreted in terms of electron density interactions. Morse-type potentials accurately fit the energetic profiles at different interlayer separations, and provide simple analytical expressions for evaluating harmonic and anharmonic contributions to the Γ -point E2 g(1) frequency ωE2g(1 ) under a perturbative algebraic treatment. We quantify how the anharmonic contribution increases with the available energy (E ) at zero pressure, and how this contribution decreases as hydrostatic pressure (p ) or uniaxial stress is applied for a given available energy. The calculated ωE2g(1 )-p and ωE2g(1 )-E trends indicate an increasing (decreasing) of frictional forces in graphite with pressure (temperature). Our conclusions are supported by the good agreement of the calculated frequencies with existing Raman experiments under hydrostatic pressure conditions.
Vibration analysis with MADYMO human models
Verver, M.M.; Hoof, J.F.A.M. van
2002-01-01
The importance of comfort for the automotive industry is increasing. Car manufacturers use comfort to distinguish their products from their competitors. However, the development and design of a new car seat or interior is very time consuming and expensive. The introduction of computer models of huma
Forced vibration test of the Hualien large scale SSI model
A Large-Scale Seismic Test (LSST) Program has been conducted at Hualien, Taiwan (Tang et al., 1991), to obtain earthquake-induced soil-structure interaction (SSI) data in a stiff soil site environment The Hualien program is a follow on of the Lotung program which is of soft soil site. Forced vibration tests of the Hualien 1/4-scale containment SSI test model were conducted in October, 1992 before backfill (without embedment) and in February, 1993 after backfill (with embedment) for the purpose of defining basic dynamic characteristics of the soil-structure system. Two horizontal directions excitation (NS, EW) are applied on the roof floor and on the basemat. Vertical excitation is applied on the basemat only. This paper describes the results of the forced vibration tests of the model without embedment. (author)
Perturbation Theory of Anharmonicity Effects in Slow Neutron Inelastic Scattering by Crystals
An earlier perturbation treatment of the corresponding X-ray scattering problem is generalized into a calculation of the effect of vibrational anharmonicity on the scattering of slow neutrons by crystals. Of an expansion of the lattice potential in powers of the deviations from the thermally averaged sites, the cubic terms are taken into account up to second order; only first order terms are kept in the quartic anharmonicities. All higher terms are neglected. In particular, formulae for the shifts and broadenings of the one-phonon peaks in coherent scattering are derived in terms of the third and fourth order coupling coefficients. As in X-ray scattering, a simple quadratic relation exists between the shifted ''effective frequencies'' of the long wavelength lattice vibrations and the isothermal elastic constants of the crystal. The lattice frequencies of the harmonic approximation may be obtained by extrapolating to absolute zero the linear dependence on temperature shown by the shifted frequencies above the Debye temperature. (author)
Vibration testing of a 1/4-scale containment model
Both the U.S. Nuclear Regulatory Commission (USNRC) and the Electric Power Research Institute (EPRI) have undertaken programs to validate soil-structure interactions analysis methods with data that include ground and structural response motions during natural earthquakes and structural response motions from low level vibration tests. The primary source of the data is the 1/4-scale containment building situated in Lotung in a seismically active region of Taiwan. The analysis validation program involves blind predictions of site and structural responses to the vibration test excitations and to a selected strong-motion seismic event, and the subsequent comparison of these predictions with corresponding measurements. The details of these programs are described more fully elsewhere. The present paper focuses on the vibration testing of the model containment structure and the determination of its dynamic characteristics from the experimental data. The 1/4-scale reinforced concrete containment structure, built by EPRI in cooperation with Taiwan Power Company, is located within an array of strong-motion seismographs, known as the SMART-1 array. Figure 1 shows a cross section of the structure. The structure is not a replica model of a typical nuclear power plant containment building. The roof slab had to be made massive to ensure that the fundamental frequencies of the model structure would fall within the frequency range of seismic excitation typical for the site
Vibration signal models for fault diagnosis of planetary gearboxes
Feng, Zhipeng; Zuo, Ming J.
2012-10-01
A thorough understanding of the spectral structure of planetary gear system vibration signals is helpful to fault diagnosis of planetary gearboxes. Considering both the amplitude modulation and the frequency modulation effects due to gear damage and periodically time variant working condition, as well as the effect of vibration transfer path, signal models of gear damage for fault diagnosis of planetary gearboxes are given and the spectral characteristics are summarized in closed form. Meanwhile, explicit equations for calculating the characteristic frequency of local and distributed gear fault are deduced. The theoretical derivations are validated using both experimental and industrial signals. According to the theoretical basis derived, manually created local gear damage of different levels and naturally developed gear damage in a planetary gearbox can be detected and located.
Model reduction and analysis of a vibrating beam microgyroscope
Ghommem, Mehdi
2012-05-08
The present work is concerned with the nonlinear dynamic analysis of a vibrating beam microgyroscope composed of a rotating cantilever beam with a tip mass at its end. The rigid mass is coupled to two orthogonal electrodes in the drive and sense directions, which are attached to the rotating base. The microbeam is driven by an AC voltage in the drive direction, which induces vibrations in the orthogonal sense direction due to rotation about the microbeam axis. The electrode placed in the sense direction is used to measure the induced motions and extract the underlying angular speed. A reduced-order model of the gyroscope is developed using the method of multiple scales and used to examine its dynamic behavior. © The Author(s) 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.
Comprehensive modeling approach of axial ultrasonic vibration grinding force
HE Yu-hui; ZHOU Qun; ZHOU Jian-jie; LANG Xian-jun
2016-01-01
The theoretical model of axial ultrasonic vibration grinding force is built on the basis of a mathematical model of cutting deforming force deduced from the assumptions of thickness of the undeformed debris under Rayleigh distribution and a mathematical model of friction based on the theoretical analysis of relative sliding velocity of abrasive and workpiece. Then, the coefficients of the ultrasonic vibration grinding force model are calculated through analysis of nonlinear regression of the theoretical model by using MATLAB, and the law of influence of grinding depth, workpiece speed, frequency and amplitude of the mill on the grinding force is summarized after applying the model to analyze the ultrasonic grinding force. The result of the above-mentioned law shows that the grinding force decreases as frequency and amplitude increase, while increases as grinding depth and workpiece speed increase; the maximum relative error of prediction and experimental values of the normal grinding force is 11.47% and its average relative error is 5.41%; the maximum relative error of the tangential grinding force is 10.14% and its average relative error is 4.29%. The result of employing regression equation to predict ultrasonic grinding force approximates to the experimental data, therefore the accuracy and reliability of the model is verified.
Living systems as coherent anharmonic oscillators
A model of living systems considered as coherent, time-dependent anharmonic oscillators is presented. It is based on the concept of space-like coherent states minimizing the time-energy uncertainty relation, adapted to the case of biological systems whose growth is described by the Gompertz or West-Brown-Enquist functions. The coherent states of biological growth evolve coherently in space being localized along the classical time trajectory; hence, the growth is predicted to be coherent in space. It is proven that the Gompertz function is a special solution of the space-like Horodecki-Feinberg equation for the time-dependent Morse oscillator in the dissociation state. Its eigenvalue represents the momentum of biological growth, associated with a space-like component whose properties resemble those attributed by vitalists to the life momentum or vital impulse. The physical characteristics of the life energy and momentum and their connection with the concept of zero-point momentum of vacuum are presented.
Model-based design approach to reducing mechanical vibrations
P. Czop
2013-09-01
Full Text Available Purpose: The paper presents a sensitivity analysis method based on a first-principle model in order to reduce mechanical vibrations of a hydraulic damper. Design/methodology/approach: The first-principle model is formulated using a system of continuous ordinary differential equations capturing usually nonlinear relations among variables of the hydraulic damper model. The model applies three categories of parameters: geometrical, physical and phenomenological. Geometrical and physical parameters are deduced from construction and operational documentation. The phenomenological parameters are the adjustable ones, which are estimated or adjusted based on their roughly known values, e.g. friction/damping coefficients. Findings: The sensitivity analysis method provides major contributors and their magnitude that cause vibrations Research limitations/implications: The method accuracy is limited by the model accuracy and inherited nonlinear effects. Practical implications: The proposed model-based sensitivity method can be used to optimize prototypes of hydraulic dampers. Originality/value: The proposed sensitivity-analysis method minimizes a risk that a hydraulic damper does not meet the customer specification.
Modeling and control of vibration in mechanical structures
Nauclér, Peter
2005-01-01
All mechanical systems exhibit vibrational response when exposed to external disturbances. In many engineering applications vibrations are undesirable and may even have harmful effects. Therefore, control of mechanical vibration is an important topic and extensive research has been going on in the field over the years. In active control of vibration, the ability to actuate the system in a controlled manner is incorporated into the structure. Sensors are used to measure the vibrations and seco...
Monitoring Vibration of A Model of Rotating Machine
Arko Djajadi; Arsi Azavi; Rusman Rusyadi; Erikson Sinaga
2012-01-01
Mechanical movement or motion of a rotating machine normally causes additional vibration. A vibration sensing device must be added to constantly monitor vibration level of the system having a rotating machine, since the vibration frequency and amplitude cannot be measured quantitatively by only sight or touch. If the vibration signals from the machine have a lot of noise, there are possibilities that the rotating machine has defects that can lead to failure. In this experimental research proj...
Bandshapes in vibrational spectroscopy
A detailed account is given of the development of modern bandshape theories since 1965. An investigation into the relative contributions of statistical irreversible relaxation processes is described, for a series of molecules in which gradually the length of one molecular axis is increased. An investigation into the theoretical and experimental investigation of the broadening brought about by the effect of fluctuating intermolecular potentials on the vibrational frequency is also described. The effect of an intermolecular perturbative potential on anharmonic and Morse oscillators is discussed and the results are presented of a computation on the broadening of the vibrational band of some diatomic molecules in a rigid lattice type solvent. The broadening of the OH-stretching vibration in a number of aliphatic alcohols, the vibrational bandshapes of the acetylenic C-H stretching vibration and of the symmetric methyl stretching vibration are investigated. (Auth./ C.F.)
Errea, Ion; Calandra, Matteo; Pickard, Chris J.; Nelson, Joseph; Needs, Richard J.; Li, Yinwei; Liu, Hanyu; Zhang, Yunwei; Ma, Yanming; Mauri, Francesco
2015-04-01
We use first-principles calculations to study structural, vibrational, and superconducting properties of H2S at pressures P ≥200 GPa . The inclusion of zero-point energy leads to two different possible dissociations of H2S , namely 3 H2S →2 H3S +S and 5 H2S →3 H3S +HS2 , where both H3S and HS2 are metallic. For H3S , we perform nonperturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction (λ ≈2.64 at 200 GPa) and Tc. Anharmonicity hardens H-S bond-stretching modes and softens H-S bond-bending modes. As a result, the electron-phonon coupling is suppressed by 30% (λ ≈1.84 at 200 GPa). Moreover, while at the harmonic level Tc decreases with increasing pressure, the inclusion of anharmonicity leads to a Tc that is almost independent of pressure. High-pressure hydrogen sulfide is a strongly anharmonic superconductor.
