Analysis of Multiterminal Piezoelectric Plates

Abstract

Mathematical techniques are discussed whereby one may analyze a thin piezoelectric plate with arbitrary electrodes, external electrical loads, and external mechanical tractions. These techniques include tensor Green's-function operations, Fourier-eigenmode expansions, and circuit-theory manipulations. Application of these techniques leads to admittance matrices interrelating the linear responses of the various mechanical terminals (i.e., the sites of external-force application) and electrical terminals (i.e., electrodes). It is demonstrated that these admittance matrices may be represented by quite simple equivalent circuits. External mechanical forces may be applied either at a point or over a distributed area. These two types are represented best by separate methods, both of which are discussed here. Two specific, nontrivial examples of actual piezoelectric devices are analyzed at the conclusion of this work, and results are compared with experimental observations. These examples are a symmetrically electroded ferroelectric ceramic disk bonded to a substrate and an asymmetrically electroded, mechanically free, ferroelectric ceramic disk. Effects due to loss, nonuniform density, and nonuniform material coefficients (elastic, dielectric, and piezoelectric) have been included in this work. However, finite-plate-thickness effects, such as electrical fringing and particle accelerations perpendicular to the plane of the plate, are not included.