On the performance of a nonlinear vibration isolator consisting of axially loaded curved beams

Abstract

A desirable characteristic for nonlinear vibration isolators is a high static stiffness and a low dynamic stiffness. A curved beam is a possible candidate for this role provided that the amplitude of vibration about the static equilibrium position is sufficiently small. However, for large amplitude oscillations, the nonlinear dynamics may have a detrimental effect. This paper considers the force transmissibility of a single degree-of-freedom system where the stiffness element is a curved, axially loaded beam. The transmitted force is calculated by numerical time domain integration of the equations of motion. The exact force-deflection relation for the beam is used for the spring. By comparison, a frequency domain solution is sought using the Harmonic Balance (HB) method in which the system is modelled as a Duffing oscillator. It is shown that the HB and time domain solutions are in close agreement for small amplitudes of excitation and both predict advantageous performance of the nonlinear isolator compared with its equivalent linear counterpart. However, significant discrepancies occur between the two solutions for large excitation since the beam can no longer be approximated by a linear and a cubic stiffness. It is also strongly asymmetric – soft in compression but stiff in extreme extension– which gives rise to an impulse in the transmitted force in each fundamental period. This numerical problem is alleviated by inserting a linear spring in series with the beam isolator with a modest compromise in isolation performance at the excitation frequency.

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