Passive flutter suppression using a nonlinear tuned vibration absorber

Abstract

Limit cycle oscillations (LCOs) occur in many mechanical systems and they are often a source of danger. The addition of a relatively small mass to the host system, attached through a linear spring and a damper (linear tuned vibration absorber, LTVA), significantly improves its stability. The use of a purely nonlinear spring in the absorber (nonlinear energy sink, NES) increases the frequency bandwidth of the absorber, reduce LCO amplitude and avoid subcritical bifurcation at the loss of stability. Recently, a nonlinear tuned vibration absorber (NLTVA) has been proposed, whose restoring force is tailored according to the functional form of the nonlinearity of the primary system. The NLTVA is designed to exploit the positive features of both the LTVA and the NES. In this paper we show that the NLTVA can compensate the detrimental effect of the nonlinearities of the primary system. In other words, the coupled system exhibits a linear-like dynamics, similar to the same system without structural nonlinearities. Considering a Van der Pol—Duffing oscillator as primary system, a closed-form solution for the local compensation of nonlinearities is obtained analytically. Numerical continuation techniques show that the compensation is valid also for large amplitudes of the response.