Development of an electrical analogue for modeling natural vibrations of a viscoelastic structure with piezoelectric element

This paper focuses on the development of an equivalent electrical model with lumped parameters capable of describing the natural vibrations of an electromechanical system comprising a viscoelastic structure with a piezoelectric element attached to its surface. The important advantage of the model is that it takes into account the energy losses associated with the viscoelastic properties of the material of the main structure. Two versions of the equivalent electric analogue of the initial electro-viscoelastic system in the form of electric circuits, the elements of which are described by the real or complex quantities, are considered. The approaches to the formulation of the problem of natural vibrations in the developed electric analogue are based on Kirchhoff’s laws for electric circuits and Ohm’s law for alternating current. Special attention is paid to the identification of model parameters. A procedure for determining the parameters for the equivalent electrical model is based on the results gained from the solution of a coupled problem of natural vibrations of the initial electromechanical system; problem formulation is also given here. The effectiveness and reliability of the developed equivalent electric models with lumped parameters for the determination of complex eigenfrequencies of the electromechanical system containing energy dissipation elements are demonstrated by analyzing the behavior of structures in the form of a rectangular plate and a semi-cylindrical shell.