Dynamic Response Optimization of Piezoelectrically Excited Thin Resonant Beams

Piezoelectrically excited, resonant, elastic beams find wide use as piezoelectric fans, optical choppers, MEMS sensors, and piezoelectric motors. The devices consist of either one piezoelectric ceramic patch (piezopatch) bonded on one side (asymmetric configuration), or of two oppositely poled patches placed symmetrically on either side of a thin, flexible elastic beam (symmetric configuration). Field equations of the coupled structure governing the coupled longitudinal and bending motions of the resonator are derived using linear constitutive equations, slender beam approximations, and Hamilton's principle. Analytical solutions are found to the coupled eigenvalue problem. Eigenvalues and eigenfunctions for the short-circuited and open-circuited configurations are predicted analytically and are found to be in excellent agreement with results from three-dimensional finite element simulations. Electromechanical coupling factors (EMCF) are computed using the analytical and finite element model and optimal resonator geometries are identified for maximal EMCF. The EMCF predictions are also compared with experiments for an asymmetrically configured resonator. The analytical solution provides a convenient tool for the optimal design of such devices.