Errea, Ion; Calandra, Matteo; Pickard, Chris J; Nelson, Joseph; Needs, Richard J; Li, Yinwei; Liu, Hanyu; Zhang, Yunwei; Ma, Yanming; Mauri, Francesco
2015-04-17
We use first-principles calculations to study structural, vibrational, and superconducting properties of H_{2}S at pressures P≥200 GPa. The inclusion of zero-point energy leads to two different possible dissociations of H2S, namely 3H2S→2H3S+S and 5H2S→3H3S+HS2, where both H3S and HS2 are metallic. For H3S, we perform nonperturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction (λ≈2.64 at 200 GPa) and Tc. Anharmonicity hardens H─S bond-stretching modes and softens H─S bond-bending modes. As a result, the electron-phonon coupling is suppressed by 30% (λ≈1.84 at 200 GPa). Moreover, while at the harmonic level Tc decreases with increasing pressure, the inclusion of anharmonicity leads to a Tc that is almost independent of pressure. High-pressure hydrogen sulfide is a strongly anharmonic superconductor. PMID:25933334
Interval process model and non-random vibration analysis
Jiang, C.; Ni, B. Y.; Liu, N. Y.; Han, X.; Liu, J.
2016-07-01
This paper develops an interval process model for time-varying or dynamic uncertainty analysis when information of the uncertain parameter is inadequate. By using the interval process model to describe a time-varying uncertain parameter, only its upper and lower bounds are required at each time point rather than its precise probability distribution, which is quite different from the traditional stochastic process model. A correlation function is defined for quantification of correlation between the uncertain-but-bounded variables at different times, and a matrix-decomposition-based method is presented to transform the original dependent interval process into an independent one for convenience of subsequent uncertainty analysis. More importantly, based on the interval process model, a non-random vibration analysis method is proposed for response computation of structures subjected to time-varying uncertain external excitations or loads. The structural dynamic responses thus can be derived in the form of upper and lower bounds, providing an important guidance for practical safety analysis and reliability design of structures. Finally, two numerical examples and one engineering application are investigated to demonstrate the feasibility of the interval process model and corresponding non-random vibration analysis method.
Non-linear vibrational modes in biomolecules: A periodic orbits description
Kampanarakis, Alexandros [Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas (FORTH), Vasilika Vouton, Heraklion 71110, Crete (Greece); Farantos, Stavros C., E-mail: farantos@iesl.forth.gr [Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas (FORTH), Vasilika Vouton, Heraklion 71110, Crete (Greece); Daskalakis, Vangelis; Varotsis, Constantinos [Department of Environmental Science and Technology, Cyprus University of Technology, 31 Archbishop Kyprianos St., P.O. Box 50329, 3603 Lemesos (Cyprus)
2012-05-03
Graphical abstract: Vibrational frequency shifts in Fe{sup IV} = O species of the active site of cytochrome c oxidase are attributed to changes in the surrounding Coulomb field. Periodic orbits analysis assists to find the most anharmonic modes in model biomolecules. Highlights: Black-Right-Pointing-Pointer Periodic orbits are extended to multidimensional potentials of biomolecules. Black-Right-Pointing-Pointer Highly anharmonic vibrational modes and center-saddle bifurcations are detected. Black-Right-Pointing-Pointer Vibrational frequencies shifts in Oxoferryl species of CcO are observed. - Abstract: The vibrational harmonic normal modes of a molecule, which are valid at energies close to an equilibrium point (a minimum, maximum or saddle of the potential energy surface), are extended by periodic orbits to high energies where anharmonicity and coupling of the degrees of freedom are significant. In this way the assignment of the spectra, and thus the extraction of dynamics in highly excited molecules, can be obtained. New vibrational modes emanating from bifurcations of periodic orbits and long living localized trajectories signal the birth and localization of new quantum states. In this article we review and further study non-linear vibrational modes for model biomolecules such as alanine dipeptide and the active site in the oxoferryl oxidation state of the enzyme cytochrome c oxidase. We locate periodic orbits which exhibit high anhamonicity and lead to center-saddle bifurcations. These modes are associated to an isomerization process in alanine dipeptide and to frequency shifts in the oxoferryl observed by modifying the Coulomb field around the Imidazole-Fe{sup IV} = O species.
The anharmonic effect study of coupled Morse oscillators for the unimolecular reaction
2008-01-01
The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential on unimolecular reaction. We shall use the systematic theoretical approach, YL method, proposed by Yao and Lin (YAO L, et. al. J Phys Chem A, 2007, 111(29): 6722-6729), which can evaluate anharmonic effects on the rate constants based on the transition state theory. In treating the anharmonic effect with the Morse oscillator potential on unimolecular reactions under collision-free conditions by using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory, the in-verse Laplace transformation of the partition functions was used to obtain the total amount of state and density of state by using the first-order and the second-order approximations of the saddle-point method. To demonstrate the anharmonic effect of the SBF Morse model, we choose some model systems and a real reaction as examples.
Impeller leakage flow modeling for mechanical vibration control
Palazzolo, Alan B.
1996-01-01
HPOTP and HPFTP vibration test results have exhibited transient and steady characteristics which may be due to impeller leakage path (ILP) related forces. For example, an axial shift in the rotor could suddenly change the ILP clearances and lengths yielding dynamic coefficient and subsequent vibration changes. ILP models are more complicated than conventional-single component-annular seal models due to their radial flow component (coriolis and centrifugal acceleration), complex geometry (axial/radial clearance coupling), internal boundary (transition) flow conditions between mechanical components along the ILP and longer length, requiring moment as well as force coefficients. Flow coupling between mechanical components results from mass and energy conservation applied at their interfaces. Typical components along the ILP include an inlet seal, curved shroud, and an exit seal, which may be a stepped labyrinth type. Von Pragenau (MSFC) has modeled labyrinth seals as a series of plain annular seals for leakage and dynamic coefficient prediction. These multi-tooth components increase the total number of 'flow coupled' components in the ILP. Childs developed an analysis for an ILP consisting of a single, constant clearance shroud with an exit seal represented by a lumped flow-loss coefficient. This same geometry was later extended to include compressible flow. The objective of the current work is to: supply ILP leakage-force impedance-dynamic coefficient modeling software to MSFC engineers, base on incompressible/compressible bulk flow theory; design the software to model a generic geometry ILP described by a series of components lying along an arbitrarily directed path; validate the software by comparison to available test data, CFD and bulk models; and develop a hybrid CFD-bulk flow model of an ILP to improve modeling accuracy within practical run time constraints.
Scattering of Neutrons by an Anharmonic Crystal
Numerical calculations have been performed for the anharmonic effects in neutron scattering. The phonon frequency widths and shifts have been calculated as a function of neutron frequency at different wave numbers and temperatures for a potential with central symmetry and for a face-centered cubic lattice
Modeling of Axial Spring Stiffness in Active Vibration Controlled Drilling
Pao William; Hashim Fakhruldin M; Parman Setyamartana
2014-01-01
During drilling process, substantial amount of vibration and shock are induced to the drill string. Active vibration controlled drilling is introduced to reduce the vibration and increase the efficiency of drilling process. In this system, two main components that determine the damping coefficient are magnetorheological (MR) damper and spring assembly. Performance of vibration damping system is depending on the viscosity of MR fluid in the damper and spring constant of spring assembly. One of...
Coupled mode parametric resonance in a vibrating screen model
Slepyan, Leonid I
2013-01-01
We consider a simple dynamic model of the vibrating screen operating in the parametric resonance (PR) mode. This model was used in the course of designing and setting of such a screen in LPMC. The PR-based screen compares favorably with conventional types of such machines, where the transverse oscillations are excited directly. It is characterized by larger values of the amplitude and by insensitivity to damping in a rather wide range. The model represents an initially strained system of two equal masses connected by a linearly elastic string. Self-equilibrated, longitudinal, harmonic forces act on the masses. Under certain conditions this results in transverse, finite-amplitude oscillations of the string. The problem is reduced to a system of two ordinary differential equations coupled by the geometric nonlinearity. Damping in both the transverse and longitudinal oscillations is taken into account. Free and forced oscillations of this mass-string system are examined analytically and numerically. The energy e...
Tian, Jialin; Wu, Chunming; Yang, Lin; Yang, Zhi; Liu, Gang; Yuan, Changfu
2016-01-01
Comparative analysis whether considering the lateral inertia or not, aiming at the longitudinal vibration of the drill string in drilling progress, is proposed. In the light of the actual condition, the mechanical model of the drill string about vibration is established on the basis of the theoretical analysis. Longitudinal vibration equation of the drill string is derived from the Rayleigh-Love model and one-dimensional viscoelastic model. According to the Laplace transform method and the re...
On the Elastic Vibration Model for High Length-Diameter Ratio Rocket with Attitude Control System
朱伯立; 杨树兴
2003-01-01
An elastic vibration model for high length-diameter ratio spinning rocket with attitude control system which can be used for trajectory simulation is established. The basic theory of elastic dynamics and vibration dynamics were both used to set up the elastic vibration model of rocket body. In order to study the problem more conveniently, the rocket's body was simplified to be an even beam with two free ends. The model was validated by simulation results and the test data.
Modelling nuclear fuel vibrations in horizontal CANDU reactors
Flow-induced fuel vibrations in the pressure tubes of CANDU reactors are of vital interest to designers because fretting damage may result. Computer simulation is being used to study how bundles vibrate and to identify bundle design features which will reduce vibration and hence fretting. (author)
The results of experimental investigations on tube vibration of model BN-1200 steam generator
Self and forced vibrations of 61-tube model of BN-1200 steam generator are studied as well as the effect of the design and operational factors on vibrational response of heat-exchanging tubes (HET). It is stated that vibrations on the frequencies near to self ones give the main contribution into total vibration level of HET in the coolant flow. The maximal of vibration level of HET is determined in the area of coolant input into the model. In the area of longitudinal flow and in the area of coolant output the level of vibrational accelerations of HET is less by several times. It is pointed out that with flow rate increase vibration level of different HET in the input area grows according to the law from linear to quadratic
Design of CAP1400 reactor internals flow-induced vibration simulation test model
While the first CAP1400 reactor internals is defined as a 'prototype', it is necessary to carry out the reactor internals flow-induced vibration simulation test for verifying the structure integrity of reactor internals and providing data for vibration assessment of CAP1400 reactor internals. The reactor internals flow-induced vibration simulation test is usually a reduced scale model test. This paper describes in detail the main factors of model scale, similarity criterion and the simplification of test model. The simplification of model will not only reduce the fabrication cost, but also obtain more accurate test data from the flow-induced vibration simulation test. (authors)
The angular distribution of the elastic and inelastic scattering of a particles corresponding to the excitation of the low-lying collective states of 142Ce were measured at an incident energy of 18.0 MeV. The angular distribution of the following excited states were obtained: 641, 1.219, 1.450, 1.536, 1.653, 1.742, 2.004, 2.043, 2.114, 2.125, 2.279, 2.364, 2.542, 2.604 e 3.067 MeV. The angular distributions of the ground state and the first six excited states were analysed within the flamework of the Anharmonic Vibrational and Symmetric Rotational Models, with the Coupled Channel Theory. The Anharmonic Vibrational Model gave the best and most complete description of the experimental data. The wave functions and the deformation parameters of the analysed states were determined. (Author)
Vibration modeling of structural fuzzy with continuous boundary
Friis, Lars; Ohlrich, Mogens
2008-01-01
From experiments it is well known that the vibration response of a main structure with many attached substructures often shows more damping than structural losses in the components can account for. In practice, these substructures, which are not attached in an entirely rigid manner, behave like a...... multitude of different sprung masses each strongly resisting any motion of the main structure (master) at their base antiresonance. The “theory of structural fuzzy” is intended for modeling such high damping. In the present article the theory of fuzzy structures is briefly outlined and a method of modeling...... effect of the fuzzy with spatial memory is demonstrated by numerical simulations of a main beam structure with fuzzy attachments. It is shown that the introduction of spatial memory reduces the damping effect of the fuzzy and in certain cases the damping effect may even be eliminated completely....
