Modelling of vibrational processes in systems with piezoelements and external electric circuits on the basis of their electrical analogue

The dissipative properties of electromechanical systems based on structure with elements made of piezomaterial can be controlled by attaching external electric circuits to the piezoelements. One can change electric circuit parameters in such a way as to ensure the greatest possible energy dissipation on an external electric circuit and, thereby, the best damping of the system’s specified oscillation frequency. Since the external electric circuits are a collection of elements with lumped parameters attached to a system with distributed parameters, the solution for such a system of electro-viscoelasticity problems in the complete formulation by the finite element method leads to a large solving system of algebraic equations. The solution of this system requires considerable time and computational resources. There are known approaches in mechanics that make it possible to represent mechanical systems with distributed parameters in the form of discrete systems with lumped parameters, such as a spring–mass–damper. In this article, it is proposed to model electromechanical systems with external electric circuits based on their electrical analogue in the form of equivalent electric substitution circuits, which are discrete electrical systems with lumped parameters. These discrete systems are analogues of the initial electromechanical systems in terms of frequency characteristics and the electrical processes that take place in them. The equivalent substitution circuit is based on the Van Dyke model and allows one to obtain the required number of complex eigenfrequencies of the electromechanical system under consideration.