Alteration of Natural Vibration Frequencies by Piezoelectric Elements Embedded in Elastic Bodies

This paper addresses the problem of altering the natural vibration frequencies of an elastic body with embedded piezoelectric elements by applying an electric potential to them. Presented mathematical formulation of the problem based on the principle of virtual displacements for a piecewise-homogeneous electroelastic body. Finite deformations are represented as the sum of linear and nonlinear parts, which are linearized with respect to a state featuring a small deviation from the initial equilibrium position caused by the reverse piezoelectric effect. Provided experimental and numerical results validate the reliability of the numerical algorithm based on the finite element method. Using a plate with an embedded piezoelectric element as an example, presented numerical results demonstrate the influence of various parameters on the change in natural vibration frequencies: the stiffness characteristics of the elastic body; the dimensions, location, and number of piezoelectric actuators; the area ratio of the piezoelectric element to the elastic body; and the magnitude and sign of the electric potential.