Electrons in anharmonic phonon fields of low-dimensional high-Tc superconductors
A general mathematical formulation is developed for calculating the electron response function of layered superconductors. A model Hamiltonian for the low-dimensional superconducting system is developed which includes (i) bare electron interactions, (ii) harmonic phonon fields, (iii) electron-phonon interactions, (iv) anharmonic phonons and (v) effects of localized phonon fields. Quantum dynamics of electrons is studied adopting the Green's function theory via this advanced Hamiltonian in order to describe the many-body problem. This work remarkably describes that the electron-phonon coupling coefficient shows its inevitable presence in all sectors of phonon fields, namely, the fields of (i) anharmonic phonons (ii) localized phonons and (iii) the impurity-anharmonicity interaction. The expressions for electron density of states and electron heat capacity are also obtained in the new framework. (orig.)
Interaction energies, molecular structure and vibrational frequencies of the binary complex formed between H(D)Cl and dimethyl ether have been obtained using quantum-chemical methods. Equilibrium and vibrationally averaged structures, harmonic and anharmonic wavenumbers of the complex and its deuterated isotopomer were calculated using harmonic and anharmonic second-order perturbation theory procedures with Density Functional Theory B3LYP and B2PLYP-D and ab initio Møller-Plesset second-order methods, and a 6-311++G(3d,3p) basis set. A phenomenological model describing anharmonic-type vibrational couplings within hydrogen bonds was developed to explain the unique broadening and fine structure, as well as the isotope effect of the Cl–H and Cl–D stretching IR absorption bands in the gaseous complexes with dimethyl ether, as an effect of hydrogen bond formation. Simulations of the rovibrational structure of the Cl–H and Cl–D stretching bands were performed and the results were compared with experimental spectra
Boda, Łukasz, E-mail: lboda@chemia.uj.edu.pl; Boczar, Marek; Gług, Maciej; Wójcik, Marek J. [Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Kraków (Poland)
2015-11-28
Interaction energies, molecular structure and vibrational frequencies of the binary complex formed between H(D)Cl and dimethyl ether have been obtained using quantum-chemical methods. Equilibrium and vibrationally averaged structures, harmonic and anharmonic wavenumbers of the complex and its deuterated isotopomer were calculated using harmonic and anharmonic second-order perturbation theory procedures with Density Functional Theory B3LYP and B2PLYP-D and ab initio Møller-Plesset second-order methods, and a 6-311++G(3d,3p) basis set. A phenomenological model describing anharmonic-type vibrational couplings within hydrogen bonds was developed to explain the unique broadening and fine structure, as well as the isotope effect of the Cl–H and Cl–D stretching IR absorption bands in the gaseous complexes with dimethyl ether, as an effect of hydrogen bond formation. Simulations of the rovibrational structure of the Cl–H and Cl–D stretching bands were performed and the results were compared with experimental spectra.
Allen, Philip B.
2015-08-01
The quasiharmonic (QH) approximation uses harmonic vibrational frequencies ωQ ,H(V ) computed at volumes V near V0 where the Born-Oppenheimer (BO) energy Eel(V ) is minimum. When this is used in the harmonic free energy, QH approximation gives a good zeroth order theory of thermal expansion and first-order theory of bulk modulus, where nth-order means smaller than the leading term by ɛn, where ɛ =ℏ ωvib/Eel or kBT /Eel , and Eel is an electronic energy scale, typically 2 to 10 eV. Experiment often shows evidence for next-order corrections. When such corrections are needed, anharmonic interactions must be included. The most accessible measure of anharmonicity is the quasiparticle (QP) energy ωQ(V ,T ) seen experimentally by vibrational spectroscopy. However, this cannot just be inserted into the harmonic free energy FH. In this paper, a free energy is found that corrects the double-counting of anharmonic interactions that is made when F is approximated by FH( ωQ(V ,T ) ) . The term "QP thermodynamics" is used for this way of treating anharmonicity. It enables (n +1 ) -order corrections if QH theory is accurate to order n . This procedure is used to give corrections to the specific heat and volume thermal expansion. The QH formulas for isothermal (BT) and adiabatic (BS) bulk moduli are clarified, and the route to higher-order corrections is indicated.
1/N-expansion and nonclassical state generation in higher-order anharmonic oscillators
Alekseev, K N; Perina, J; Alekseev, Kirill N.; Alekseeva, Natasha V.; Perina, Jan
1998-01-01
We consider the nonclassical states generation in weakly dissipative high-order anharmonic oscillators in the limit of large number of photons. We find the explicit time dependences of squeezing and Fano factor in the short-time approximation and for a finite temperature of reservoir. We show that the rate of squeezing is determined by an interplay between the polarization of the nonlinear medium modelled by the anharmonic oscillator and the thermal fluctuations of a reservoir. We demonstrate that photon statistics is super-Poissonian for any degree of the nonlinearity and determine the critical temperature of reservoir destroying light squeezing.
Crystal anharmonicity in Li(H,D) and Na(H,D) systems
The reliability of our recently developed potential model is tested by extending the study to various anharmonic properties, e.g., third order elastic constants, fourth order elastic constants, Grueneisen parameters, and the pressure derivatives of second order elastic constants of hydrides and deuterides of lithium and sodium. A comparison of the calculated properties with the available experimental results and other theoretical estimates shows the validity and reliability of the derived potential in the study of crystal anharmonicities also. (author). 43 refs, 2 figs, 4 tabs
Anharmonicities and non-linearities in the excitation of double giant resonances
The non-linear response of a quantum anharmonic oscillator is investigated as a model for the excitation of giant resonances in heavy ion collisions. It is shown that the introduction of small anharmonicities and non-linearities can double the predicted cross section for the excitation of the two-phonon states. These findings suggest that such ingredients must be included in future more complete calculations in order to reduce the huge discrepancy between the previous theoretical predictions and the experimental cross section of double giant resonance states. (author)
Vibrational exciton-mediated quantum state transfert: a simple model
Pouthier, Vincent J C
2012-01-01
A communication protocol is proposed in which quantum state transfer is mediated by a vibrational exciton. We consider two distant molecular groups grafted on the sides of a lattice. These groups behave as two quantum computers where the information in encoded and received. The lattice plays the role of a communication channel along which the exciton propagates and interacts with a phonon bath. Special attention is paid for describing the system involving an exciton dressed by a single phonon mode. The Hamiltonian is thus solved exactly so that the relevance of the perturbation theory is checked. Within the nonadiabatic weak-coupling limit, it is shown that the system supports three quasi-degenerate states that define the relevant paths followed by the exciton to tunnel between the computers. When the model parameters are judiciously chosen, constructive interferences take place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperat...
Forced vibration tests of a model foundation on rock ground
The response of very stiff structures, such as nuclear reactor buildings, to earthquake ground motion is significantly affected by radiation damping due to the soil-structure interaction. The radiation damping can be computed by vibration admittance theory or dynamical ground compliance theory. In order to apply the values derived from these theories to the practical problems, comparative studies between theoretical results and experimental results concerning the soil-structure interaction, especially if the ground is rock, are urgently needed. However, experimental results for rock are less easily obtained than theoretical ones. The purpose of this paper is to describe the harmonic excitation tests of a model foundation on rock and to describe the results of comparative studies. (orig./HP)
A Spin Glass Model with Vibrations of Crystal Lattices
SHANG Yu-Min; CHENG Li-Min; YAO Kai-Lun
2005-01-01
@@ With the help of the replica method and imaginary-time functional-integrate technique, the spin glas s model with the vibrations of crystal lattices is investigated. In the limit of the replica symmetry and the imaginary-time staticapproximation, the magnetic and thermodynamic quantities have been obtained. By the numerical calculations,we found that the magnetization of the system has the typical spin-glass behaviour. A peak is found in the susceptibility-temperature curve and is shifted to lower temperature with increasing applied field. Due to the lattice contribution, the specific heat increas es strongly at high temperature. Due to the magnetic contribution,the anomaly in the specific heat-temperature curve forms a λ-type peak, which agrees with the observation ofRojo et al. [Phys. Rev. B 66 (2002) 094406].
Nonlinear Models for Transverse Forced Vibration of Axially Moving Viscoelastic Beams
Hu Ding
2011-01-01
Full Text Available Nonlinear models of transverse vibration of axially moving viscoelastic beams subjected external transverse loads via steady-state periodical response are numerically investigated. An integro-partial-differential equation and a partial-differential equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. The finite difference scheme is developed to calculate steady-state response for the model of coupled planar and the two models of transverse motion under the simple support boundary. Numerical results indicate that the amplitude of the steady-state response for the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters and the integro-partial-differential equation gives results more closely to the coupled planar vibration.
Torsional Vibrations at Guide-Vane Shaft of Pump–Turbine Model
Andrej Predin
1997-01-01
Full Text Available This article focuses on the problem of guide-vane vibrations of reversible pump–turbines, especially, in the pump mode. These vibrations are transmitted to the guide-vane shaft torque. The guide-vane vibrations are caused by the impeller exit flow, which has a turbulent and partly nondeterministic property. Experimentally determined flow velocities at the impeller exit are given. The mathematical models for theoretical torsional vibration prediction formulated using linear and nonlinear differential equations are presented. The results of theoretical calculations are compared with measurement results. The possibility of transferring the parameters from the model to the prototype is discussed.
ANALYSIS AND MODELLING OF BIODYNAMIC RESPONSE TO HAND ARM VIBRATION SYSTEM
Mohod Chandrashekhar D
2016-01-01
Full Text Available Hand operated tools are widely used in industrial and commercial sector. These tools generate vibrations which have impact on health of an operator. Hence study of Hand Vibration Syndrome is one of the key areas where major researchers are attracted. This study considers the literature review for hand operated vibration measurement and analysis that are extensively used. Objective of this review was to understand results and effects of hand vibration transmission on health. The review could be used to develop a prediction model with use of Adaptive Neuro Fuzzy Inference System hence another objective is to represent the applicability of ANFIS in development of the model
Modelling and Analysis of Vibrations in a UAV Helicopter with a Vision System
G. Nicolás Marichal Plasencia; María Tomás Rodríguez; Salvador Castillo Rivera; Ángela Hernández López
2012-01-01
The analysis of the nature and damping of unwanted vibrations on Unmanned Aerial Vehicle (UAV) helicopters are important tasks when images from on‐board vision systems are to be obtained. In this article, the authors model a UAV system, generate a range of vibrations originating in the main rotor and design a control methodology in order to damp these vibrations. The UAV is modelled using VehicleSim, the vibrations that appear on the fuselage are analysed to study their effects on the on‐boar...
