Construction of an electric analogue for determining the dissipative characteristics of electric viscoelastic bodies with external electric circuits

Abstract

The problem of damping vibrations of structural elements in various branches of technology does not lose its relevance over time but rather becomes a key issue for development of modern devices in airspace, aircraft, automotive industry. The use of piezoelectric elements and external electric circuits opens up novel possibilities for controlling the dynamic behavior of structures. Modeling the dynamic behavior of such electromechanical systems requires solving a related problem of electroviscoelasticity. Optimization of the dissipative properties of electromechanical systems under consideration is carried out through the selection of circuit parameters (tuning) that provide the best vibrations damping at a specified frequency. In this case, the most efficient tool is the problem of natural vibrations of piecewise homogeneous electroviscoelastic body with external electric circuits. However, the numerical procedure for finding the optimal parameters of electric circuits is related to multiple solution of the problem for each combination of the values of the circuit elements using complex large-sized matrices, including solving the algebraic problem of complex eigenvalues for these matrices. At the same time, the generality of mathematical equations, which describe oscillations in mechanical systems and oscillations of current and voltage in electric circuits, makes it possible to apply the method of dynamical analogies and consider equivalent electric system instead of coupled electromechanical one, replacing the equations of motion of electromechanical system with the corresponding analogues of equations for an equivalent electrical system. This allows to considerably decrease computational time and reduce the requirements for hardware resources. The developed discrete analogue is completely equivalent to the original electromechanical system with external electric circuit in terms of the spectrum of natural vibration frequencies. The results obtained with the aid of the electric analogue were verified by solving problems on natural vibrations of electroviscoelastic bodies, including those with external electric circuits, according to the mathematical statement of continuous media mechanics.