Justification of equivalent substitution circuits used to optimize the dissipative properties of electroelastic bodies with external electric circuits

Abstract

We consider elastoplastic systems which are piecewise homogeneous bodies composed of piezoelectric elements some of which have piezoelectrical properties. Electric series circuits consisting of resistors, capacitors, and inductance coils are applied to piezoelectric elements through the electrode coating on the body surface. The goal of the study is to develop efficient methods of mathematical modelling for determining the parameters of elements of the external electric circuit, which ensure, at prescribed resonance frequencies, the maximum damping properties of electroelastic bodies with external electric circuits. To choose effective circuits for solving the problem posed above, we suggest to pose the problem of natural vibrations of elastic bodies whose elements exhibit piezoeffect and have external electric circuits.As the most efficient approaches for calculating the electric circuit parameters necessary for the maximal damping, we propose some versions of equivalent circuits, which can be used to substitute elastic systems with piezoelectric elements. The most reliable equivalent substitution circuits are justified on the basis of the proposed problem of natural vibrations. Numerical results are obtained for a cantilever plate with a piezoelement connected through the electrode coated surface with a series electric circuit consisting of resistors, capacitors and inductance coils.