The equivalent circuit of an N-electrode piezoelectric bar

Abstract

A new interpretation of the piezoelectric equations of state has been developed. In this representation, electromechanical energy conversion occurs only at the electrode edges, rather than everywhere under the electrodes. The present paper utilizes this concept to formulate an acoustic wave equation with inhomogeneous or driving terms occurring at the electrode edges. This equation is then solved by means of Green's function techniques. From this solution the admittance matrix and equivalent circuit of a slim, N-electrode piezoelectric bar are developed. Admittance functions were measured on several two-electrode bars; results agreed within 10 percent of theoretical predictions. The mathematical techniques utilized in this paper have applications which are not restricted to piezoelectric bars. These techniques are helpful for many piezoelectric problems in which it is desirable to perform analyses that do not increase in tediousness as electrode configuration increases in complexity.