Quantum anharmonic oscillator: The airy function approach
Maiz, F., E-mail: fethimaiz@gmail.com [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia); University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); AlFaify, S. [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia)
2014-05-15
New and simple numerical method is being reported to solve anharmonic oscillator problems. The method is setup to approach the real potential V(x) of the anharmonic oscillator system as a piecewise linear potential u(x) and to solve the Schrödinger equation of the system using the Airy function. Then, solutions continuity conditions lead to the energy quantification condition, and consequently, the energy eigenvalues. For testing purpose, the method was applied on the sextic and octic oscillators systems. The proposed method is found to be realistic, computationally simple, and having high degrees of accuracy. In addition, it can be applied to any form of potential. The results obtained by the proposed method were seen closely agreeing with results reached by other complicated methods.
Anharmonic oscillations of a conical buoy
Oliveira, J Brochado; da Silva, J M Machado
2011-01-01
A study of the foating of a circular cone shaped buoy in an ideal fluid has revealed some new interesting results. Using reduced variables it is shown, that at a crossover value (3/4) of the ratio of the specific masses of the fluid and of the buoy, the anharmonicity of the oscillation is the highest and that, unexpectedly, above this crossover value the normalized period is constant.
Two-phase CFD modeling of flow causing the heater vibration
Vibrations of heater rods were observed in a heated annulus with water flow under boiling conditions. In order to find out the cause of such vibrations, CFD model of this annulus has been prepared in CFD code STAR-CCM+. Two-phase flow in the annulus was described using a two-fluid model with number of sub-models to describe the mass, momentum and energy transfer between phases. The model was validated using experimental data from reference. The validated model was used to perform a steady state calculation of flow parameters under different conditions. Results of CFD simulations were compared to experimentally detected vibration offset. It was found out that vibration increase caused by heating the channel is connected with the vibration offset. The results and their extension to nuclear safety were discussed. (author)
Aerodynamic and structural modeling for vortex-excited vibrations in bundled conductors
Verma, Himanshu
2009-01-01
Wind excited vibrations generated by the vortex shedding are very common in high-voltage overhead transmission lines. Although such vibrations are barely perceptible due to their low amplitudes (less than a conductor diameter), controlling them, however, is extremely important since they may lead to conductor fatigue. Mathematical models are therefore necessary for the computation of these vibrations, not only to evaluate the risk of potential damage to the transmission line but also for stud...
Modelling of vibrational optical activity of fibrillar systems
Kessler, Jiří; Kapitán, J.; Yamamoto, S.; Kiederling, T. A.; Bouř, Petr
Vienna : Vienna University of Technology, 2015 - (Lendl, B.; Koch, C.; Kraft, M.; Ofner, J.; Ramer, G.). s. 504-505 ISBN 978-3-200-04205-6. [ICAVS8. International Conference on Advanced Vibrational Spectroscopy /8./. 12.07.2015-17.07.2015, Vienna] Institutional support: RVO:61388963 Keywords : vibrational optical activity * proteins * fibrills Subject RIV: CF - Physical ; Theoretical Chemistry
No suitable handy tool is available to predict train-induced vibration on environmental impact assessment. A simple prediction model is proposed which has been calibrated for high speed trains. The model input data are train characteristics, train speed and track properties; model output data are soil time-averaged velocity and velocity level. Model results have been compared with numerous vibration data retrieved from measurement campaigns led along the most important high-speed European rail tracks. Model performances have been tested by comparing measured and predicted vibration values
Hernández-Rojas, Javier; Calvo, Florent; Noya, Eva Gonzalez
2015-03-10
The semiclassical method of quantum thermal baths by colored noise thermostats has been used to simulate various atomic systems in the molecular and bulk limits, at finite temperature and in moderately to strongly anharmonic regimes. In all cases, the method performs relatively well against alternative approaches in predicting correct energetic properties, including in the presence of phase changes, provided that vibrational delocalization is not too strong-neon appearing already as an upper limiting case. In contrast, the dynamical behavior inferred from global indicators such as the root-mean-square bond length fluctuation index or the vibrational spectrum reveals more marked differences caused by zero-point energy leakage, except in the case of isolated molecules with well separated vibrational modes. To correct for such deficiencies and reduce the undesired transfer among modes, empirical modifications of the noise power spectral density were attempted to better describe thermal equilibrium but still failed when used as semiclassical preparation for microcanonical trajectories. PMID:26579740
Vibrations of liquid drops in film boiling phenomena: the mathematical model
Casal, Pierre
2008-01-01
Flattened liquid drops poured on a very hot surface evaporate quite slowly and float on a film of their own vapour. In the cavities of a surface, an unusual type of vibrational motions occurs. Large vibrations take place and different forms of dynamic drops are possible. They form elliptic patterns with two lobes or hypotrochoid patterns with three lobes or more. The lobes are turning relatively to the hot surface. We present a model of vibrating motions of the drops. Frequencies of the vibrations are calculated regarding the number of lobes. The computations agree with experiments.
Modeling of metallic surface topography modification by high-frequency vibration
Yao, Zhehe; Mei, Deqing; Chen, Zichen
2016-02-01
High-frequency vibration is capable of modifying metallic surface topography significantly, while the underlying mechanisms are still unclear. In this study, the acoustic softening effect is considered to explain and model the effects of high-frequency normal vibration on surface topography. The surface asperities can be softened by the high-frequency vibration due to acoustic softening, leading to the enhancement of surface topography modification. A theoretical model for metallic surface topography modification by high-frequency vibration is proposed based on the acoustic plasticity. Numerical predictions of surface roughness evolution were conducted under various working conditions based on the model developed. It was found that the reduction of surface roughness (RSR) after vibration-assisted forming was affected by static stress, vibration amplitude, material properties and initial specimen surface roughness. The predictions using the developed model were compared with experimental data. Results showed that the predicted RSR agreed well with the experimental results, indicating that the analytical model is able to accurately capture surface topography evolution during vibration-assisted metal forming. This study provides a basis for understanding the underlying mechanisms of surface topography modification in vibration-assisted manufacturing.
Quadrupole and monopole large amplitude vibrations
A set of nonlinear dynamical equations for quadrupole and monopole moments of nuclei is derived from the TDHF equation with the help of the so-called Wigner function moments. It allows the description of coupled large amplitude monopole and quadrupole vibrations. These equations are solved numerically for 208Pb and 40Ca in a model with separable forces. The giant quadrupole and monopole resonances are reproduced very well. However the essential feature of the large amplitude motion is the existence of multiphonon states. They are analyzed in detail. The classical and quantum aspects of the analytically solvable one-dimensional pure monopole model are studied to clarify the problem of the anharmonicity of the collective spectrum. 26 refs., 2 figs., 2 tabs
Implementation of a vibrationally linked chemical reaction model for DSMC
Carlson, A. B.; Bird, Graeme A.
1994-01-01
A new procedure closely linking dissociation and exchange reactions in air to the vibrational levels of the diatomic molecules has been implemented in both one- and two-dimensional versions of Direct Simulation Monte Carlo (DSMC) programs. The previous modeling of chemical reactions with DSMC was based on the continuum reaction rates for the various possible reactions. The new method is more closely related to the actual physics of dissociation and is more appropriate to the particle nature of DSMC. Two cases are presented: the relaxation to equilibrium of undissociated air initially at 10,000 K, and the axisymmetric calculation of shuttle forebody heating during reentry at 92.35 km and 7500 m/s. Although reaction rates are not used in determining the dissociations or exchange reactions, the new method produces rates which agree astonishingly well with the published rates derived from experiment. The results for gas properties and surface properties also agree well with the results produced by earlier DSMC models, equilibrium air calculations, and experiment.
Vibration modeling of structural fuzzy with continuous boundary.
Friis, Lars; Ohlrich, Mogens
2008-02-01
From experiments it is well known that the vibration response of a main structure with many attached substructures often shows more damping than structural losses in the components can account for. In practice, these substructures, which are not attached in an entirely rigid manner, behave like a multitude of different sprung masses each strongly resisting any motion of the main structure (master) at their base antiresonance. The "theory of structural fuzzy" is intended for modeling such high damping. In the present article the theory of fuzzy structures is briefly outlined and a method of modeling fuzzy substructures examined. This is done by new derivations and physical interpretations are provided. Further, the method is extended and simplified by introducing a simple deterministic approach to determine the boundary impedance of the structural fuzzy. By using this new approach, the damping effect of the fuzzy with spatial memory is demonstrated by numerical simulations of a main beam structure with fuzzy attachments. It is shown that the introduction of spatial memory reduces the damping effect of the fuzzy and in certain cases the damping effect may even be eliminated completely. PMID:18247876
Accurate ab initio anharmonic force field and heat of formation for silane, $SiH_{4}$
Martin, J M L; Lee, T J; Martin, Jan M.L.; Baldridge, Kim K.; Lee, Timothy J.
1999-01-01
From large basis set coupled cluster calculations and a minor empirical adjustment, an anharmonic force field for silane has been derived that is consistently of spectroscopic quality ($\\pm 1 cm^{-1}$ on vibrational fundamentals) for all isotopomers of silane studied. Inner-shell polarization functions have an appreciable effect on computed properties and even on anharmonic corrections. From large basis set coupled cluster calculations and extrapolations to the infinite-basis set limit, we obtain TAE_0=303.80 \\pm 0.18 kcal/mol, which includes an anharmonic zero-point energy (19.59 kcal/mol), inner-shell correlation (-0.36 kcal/mol), scalar relativistic corrections (-0.70 kcal/mol), and atomic spin-orbit corrections (-0.43 kcal/mol). In combination with the recently revised \\HVSI{0}, we obtain $\\Delta H^{\\circ}_{f,0}[SiH_4(g)]=9.9 \\pm 0.4 kcal/mol$, in between the two established experimental values.
Active control of structural vibration with on-line secondary path modeling
YANG Tiejun; GU Zhongquan
2004-01-01
An active control strategy with on-line secondary path modeling is proposed and applied in active control of helicopter structural vibration. Computer simulations of the secondary path modeling performance demonstrate the superiorities of the active control strategy. A 2-input 4-output active control simulation for a helicopter model is performed and great reduction of structural vibration is achieved. 2-input 2-output and 2-input 4-output experimental studies of structural vibration control for a free-free beam are also carried out in laboratory to simulate a flying helicopter. The experimental results also show better reduction of the structural vibration, which verifies that the proposed method is effective and practical in structural vibration reduction.
