Forced harmonic vibration of a non-uniform elastic beam with attached dynamic vibration absorbers (DVA) is studied. Analytical approximation of the solution is obtained by the functional perturbation method (FPM). The problem has application to cutting tools operations where the resistance of the tool holder against regenerative chatter can be enhanced by optimizing the real part of the frequency response function (FRF). A test case of a beam with step-like heterogeneity and single DVA at the tip shows that the FPM solution is very accurate for up to ?40 percent deviation in both stiffness and mass density. Using the analytical results and Sims approach, optimal DVA tuning is found for each set of beam heterogeneity parameters by solving a set of nonlinear algebraic equations numer...
The regenerative-chatter resistance of a viscoelastic cantilever beam is analyzed and compared to the common dynamic vibration absorber (DVA) system. The beam represents a tool holder for turning operation in machining. The optimum structural parameters are found by maximizing the most negative real part of the frequency response function (FRF). The FRF is found analytically by using an appropriate Greens function. Keeping the cantilever static stiffness constant, further increase in the optimal resistance is achieved by changing the ratio between the two elastic moduli in the 3-parameter solid viscoelastic material model. Three additional chatter resistance indicators are also investigated: the most positive real part of the FRF, the magnitude of the FRF and the resonant frequency. It is ...