Finite element approach to problems of harmonic vibrations of electromechanical systems (Q2754725)

The proposed numerical approach for solving problems of electromechanical vibrations is a generalization of the finite element method (FEM) used in elasticity. Governing equations of the problem combine the equations of electroelasticity and Kirchhoff equations for electric circuits. A functional, that provides basis for developing the FEM approach, is derived. Next, principles of formation of algebraic systems of FEM are explained. The resulting system combines a discrete problem of potentials at nodes of an electric circuit and a finite element discretization of the problem of electroelasticity by Galerkin technique or by the technique of weighted residuals. In the absence of controlled energy sources, the matrix of this system of equations is symmetric.