Peng Guo
2012-12-01
Full Text Available With appropriate vibration modeling and analysis the incipient failure of key components such as the tower, drive train and rotor of a large wind turbine can be detected. In this paper, the Nonlinear State Estimation Technique (NSET has been applied to model turbine tower vibration to good effect, providing an understanding of the tower vibration dynamic characteristics and the main factors influencing these. The developed tower vibration model comprises two different parts: a sub-model used for below rated wind speed; and another for above rated wind speed. Supervisory control and data acquisition system (SCADA data from a single wind turbine collected from March to April 2006 is used in the modeling. Model validation has been subsequently undertaken and is presented. This research has demonstrated the effectiveness of the NSET approach to tower vibration; in particular its conceptual simplicity, clear physical interpretation and high accuracy. The developed and validated tower vibration model was then used to successfully detect blade angle asymmetry that is a common fault that should be remedied promptly to improve turbine performance and limit fatigue damage. The work also shows that condition monitoring is improved significantly if the information from the vibration signals is complemented by analysis of other relevant SCADA data such as power performance, wind speed, and rotor loads.
Vibration measurements of a wire scanner - Experimental setup and models
Herranz, Juan; Barjau, Ana; Dehning, Bernd
2016-03-01
In the next years the luminosity of the LHC will be significantly increased. This will require a much higher accuracy of beam profile measurement than actually achievable by the current wire scanner. The new performance demands a wire travelling speed up to 20 m s-1 and a position measurement accuracy of the order of 1 μm. The vibrations of the mechanical parts of the system and particularly the vibrations of the thin carbon wire have been identified as the major error sources of wire position uncertainty. Therefore the understanding of the wire vibrations has been given high priority for the design and operation of the new device. This article presents a new strategy to measure the wire vibrations based on the piezoresistive effect of the wire itself. An electronic readout system based on a Wheatstone bridge is used to measure the variation of the carbon wire resistance, which is directly proportional to the wire elongation caused by the oscillations.
The theoretical modeling and monitoring of WWER fuel assembly vibrations under operating conditions
A configuration of a fuel assembly (FA) vibration monitoring system is proposed in the paper. The vibration monitoring of the fuel assembly (FA) is the main experimental support during the processes of FA design, FA commissioning and FA commercial operation. Such monitoring is addressed to define the limits for hydrodynamic loadings of the FA and to estimate the characteristics of FA dynamic response. The last should include the estimation of vibration both FA and internal as a whole, because the oscillations of the FA and internals have interdependent nature and in many respects are determined by an actual conditions of support structures. The paper also presents a flow chart of the FA vibration analysis including internal relations and feedbacks as well as a configuration of FA vibration monitoring system. The necessity of the theoretical modeling of fuel vibration characteristics is discussed and used for interpretation of the monitoring results related to the probable abnormal vibrational conditions. Some results of vibration-noise measurements of WWER-440 fuel assemblies as an example of vibration monitoring system application are also given in this work
Modelling flow-induced vibrations of gates in hydraulic structures
Erdbrink, C.D.
2014-01-01
The dynamic behaviour of gates in hydraulic structures caused by passing flow poses a potential threat to flood protection. Complex interactions between the turbulent flow and the suspended gate body may induce undesired vibrations. This thesis contributes to a better understanding and prevention of gate vibrations by employing a variety of computational approaches. Simulations with the finite-element method are used to analyse the fluid-structure interaction of a new underflow gate type whic...
Non-linear model of a ball vibration absorber
Náprstek, Jiří; Fischer, Cyril; Pirner, Miroš; Fischer, Ondřej
Vol. 2. Dordrecht : Springer, 2013 - (Papadrakakis, M.; Fragiadakis, M.; Plevris, V.), s. 381-396 ISBN 978-94-007-6572-6. - (Computational Methods in Applied Sciences. 30) R&D Projects: GA ČR(CZ) GA103/09/0094; GA AV ČR(CZ) IAA200710902; GA AV ČR(CZ) IAA200710805 Institutional support: RVO:68378297 Keywords : vibration ball absorber * dynamic stability * nonlinear vibration Subject RIV: JM - Building Engineering
Lei, Yaguo; Liu, Zongyao; Lin, Jing; Lu, Fanbo
2016-05-01
Condition monitoring and fault diagnosis of epicyclic gearboxes using vibration signals are not as straightforward as that of fixed-axis gearboxes since epicyclic gearboxes behave quite differently from fixed-axis gearboxes in many aspects, like spectral structures. Aiming to present the spectral structures of vibration signals of epicyclic gearboxes, phenomenological models of vibration signals of epicyclic gearboxes are developed by algebraic equations and spectral structures of these models are deduced using Fourier series analysis. In the phenomenological models, all the possible vibration transfer paths from gear meshing points to a fixed transducer and the effects of angular shifts of planet gears on the spectral structures are considered. Accordingly, time-varying vibration transfer paths from sun-planet/ring-planet gear meshing points to the fixed transducer due to carrier rotation are given by window functions with different amplitudes. And an angular shift in one planet gear position is introduced in the process of modeling. After the theoretical derivations, three experiments are conducted on an epicyclic gearbox test rig and the spectral structures of collected vibration signals are analyzed. As a result, the effects of angular shifts of planet gears are verified, and the phenomenological models of vibration signals when a local fault occurs on the sun gear and the planet gear are validated, respectively. The experiment results demonstrate that the established phenomenological models in this paper are helpful to the condition monitoring and fault diagnosis of epicyclic gearboxes.
Equivalent linearization technique for quantum anharmonic oscillators
Quantum dynamics means studying the evolution of an initially prescribed wave function. This is analytically tractable for special wavefunctions for the simplest of the situations—free particle and simple harmonic oscillator. The purely anharmonic oscillators are virtually impossible to handle. We show here that the study of Ehrenfest's equation provides an alternative route to studying quantum dynamics. It does not give exact answers but clarifies some basic aspects of quantum dynamics by providing a prescription for constructing equivalent simple harmonic oscillators. (paper)
A microscopic nuclear collective rotation-vibration model: 2D submodel
Gulshani, Parviz
2016-01-01
The previous microscopic collective rotation-vibration model is improved to include interaction between collective oscillations in a pair of spatial directions, and to remove many of the previous-model approximations. As in the previous model, the nuclear Schrodinger equation (instead of the Hamiltonian) is canonically transformed to obtain a Schrodinger equation for collective rotation and vibration of a nucleus coupled to an intrinsic motion, with the related constraints imposed on the wave...
Quantum dissipative effect of one dimension coupled anharmonic oscillator
Quantum dissipative effect of one dimension coupled anharmonic oscillator is investigated. The systems are two coupled harmonic oscillator with the different masses. The dissipative effect is studied based on the quantum state diffusion formalism. The result show that the anharmonic effect increase the amplitude but the lifetime of the oscillation depend on the damping coefficient and do not depend on the temperature
Quantum dissipative effect of one dimension coupled anharmonic oscillator
Sulaiman, A. [Badan Pengkajian dan Penerapan Teknologi, BPPT Bld. II (19thfloor), Jl. M.H. Thamrin 8, Jakarta 10340 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10, Bandung 40132 (Indonesia); Zen, Freddy P. [Theoretical Physics Laboratory (THEPI), Department of Physics, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10, Bandung 40132 (Indonesia)
2015-04-16
Quantum dissipative effect of one dimension coupled anharmonic oscillator is investigated. The systems are two coupled harmonic oscillator with the different masses. The dissipative effect is studied based on the quantum state diffusion formalism. The result show that the anharmonic effect increase the amplitude but the lifetime of the oscillation depend on the damping coefficient and do not depend on the temperature.
Ahmed, M.; Gu, F.; Ball, A. D.
2012-05-01
Traditional vibration monitoring techniques have found it difficult to determine a set of effective diagnostic features due to the high complexity of the vibration signals originating from the many different impact sources and wide ranges of practical operating conditions. In this paper Principal Component Analysis (PCA) is used for selecting vibration feature and detecting different faults in a reciprocating compressor. Vibration datasets were collected from the compressor under baseline condition and five common faults: valve leakage, inter-cooler leakage, suction valve leakage, loose drive belt combined with intercooler leakage and belt loose drive belt combined with suction valve leakage. A model using five PCs has been developed using the baseline data sets and the presence of faults can be detected by comparing the T2 and Q values from the features of fault vibration signals with corresponding thresholds developed from baseline data. However, the Q -statistic procedure produces a better detection as it can separate the five faults completely.
Analysis and Modelling of Muscles Motion during Whole Body Vibration
La Gatta A
2010-01-01
Full Text Available The aim of the study is to characterize the local muscles motion in individuals undergoing whole body mechanical stimulation. In this study we aim also to evaluate how subject positioning modifies vibration dumping, altering local mechanical stimulus. Vibrations were delivered to subjects by the use of a vibrating platform, while stimulation frequency was increased linearly from 15 to 60 Hz. Two different subject postures were here analysed. Platform and muscles motion were monitored using tiny MEMS accelerometers; a contra lateral analysis was also presented. Muscle motion analysis revealed typical displacement trajectories: motion components were found not to be purely sinusoidal neither in phase to each other. Results also revealed a mechanical resonant-like behaviour at some muscles, similar to a second-order system response. Resonance frequencies and dumping factors depended on subject and his positioning. Proper mechanical stimulation can maximize muscle spindle solicitation, which may produce a more effective muscle activation.
Electromagnetic Vibration Energy Harvesting Devices Architectures, Design, Modeling and Optimization
Spreemann, Dirk
2012-01-01
Electromagnetic vibration transducers are seen as an effective way of harvesting ambient energy for the supply of sensor monitoring systems. Different electromagnetic coupling architectures have been employed but no comprehensive comparison with respect to their output performance has been carried out up to now. Electromagnetic Vibration Energy Harvesting Devices introduces an optimization approach which is applied to determine optimal dimensions of the components (magnet, coil and back iron). Eight different commonly applied coupling architectures are investigated. The results show that correct dimensions are of great significance for maximizing the efficiency of the energy conversion. A comparison yields the architectures with the best output performance capability which should be preferably employed in applications. A prototype development is used to demonstrate how the optimization calculations can be integrated into the design–flow. Electromagnetic Vibration Energy Harvesting Devices targets the design...
Structure and vibrational spectra of a model of a-Si:H with periodic boundary conditions
Winer, K.; Wooten, F.
1983-08-01
A ball-and -stick model of a-Si:H with periodic boundary conditions has been constructed. A computer replica of the structure has been relaxed and the density, radial distribution function and vibrational spectra calculated.
