Numerical algorithm for searching for layouts of electroelastic bodies with external electric circuits for obtaining the best damping properties

This paper presents an algorithm which allows finding such layouts of electromechanical systems that provide the best vibration damping whether for one mode or a set of vibration modes within some continuous frequency ranges. The basis for the algorithm is the problem solution about natural vibrations. An elastic structure with a piezoelectric element located on its surfaces, which electrodes are connected to a passive external electric circuit, is treated as an electromechanical system. The piezoelectric elements shunted with an electric circuit are the devices where energy dissipation occurs, thus leads to damping of vibrations. A change in damping properties of such systems can be reached by a proper choice of parameters of the electric circuits and corresponding location of the piezoelectric element, which provides the highest energy withdrawal into the electric circuit. The paper presents the mathematical formulation of the natural vibrations problem for piecewise-homogeneous electroelastic bodies shunted with passive external electric circuits. Within the proposed mathematical statement, the problem solution of natural vibrations for such objects is based on values of complex natural vibration frequencies. Real parts of the complex natural vibration frequencies are the circular frequency of vibrations, and the imaginary parts are the damping indices of vibrations. We proposed techniques aimed at determining the location of the piezoelectric element and selecting parameters of shunting the external electric circuit. These approaches are based on values of the complex natural vibration frequencies obtained as results of solving the natural vibrations problem. The proposed approach is demonstrated using a specimen of a thin-walled shell in the semi-cylinder form. The piezoelectric element has a form of a segment of a ring made of PZT-4 piezoceramics. Electrodes of the piezoelectric element are connected to the series resonant RL -circuit. The formulated problem is solved numerically using the finite element method and ANSYS commercial package.