AVERAGING MODELS FOR LINEAR PIEZOSTRUCTURAL SYSTEMS

摘要

In this paper, we consider a linear piezoelectric structure which employs a fast-switched, capacitively shunted subsystemto yield a tunable vibration absorber or energy harvester. The dynamics of the system is modeled as a hybrid system,where the switching law is considered as a control input and the ambient vibration is regarded as an external disturbance.It is shown that under mild assumptions of existence and uniqueness of the solution of this hybrid system, averagingtheory can be applied, provided that the original system dynamics is periodic. The resulting averaged system iscontrolled by the duty cycle of a driven pulse-width modulated signal. The response of the averaged systemapproximates the performance of the original fast-switched linear piezoelectric system. It is analytically shown that theaveraging approximation can be used to predict the electromechanically coupled system modal response as a function ofthe duty cycle of the input switching signal. This prediction is experimentally validated for the system consisting of apiezoelectric bimorph connected to an electromagnetic exciter. Experimental results show that the analytical predictionsare observed in practice over a fixed "effective range" of switching frequencies. The same experiments show that theresponse of the switched system is insensitive to an increase in switching frequency above the effective frequency range.