Simplified vibration analysis method of shells of revolution using beam model
A simplified vibration analysis method for the shells of revolution using the beam model is now under consideration. In the beam model, the relations between the shear forces and horizontal deformations are used for the calculations of the shear area and the relations between the overturning moments and rotation angles are for those of the inertia moment. The calculations of the vibration characteristics of the cylindrical shell, spherical shell and the cylindrical shell with the spherical cap were conducted to verify the accuracy of the beam model. The natural frequencies and the vibration modes of the proposed method are in good agreement with that of the FEM analysis using the axisymmetrical shell model. The proposed method is easily applicable to the vibration analysis of actual shell structures. (author)
Cohesive and anharmonic elastic properties of mixed fluorite crystals
The cohesive and anharmonic elastic properties of four mixed fluorite crystals (CaxSr1-xF2, SrxBa1-xF2, BaxCa1-xF2 and CdxPb1-xF2) have been investigated by means of a three-body potential (TBP) model which consists of the long-range Coulomb and three-body interactions and the short-range van der Waals attraction and overlap repulsion effective upto the second neighbour ions. Due to the lack of measured data on cohesive energy, third-order elastic constants and pressure derivatives of the second-order elastic constants of mixed fluorites, the accuracy of the present results has been tested by comparing them with the so-called experimental results generated by the application of Vegard's law to their corresponding experimental values for the host fluorites. (author). 32 refs, 3 figs, 1 tab
Approximation methods for the partition functions of anharmonic systems
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations
Estimation of Reversed Flow in Long Pipeline Based on Axial Vibration Model of Dense Paste
Fuyan Lyu
2016-01-01
Full Text Available Intense axial vibration of the paste and the reversed flow make damage to the transportation system and lag the transport progress. This paper analyzed the axial vibration of the paste by building the vibration model according to the working situations of the system. The amount of the reversed flow share is then estimated based on the formed axial vibration model. The estimation of the reversed flow is carried out by counting the amount of the decompressed paste in certain time, which is being relative to the displacement in a single process of the vibration in numerical. The estimation of the reversed flow share of coal slime paste under certain transportation conditions was given and compared with the result based on the wave velocity method. It is evident that the introduction of axial vibration model into the study of the pipeline transportation system is feasible and reasonable, which also supplements the theoretical foundation for the analysis of dense paste vibrations in pipeline transportation system and its impacts on the system.
Nonlinear Model and Qualitative Analysis for Coupled Axial/Torsional Vibrations of Drill String
Fushen Ren; Baojin Wang; Suli Chen; Zhigang Yao; Baojun Bai
2016-01-01
A nonlinear dynamics model and qualitative analysis are presented to study the key effective factors for coupled axial/torsional vibrations of a drill string, which is described as a simplified, equivalent, flexible shell under axial rotation. Here, after dimensionless processing, the mathematical models are obtained accounting for the coupling of axial and torsional vibrations using the nonlinear dynamics qualitative method, in which excitation loads and boundary conditions of the drill stri...
Yao, J M
2016-01-01
We discuss anharmonicity of the multi-octupole-phonon states in $^{208}$Pb based on a covariant density functional theory, by fully taking into account the interplay between the quadrupole and the octupole degrees of freedom. Our results indicate the existence of a large anharmonicity in the transition strengths, even though the excitation energies are similar to those in the harmonic limit. We also show that the quadrupole-shape fluctuation significantly enhances the fragmentation of the two-octupole-phonon states in $^{208}$Pb. Using those transition strengths as inputs to coupled channels calculations, we then discuss the fusion reaction of $^{16}$O+$^{208}$Pb at energies around the Coulomb barrier. We show that the anharmonicity of the octupole vibrational excitation considerably improves previous coupled-channels calculations in the harmonic oscillator limit, significantly reducing the height of the main peak in the fusion barrier distribution.
A new online secondary path modeling method for adaptive active structure vibration control
This paper proposes a new variable step size FXLMS algorithm with an auxiliary noise power scheduling strategy for online secondary path modeling. The step size for the secondary path modeling filter and the gain of auxiliary noise are varied in accordance with the parameters available directly. The proposed method has a low computational complexity. Computer simulations show that an active vibration control system with the proposed method gives much better vibration attenuation and modeling accuracy at a faster convergence rate than existing methods. National Instruments’ CompactRIO is used as an embedded processor to control simply supported beam vibration. Experimental results indicate that the vibration of the beam has been effectively attenuated. (papers)
RESEARCH ON ACTIVE VIBRATION CONTROL BASED ON COMBINED MODEL FOR COUPLED SYSTEMS
Niu Junchuan; Zhao Guoqun; Song Kongjie
2004-01-01
A novel combined model of the vibration control for the coupled flexible system and its general mathematic description are developed. In presented model, active and passive controls as well as force and moment controls are combined into a single unit to achieve the efficient vibration control of the flexible structures by multi-approaches. Considering the complexity of the energy transmission in the vibrating system, the transmission channels of the power flow transmitted into the foundation are discussed, and the general forces and the corresponding velocities are combined into a single function, respectively. Under the control strategy of the minimum power flow, the transmission characteristics of the power flow are investigated. From the presented numerical examples, it is obvious that the analytical model is effective, and both force and moment controls are able to depress vibration energy substantially.
Vibrational relaxation in liquids: Comparisons between gas phase and liquid phase theories
The vibrational relaxation of iodine in liquid xenon was studied to understand what processes are important in determining the density dependence of the vibrational relaxation. This examination will be accomplished by taking simple models and comparing the results to both experimental outcomes and the predictions of molecular dynamics simulations. The vibration relaxation of iodine is extremely sensitive to the iodine potential. The anharmonicity of iodine causes vibrational relaxation to be much faster at the top of the iodine well compared to the vibrational relaxation at the bottom. A number of models are used in order to test the ability of the Isolated Binary Collision theory's ability to predict the density dependence of the vibrational relaxation of iodine in liquid xenon. The models tested vary from the simplest incorporating only the fact that the solvent occupies volume to models that incorporate the short range structure of the liquid in the radial distribution function. None of the models tested do a good job of predicting the actual relaxation rate for a given density. This may be due to a possible error in the choice of potentials to model the system
Influence of tyre-road contact model on vehicle vibration response
Múčka, Peter; Gagnon, Louis
2015-09-01
The influence of the tyre-road contact model on the simulated vertical vibration response was analysed. Three contact models were compared: tyre-road point contact model, moving averaged profile and tyre-enveloping model. In total, 1600 real asphalt concrete and Portland cement concrete longitudinal road profiles were processed. The linear planar model of automobile with 12 degrees of freedom (DOF) was used. Five vibration responses as the measures of ride comfort, ride safety and dynamic load of cargo were investigated. The results were calculated as a function of vibration response, vehicle velocity, road quality and road surface type. The marked differences in the dynamic tyre forces and the negligible differences in the ride comfort quantities were observed among the tyre-road contact models. The seat acceleration response for three contact models and 331 DOF multibody model of the truck semi-trailer was compared with the measured response for a known profile of test section.
Zhao, S.; Erturk, A.
2013-01-01
We present electroelastic modeling, analytical and numerical solutions, and experimental validations of piezoelectric energy harvesting from broadband random vibrations. The modeling approach employed herein is based on a distributed-parameter electroelastic formulation to ensure that the effects of higher vibration modes are included, since broadband random vibrations, such as Gaussian white noise, might excite higher vibration modes. The goal is to predict the expected value of the power output and the mean-square shunted vibration response in terms of the given power spectral density (PSD) or time history of the random vibrational input. The analytical method is based on the PSD of random base excitation and distributed-parameter frequency response functions of the coupled voltage output and shunted vibration response. The first of the two numerical solution methods employs the Fourier series representation of the base acceleration history in an ordinary differential equation solver while the second method uses an Euler-Maruyama scheme to directly solve the resulting electroelastic stochastic differential equations. The analytical and numerical simulations are compared with several experiments for a brass-reinforced PZT-5H bimorph under different random excitation levels. The simulations exhibit very good agreement with the experimental measurements for a range of resistive electrical boundary conditions and input PSD levels. It is also shown that lightly damped higher vibration modes can alter the expected power curve under broadband random excitation. Therefore, the distributed-parameter modeling and solutions presented herein can be used as a more accurate alternative to the existing single-degree-of-freedom solutions for broadband random vibration energy harvesting.
Fundamental studies in vibrational energy harvesting consider the electromechanically coupled devices to be excited by uniform base vibration. Since many harvester devices are mass–spring systems, there is a clear opportunity to exploit the mechanical resonance in a fashion identical to tuned mass dampers to simultaneously suppress the vibration of the host structure via reactive forces while converting the ‘absorbed’ vibration into electrical power. This paper presents a general analytical model for the coupled electro-elastic dynamics of a vibrating panel to which distributed energy harvesting devices are attached. One such device is described which employs a corrugated piezoelectric spring layer. The model is validated by comparison to measured elastic and electric frequency response functions. Tests on an excited panel show that the device, contributing 1% additional mass to the structure, concurrently attenuates the lowest panel mode accelerance by >20 dB while generating 0.441 µW for a panel drive acceleration of 3.29 m s−2. Adjustment of the load resistance connected to the piezoelectric spring layer verifies the analogy between the present harvester device and an electromechanically stiffened and damped vibration absorber. The results show that maximum vibration suppression and energy harvesting objectives occur for nearly the same load resistance in the harvester circuit. (paper)
Research on the Identification Modeling of Air-Magnet Active Vibration Isolation System
Wen Xianglong
2015-01-01
Full Text Available The methods of the identification modeling of air-magnet active vibration isolation system (AMAVIS are studied. Difference equation model and transfer function model are established respectively in the time domain and frequency domain. The models are analyzed and proved by the experiment. Identification results show that the order of frequency identification is higher than the time identification model. But when it comes to accuracy and convergence, frequency identification model has obvious advantage. This paper provides evidence for subsequent active vibration control. The conclusion is the basic of subsequent experiment and research.
Modelling and Analysis of Vibrations in a UAV Helicopter with a Vision System
G. Nicolás Marichal Plasencia
2012-11-01
Full Text Available The analysis of the nature and damping of unwanted vibrations on Unmanned Aerial Vehicle (UAV helicopters are important tasks when images from on‐board vision systems are to be obtained. In this article, the authors model a UAV system, generate a range of vibrations originating in the main rotor and design a control methodology in order to damp these vibrations. The UAV is modelled using VehicleSim, the vibrations that appear on the fuselage are analysed to study their effects on the on‐board vision system by using Simmechanics software. Following this, the authors present a control method based on an Adaptive Neuro‐Fuzzy Inference System (ANFIS to achieve satisfactory damping results over the vision system on board.
Scale-model characterization of flow-induced vibrational response of FFTF reactor internals
Fast Test Reactor core internal and peripheral components were assessed for flow-induced vibrational characteristics under scaled and simulated prototype flow conditions in the Hydraulic Core Mockup as an integral part of the Fast Test Reactor Vibration Program. The Hydraulic Core Mockup was an 0.285 geometric scale model of the Fast Test Reactor internals designed to simulate prototype vibrational and hydraulic characteristics. Using water to simulate sodium coolant, vibrational characteristics were measured and determined for selected model components over the scaled flow range of 36 to 110%. Additionally, in-situ shaker tests were conducted on selected Hydraulic Core Mockup outlet plenum components to establish modal characteristics. Most components exhibited resonant response at all test flow rates; however, the measured dynamic response was neither abnormal nor anomalously flow-rate dependent, and the predicted prototype components' response were deemed acceptable
Experimental and Numerical Investigations on Vibration Characteristics of a Loaded Ship Model
Pu Liang; Ming Hong; Zheng Wang
2015-01-01
In this paper, the vibration characteristics of the structure in the finite fluid domain are analyzed using a coupled finite element method. The added mass matrix is calculated with finite element method (FEM) by 8-node acoustic fluid elements. The vibration characteristics of the structure in the finite fluid domain are calculated combining structure FEM mass matrix. By writing relevant programs, the numerical analysis on vibration characteristics of a submerged cantilever rectangular plate in finite fluid domain and loaded ship model is performed. A modal identification experiment for the loaded ship model in air and in water is conducted and the experiment results verify the reliability of the numerical analysis. The numerical method can be used for further research on vibration characteristics and acoustic radiation problems of the structure in the finite fluid domain.
