Abstract
In this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pendulum absorber for a linear primary system. The approximate frequency analysis reveals that the nonlinear dynamics of the externally excited system are suppressed by the pendulum absorber and, under this condition, the primary Duffing system yields a time response almost equivalent to that obtained for a linear primary system, although the absorber frequency response is drastically modified and affected by the cubic stiffness, thus modifying the jumps defined by the fixed points. In the absorber frequency response can be appreciated a good absorption capability for certain ranges of nonlinear stiffness and the internal coupling is maintained by the existing damping between the pendulum and the primary system. Moreover, the stability of the coupled system is also affected by some extra fixed points introduced by the cubic stiffness, which is illustrated with several amplitude-force responses. Some numerical simulations of the approximate frequency responses and dynamic behavior are performed to show the steady-state and transient responses.
Highlights
Dynamic vibration absorbers are classical devices, consisting of masses, springs and possibly dampers, which are configured and attached to a vibrating primary system to attenuate its undesirable forced dynamic response
Dynamic vibration absorbers have to interact with nonlinear mechanical systems, situation which certainly complicates the dynamic and frequency analysis
The primary system can be externally excited by some harmonic force and, when it is connected to a secondary system can be satisfied the so-called parametric excitation, that is, a mechanism that transfers the exogenous energy to the secondary system
Summary
Dynamic vibration absorbers are classical devices, consisting of masses, springs and possibly dampers, which are configured and attached to a vibrating primary system to attenuate its undesirable forced dynamic response. Dynamic vibration absorbers have to interact with nonlinear mechanical systems, situation which certainly complicates the dynamic and frequency analysis. The analysis of a class of nonlinear dynamic vibration absorbers, with primary and secondary subsystems modelled by Duffing-van der Pol equations, is considered by Zhu et al [14] and references therein. The classical multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with similar applications of the pendulum absorber for linear primary systems in Cartmell et al [4,9,10]. The nonlinearity certainly affects the frequency response of the pendulum absorber, with an enhancement of the effective bandwidth for the autoparametric interaction, phenomenon which may be related to the passive energy pumping described in detail by Jiang et al [16] and references therein. The dynamic performance of the overall system is evaluated through numerical simulations
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