Two-dimensional exact electromechanical impedance matrix of piezoceramic disks with arbitrary aspect ratio

In this paper, the fundamental electroacoustic characteristics of piezoceramic disks with arbitrary aspect ratios are deduced in terms of its electromechanical impedance matrix. Modifying the expressions of the primary variables (i.e., displacement and electric potential) from univariate functions to bivariate functions, one-dimensional (1D) approximate impedance matrix, two-dimensional (2D) approximate impedance matrix and 2D exact impedance matrix are successively and systematically developed and the mode coupling phenomenon between the radial and thickness modes is elaborated. By means of the trigonometric functions and Bessel functions, the governing equations and boundary conditions are satisfied exactly. Compared with results of the finite element method, the electrical impedances, frequency spectrum, and mode shapes give an excellent agreement. With the aid of 2D exact impedance matrix, the effect of loads on the electromechanical behavior of piezoceramic disks can be easily evaluated. Finally, the theoretical and experimental electrical impedances of piezoceramic disks with different aspect ratios are compared and discussed. The 2D exact impedance matrix developed here provides an efficient and accurate tool for parametric and optimization analysis of coupled vibrations of piezoelectric structures.