Stabilization for the Vibrations Modeled by the `Standard Linear Model' of Viscoelasticity
Ganesh C Gorain
2010-09-01
We study the stabilization of vibrations of a flexible structure modeled by the `standard linear model’ of viscoelasticity in a bounded domain in $\\mathbb{R}^n$ with a smooth boundary. We prove that amplitude of the vibrations remains bounded in the sense of a suitable norm in a space $\\mathbb{X}$, defined explicitly in (22) subject to a restriction on the uncertain disturbing forces on $\\mathbb{X}$. We also estimate the total energy of the system over time interval [0,] for any >0, with a tolerance level of the disturbances. Finally, when the input disturbances are insignificant, uniform exponential stabilization is obtained and an explicit form for the energy decay rate is derived. These results are achieved by a direct method under undamped mixed boundary conditions.
Non-linear journal bearing model for analysis of superharmonic vibrations of rotor systems
Hannukainen, P.
2008-07-01
A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machineAEs rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non
Anharmonic potential in the oscillator representation
In the non relativistic and relativized Schroedinger equation the Wick ordering method called the oscillator representation is proposed to calculate the energy spectrum for a wide class of potentials allowing the existence of a bound state. The oscillator representation method gives a unique regular way to describe and calculate the energy levels of ground as well as orbital and radial excitation states for a wide class of potentials. The results of the zeroth approximation oscillator representation are in good agreement with the exact values for the anharmonic potentials. The oscillator representation method was applied to the relativized Schroedinger equation too. The perturbation series converges fairly fast, i.e., the highest perturbation corrections over the interaction Hamiltonian are small enough. 29 refs.; 4 tabs. (author)
Comparison of vibration test results for Atucha II NPP and large scale concrete block models
In order to study the soil structure interaction of reactor building that could be constructed on a Quaternary soil, a comparison study of the soil structure interaction springs was performed between full scale vibration test results of Atucha II NPP and vibration test results of large scale concrete block models constructed on Quaternary soil. This comparison study provides a case data of soil structure interaction springs on Quaternary soil with different foundation size and stiffness. (author)
Free Vibration Analysis for Cracked FGM Beams by Means of a Continuous Beam Model
E Chuan Yang; Xiang Zhao; Ying Hui Li
2015-01-01
Based on Euler-Bernoulli beam theory and a continuous stiffness beam model, the free vibration of rectangular-section beams made of functionally graded materials (FGMs) containing open edge cracks is studied. Assuming the material gradients follow exponential distribution along beam thickness direction, the conversion relation between the vibration governing equations of a FGM beam and that of an isotropic homogenous beam is deduced. A continuous function is used to characterize the bending s...
It is general practice to use a simple beam model in the analysis of the vibration characteristics of a slender rod for the simplicity and easiness to get the results. Besides the circular cross-section, fuel rods may have twisted square cross section in order to enhance the mechanical and thermo-hydraulic performance. In this case the modeling for the analysis of the vibration takes much efforts to simulate it properly. Instead of the more complex solid modeling, a simple beam model can be used if the simulation is properly done. In this study, the validity of the use of a simple beam model for the twisted square rod are discussed and the results of the two calculations are evaluated. The results show that the simple equivalent beam model also can be applied for this type of the rod on the vibration analysis and the effect of the twisted form on the rigidity of the rod is negligibly small
Modelling vibrational coherence in the primary rhodopsin photoproduct
Weingart, O.; Garavelli, M.
2012-12-01
Molecular dynamics simulations of the rhodopsin photoreaction reveal coherent low frequency oscillations in the primary photoproduct (photorhodopsin), with frequencies slightly higher than observed in the experiment. The coherent molecular motions in the batho-precursor can be attributed to the activation of ground state vibrational modes in the hot photo-product, involving out-of-plane deformations of the carbon skeleton. Results are discussed and compared with respect to spectroscopic data and suggested reaction mechanisms.
Agarwalla, Bijay Kumar; Jiang, Jian-Hua; Segal, Dvira
2015-12-01
We study the statistical properties of charge and energy transport in electron conducting junctions with electron-phonon interactions, specifically, the thermoelectric efficiency and its fluctuations. The system comprises donor and acceptor electronic states, representing a two-site molecule or a double-quantum-dot system. Electron transfer between metals through the two molecular sites is coupled to a particular vibrational mode which is taken to be either harmonic or anharmonic, a truncated (two-state) spectrum. Considering these models we derive the cumulant generating function in steady state for charge and energy transfer, correct to second order in the electron-phonon interaction, but exact to all orders in the metal-molecule coupling strength. This is achieved by using the nonequilibrium Green's function approach (harmonic mode) and a kinetic quantum master-equation method (anharmonic mode). From the cumulant generating function we calculate the charge current and its noise and the large-deviation function for the thermoelectric efficiency. We demonstrate that at large bias the charge current, differential conductance, and the current noise can identify energetic and structural properties of the junction. We further examine the operation of the junction as a thermoelectric engine and show that while the macroscopic thermoelectric efficiency is indifferent to the nature of the mode (harmonic or anharmonic), efficiency fluctuations do reflect this property.
Large-amplitude motion in the Suzuki model
The classical and quantum aspects for the analytically solvable one-dimensional pure monopole Suzuki model are studied to clarify the problem of quantization of classical collective motion. A set of nonlinear dynamic equations for a monopole moment of a nucleus are derived from the TDHF equation using the Wigner function moments model. It provides to describe large-amplitude monopole vibrations. The corresponding collective Hamiltonian is constructed and quantized. The anharmonicity of the collective spectra is analyzed in detal
Ice-shelf forced vibrations modelled with a full 3-D elastic model
Y. V. Konovalov
2014-12-01
Full Text Available Ice-shelf forced vibrations modelling was performed using a full 3-D finite-difference elastic model, which takes into account sub-ice seawater flow. The sub-ice seawater flow was described by the wave equation, so the ice-shelf flexures result from the hydrostatic pressure perturbations in sub-ice seawater layer. The numerical experiments were performed for idealized ice-shelf geometry, which was considered in the numerical experiments in Holdsworth and Glynn (1978. The ice-plate vibrations were modelled for harmonic ingoing pressure perturbations and for a wide spectrum of the ocean swell periodicities, ranging from infragravity wave periods down to periods of a few seconds (0.004–0.2 Hz. The spectrums for the vibration amplitudes were obtained in this range and are published in this manuscript. The spectrums contain distinct resonant peaks, which corroborate the ability of resonant-like motion in suitable conditions of the forcing. The impact of local irregularities in the ice-shelf geometry to the amplitude spectrums was investigated for idealized sinusoidal perturbations of the ice surface and the sea bottom. The results of the numerical experiments presented in this manuscript, are approximately in agreement with the results obtained by the thin-plate model in the research carried out by Holdsworth and Glynn (1978. In addition, the full model allows to observe 3-D effects, for instance, vertical distribution of the stress components in the plate. In particular, the model reveals the increasing in shear stress, which is neglected in the thin-plate approximation, from the terminus towards the grounding zone with the maximum at the grounding line in the case of considered high-frequency forcing. Thus, the high-frequency forcing can reinforce the tidal impact to the ice-shelf grounding zone additionally exciting the ice fracture there.
A theory of the strain-dependent critical field in Nb3Sn, based on anharmonic phonon generation
Valentinis, D F; Bordini, B; Rossi, L
2014-01-01
We propose a theory to explain the strain dependence of the critical properties in A15 superconductors. Starting from the strong-coupling formula for the critical temperature, and assuming that the strain sensitivity stems mostly from the electron-phonon alpha F-2 function, we link the strain dependence of the critical properties to a widening of alpha F-2. This widening is attributed to the nonlinear generation of phonons, which takes place in the anharmonic deformation potential induced by the strain. Based on the theory of sum- and difference-frequency wave generation in nonlinear media, we obtain an explicit connection between the widening of alpha F-2 and the anharmonic energy. The resulting model is fit to experimental datasets for Nb3Sn, and the anharmonic energy extracted from the fits is compared with first-principles calculations.
Model-based failure detection for cylindrical shells from noisy vibration measurements.
Candy, J V; Fisher, K A; Guidry, B L; Chambers, D H
2014-12-01
Model-based processing is a theoretically sound methodology to address difficult objectives in complex physical problems involving multi-channel sensor measurement systems. It involves the incorporation of analytical models of both physical phenomenology (complex vibrating structures, noisy operating environment, etc.) and the measurement processes (sensor networks and including noise) into the processor to extract the desired information. In this paper, a model-based methodology is developed to accomplish the task of online failure monitoring of a vibrating cylindrical shell externally excited by controlled excitations. A model-based processor is formulated to monitor system performance and detect potential failure conditions. The objective of this paper is to develop a real-time, model-based monitoring scheme for online diagnostics in a representative structural vibrational system based on controlled experimental data. PMID:25480059
This study explores the possibilities for inverse analysis and modelling from data of a nonlinearly vibrating structure. We are suggesting a statistical approach based on singular spectrum analysis (SSA). The method is based on a free decay response, when the structure is given an initial disturbance and is left to vibrate on its own. The measured vibration response is decomposed into new variables, the principal components, which are used to uncover oscillatory patterns in the structural response. In this study an application of the methodology for the purposes of delamination detection in a composite beam is explored.
Nonlinear Model and Qualitative Analysis for Coupled Axial/Torsional Vibrations of Drill String
Fushen Ren
2016-01-01
Full Text Available A nonlinear dynamics model and qualitative analysis are presented to study the key effective factors for coupled axial/torsional vibrations of a drill string, which is described as a simplified, equivalent, flexible shell under axial rotation. Here, after dimensionless processing, the mathematical models are obtained accounting for the coupling of axial and torsional vibrations using the nonlinear dynamics qualitative method, in which excitation loads and boundary conditions of the drill string are simplified to a rotating, flexible shell. The analysis of dynamics responses is performed by means of the Runge-Kutta-Fehlberg method, in which the rules that govern the changing of the torsional and axial excitation are revealed, and suggestions for engineering applications are also given. The simulation analysis shows that when the drill string is in a lower-speed rotation zone, the torsional excitation is the key factor in the coupling vibration, and increasing the torsional stress of the drill string more easily leads to the coupling vibration; however, when the drill string is in a higher-speed rotating zone, the axial excitation is a key factor in the coupling vibration, and the axial stress in a particular interval more easily leads to the coupling vibration of the drill string.
