Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber

Abstract

This paper is the second one in the series of two papers devoted to detailed investigation of the response regimes of a linear oscillator with attached nonlinear energy sink (NES) under harmonic external forcing and assessment of possible application of the NES for vibration absorption and mitigation. In this paper, we study the performance of a strongly nonlinear, damped vibration absorber with relatively small mass attached to a periodically excited linear oscillator. We present a nonlinear absorber tuning procedure in the vicinity of (1:1) resonance which provides the best total system energy suppression, using analytical and numerical tools. A linear absorber is also tuned according to the same criterion of total system energy suppression as the nonlinear one. Both optimally tuned absorbers are compared under common parameters of damping, external forcing but different absorber stiffness characteristics; certain cases for which nonlinear absorber is preferable over the linear one are revealed and confirmed numerically.

Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems

“…In the case of strongly nonlinear vibration absorber, it was shown in [57] that, depending on system parameters, weak or strong quasi-periodic regimes occur, both of them providing efficient vibration absorption. Thus, in order to perform a careful tuning, it is essential to determine the range of parameters in which quasi-periodic beating responses are possible.…”

“…The system under consideration consists of a linear oscillator and a small essentially nonlinear attachment, as described in [57]. The linear oscillator is the primary structure with mass m 1 and the nonlinear attachment with small mass m2 is the NES.…”

Responses of a two degree-of-freedom system coupled to a nonlinear damper under multi-forcing frequencies

“…On the other hand, the NES can operate efficiently only in a limited range of the amplitude of the primary system. Following these results, design and optimization of the nonlinear absorber have been addressed in [9,10].…”

Vibration absorption with a nonlinear absorder including time delay

“…The complexification method combined to the averaging method will be applied starting from the equations of motion (7)(8).…”

“…On the other hand, the NES can operate efficiently only in a limited range of the amplitude. Following these results, design and optimization of the nonlinear absorber have been addressed in [8,9].…”