In this paper, we consider a linear piezoelectric structure which employs a fast-switched, capacitively shunted subsystem
to 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, averaging
theory can be applied, provided that the original system dynamics is periodic. The resulting averaged system is
controlled by the duty cycle of a driven pulse-width modulated signal. The response of the averaged system
approximates the performance of the original fast-switched linear piezoelectric system. It is analytically shown that the
averaging approximation can be used to predict the electromechanically coupled system modal response as a function of
the duty cycle of the input switching signal. This prediction is experimentally validated for the system consisting of a
piezoelectric bimorph connected to an electromagnetic exciter. Experimental results show that the analytical predictions
are observed in practice over a fixed "effective range" of switching frequencies. The same experiments show that the
response of the switched system is insensitive to an increase in switching frequency above the effective frequency range.