Probing anharmonicity of a quantum oscillator in an optomechanical cavity
Latmiral, Ludovico; Armata, Federico; Genoni, Marco G.; Pikovski, Igor; Kim, M. S.
2016-05-01
We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the mechanical oscillator, which is prepared in a thermal state. We show how the optical field acquires a phase depending on the anharmonicity. Remarkably, one only needs small initial cooling of the mechanical motion to probe even small anharmonicities. Finally, by applying tools from quantum estimation theory, we calculate the ultimate bound on the estimation precision posed by quantum mechanics and compare it with the precision obtainable with feasible measurements such as homodyne and heterodyne detection on the cavity field. In particular we demonstrate that homodyne detection is nearly optimal in the limit of a large number of photons of the field and we discuss the estimation precision of small anharmonicities in terms of its signal-to-noise ratio.
Linear delta expansion technique for the solution of anharmonic oscillations
P K Bera; J Datta
2007-01-01
The linear delta expansion technique has been developed for solving the differential equation of motion for symmetric and asymmetric anharmonic oscillators. We have also demonstrated the sophistication and simplicity of this new perturbation technique.
Dynamic Properties of Proton Transfer in the Anharmonic-Interaction Hydrogen Bond Systems
YAN Xun-Ling; DONG Rui-Xin; PANG Xiao-Feng
2001-01-01
We analyze the properties of the excited solitary-wave model in the case of anharmonic-interaction of heavy ionic lattice in hydrogen bond systems.In this case,some new phenomena appear.We find different types of solutions for the proton displacement and influences on the kinks and pulse solitary waves by numerical calculation.For each of them we have presented a direct relation with the effective potential of the system.
Electromechanical coupling model and analysis of transient behavior for inertial vibrating machines
HU Ji-yun; YU Cui-ping; YIN Xue-gang
2004-01-01
A mathematical model of electromechanical coupling system for a planar inertial vibrating machine is built by setting up dynamical equations of discrete systems with a matrix methodology proposed. The substance of the transient behavior of the machine is unveiled by analyzing the results of the computer simulation to the model, and new methods are presented for diminishing the transient amplitude of the vibrating machine and improving the transient behavior. The reliable mathematical model is provided for intelligent control of the transient behavior of the equipment.
XU, F.
2013-05-01
Full Text Available Orbital Friction Vibration Actuator (OFVA is a core component of Orbital Friction Welding (OFW, which is a novel apertureless welding technology utilizing friction heat to implement solid-state joining. In this paper, topology and operational principle of OFVA are introduced, the analytical formulas of the electromagnetic force for the x and y directions, which can drive the mover to generate a circular motion trajectory, are derived, and the characteristic of static electromagnetic force is predicted by analytical method and 2-D (two-dimensional FEM (finite element method, 3-D and measurement. The coupled magnetic field-circuit-motion simulation models which are driven by current and voltage source are established, respectively, and some of its operational characteristics are analyzed. Simulation and experiment validate theoretical analysis and the feasibility of the fabricated prototype, demonstrate the good performance of the OFVA, and provide valuable reference for engineering applications.
Nonlocal plate model for free vibrations of single-layered graphene sheets
Ansari, R.; Sahmani, S.; Arash, B.
2010-11-01
Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.
Nonlocal plate model for free vibrations of single-layered graphene sheets
Ansari, R., E-mail: r_ansari@guilan.ac.i [Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht (Iran, Islamic Republic of); Sahmani, S.; Arash, B. [Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht (Iran, Islamic Republic of)
2010-11-15
Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.
Nonlocal plate model for free vibrations of single-layered graphene sheets
Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.
Boz, Utku; Basdogan, Ipek
2015-12-01
Structural vibrations is a major cause for noise problems, discomfort and mechanical failures in aerospace, automotive and marine systems, which are mainly composed of plate-like structures. In order to reduce structural vibrations on these structures, active vibration control (AVC) is an effective approach. Adaptive filtering methodologies are preferred in AVC due to their ability to adjust themselves for varying dynamics of the structure during the operation. The filtered-X LMS (FXLMS) algorithm is a simple adaptive filtering algorithm widely implemented in active control applications. Proper implementation of FXLMS requires availability of a reference signal to mimic the disturbance and model of the dynamics between the control actuator and the error sensor, namely the secondary path. However, the controller output could interfere with the reference signal and the secondary path dynamics may change during the operation. This interference problem can be resolved by using an infinite impulse response (IIR) filter which considers feedback of the one or more previous control signals to the controller output and the changing secondary path dynamics can be updated using an online modeling technique. In this paper, IIR filtering based filtered-U LMS (FULMS) controller is combined with online secondary path modeling algorithm to suppress the vibrations of a plate-like structure. The results are validated through numerical and experimental studies. The results show that the FULMS with online secondary path modeling approach has more vibration rejection capabilities with higher convergence rate than the FXLMS counterpart.
Xu Liu
2015-01-01
Full Text Available Unsteady aerodynamic system modeling is widely used to solve the dynamic stability problems encountering aircraft design. In this paper, single degree-of-freedom (SDF vibration model and forced simple harmonic motion (SHM model for dynamic derivative prediction are developed on the basis of modified Etkin model. In the light of the characteristics of SDF time domain solution, the free vibration identification methods for dynamic stability parameters are extended and applied to the time domain numerical simulation of blunted cone calibration model examples. The dynamic stability parameters by numerical identification are no more than 0.15% deviated from those by experimental simulation, confirming the correctness of SDF vibration model. The acceleration derivatives, rotary derivatives, and combination derivatives of Army-Navy Spinner Rocket are numerically identified by using unsteady N-S equation and solving different SHV patterns. Comparison with the experimental result of Army Ballistic Research Laboratories confirmed the correctness of the SHV model and dynamic derivative identification. The calculation result of forced SHM is better than that by the slender body theory of engineering approximation. SDF vibration model and SHM model for dynamic stability parameters provide a solution to the dynamic stability problem encountering aircraft design.
Kinetic model of vibrational relaxation in a humid-air pulsed corona discharge
Komuro, Atsushi; Ono, Ryo [Department of Advanced Energy, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 227-8568 (Japan); Oda, Tetsuji, E-mail: komuro@streamer.t.u-tokyo.ac.j, E-mail: ryo-ono@k.u-tokyo.ac.j [Department of Electrical Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656 (Japan)
2010-10-15
The effect of humidity on the vibrational relaxation of O{sub 2}(v) and N{sub 2}(v) in a humid-air pulsed corona discharge is studied using a kinetic model. We previously showed that humidity markedly increases the vibration-to-translation (V-T) rate of molecules in a humid-air pulsed corona discharge by measuring O{sub 2}(v) density (Ono et al 2010 Plasma Sources Sci. Technol. 19 015009). In this paper, we numerically calculate the vibrational kinetics of O{sub 2}, N{sub 2} and H{sub 2}O to study the reason behind the acceleration of V-T in the presence of humidity. The calculation closely reproduces the measured acceleration of V-T due to humidity, and shows that the increase in the V-T rate is caused by the fast vibration-to-vibration (V-V) processes of O{sub 2}-H{sub 2}O and N{sub 2}-H{sub 2}O and the subsequent rapid V-T process of H{sub 2}O-H{sub 2}O. In addition, it is shown that O atom density is also important in the vibrational kinetics owing to the rapid V-T process of O{sub 2}-O.
A Simplified Model for Vibration Analysis of Diesel Engine Crankshaft System
无
2006-01-01
A spatial finite element model for vibration analysis of crankshaft system was proposed. The crankshaft body was simplified as spatial rigid frame by using beam elements based on Timoshenko beam theory. The main bearings in system were simplified as linear springs and dashpots. The natural frequencies of the crankshaft system of a four in-line cylinder engine were calculated and compared with the analytical and experimental values available in other publications. In order to simulate the motion of operating crankshaft system, the gas forces, rotating masses and reciprocating masses were considered, the crankshaft and main bearings were coupled in a rotating coordinate system, and a dynamic model for vibration analysis of crankshaft system was established. By applying the dynamic model, the influence of the mass and moment of inertia of front pulley on the behavior of crankshaft vibration was investigated.
U(2) algebraic model applied to stretching vibrational spectra of tetrahedral molecules
Hou, X W; Hou, Xi-Wen; Ma, Zhong-Qi
1998-01-01
The highly excited stretching vibrational energy levels and the intensities of infrared transitions in tetrahedral molecules are studied in a U(2) algebraic model. Its applications to silane and silicon tetrafluoride are presented with smaller standard deviations than those of other models.
Deriving Vibration Modes of Semi-infinite Chain Model by "Invariant Eigen-operator"Method
ZHANG Lin-Na; FAN Hong-Yi; FU Zun-Tao; and WU Hao; LIU Shi-Kuo
2008-01-01
For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the "invariant eigen-operator" method in two different cases, which is concise and revealing.
Modeling of wave propagation in drill strings using vibration transfer matrix methods.
Han, Je-Heon; Kim, Yong-Joe; Karkoub, Mansour
2013-09-01
In order to understand critical vibration of a drill bit such as stick-slip and bit-bounce and their wave propagation characteristics through a drill string system, it is critical to model the torsional, longitudinal, and flexural waves generated by the drill bit vibration. Here, a modeling method based on a vibration transfer matrix between two sets of structural wave variables at the ends of a constant cross-sectional, hollow, circular pipe is proposed. For a drill string system with multiple pipe sections, the total vibration transfer matrix is calculated by multiplying all individual matrices, each is obtained for an individual pipe section. Since drill string systems are typically extremely long, conventional numerical analysis methods such as a finite element method (FEM) require a large number of meshes, which makes it computationally inefficient to analyze these drill string systems numerically. The proposed "analytical" vibration transfer matrix method requires significantly low computational resources. For the validation of the proposed method, experimental and numerical data are obtained from laboratory experiments and FEM analyses conducted by using a commercial FEM package, ANSYS. It is shown that the modeling results obtained by using the proposed method are well matched with the experimental and numerical results. PMID:23967925
Dynamics Modelling of a Plate Vibrating in a Perfect Fluid
Bouarroudj Nadra
2007-01-01
Full Text Available We deal with the interaction problem of a plate vibrating within a perfect fluid. We establish the equations describing the dynamics behaviour of the plate using the general equations of the elasto-dynamic. The fluid flow described by the equation of Eulers low amplitude. We presented results of the existence, the unicity and the regularity of the problem verified by the plate as well as by the fluid We used the integral equations for the numerical resolution of the problem that allowed us to determine the coupling term between the fluid and the plate. The numerical results were obtained using finite element method coupled with an implicit diagram in time.
Mathematical model for cross-flow-induced vibrations of tube rows
A mathematical model is presented for cross-flow-induced vibrations of tube banks including the effects of vortex shedding, fluidelastic coupling, drag force, fluid inertia coupling, and others. The model can predict the details of complex tube-fluid interactions: (1) natural frequencies and mode shapes of coupled vibrations; (2) critical flow velocities; (3) responses to vortex shedding, drag force, and other types of excitations; and (4) the dominant excitation mechanism at a given flow velocity. The analytical results are in good agreement with the published experimental results