Mechanical behavior and sound generation efficiency of prestressed, elastically clamped and thermomechanically driven thin film sandwiches

Abstract

A model of thermomechanically driven plates as used, e.g., for acoustic microresonators is reported. The model describes the quasibuckling, excitation, fundamental frequency and vibration mode of multilayered plates under plane strain. The plates consist of stacked thin films with individual elastic modulus, Poisson's ratio, prestress, heat capacity and coefficient of thermal expansion. Membrane edges are elastically clamped to lateral supports. In thin plates two driving mechanisms are identified: the first couples the thermomechanical bending moment to the curvature of the vibration mode; the second couples the thermomechanical line stress to the periodic length change of the vibrating quasibuckled structure. Results of the model include vibration amplitude, sound field pressure, emitted power and quality factor as functions of the membrane properties. Maximum output is obtained close to the quasibuckling transition of the structures, where their resonance frequency is minimum. Largest sound pressures are generated by structures with rigid supports or with vanishing initial bending moment. The model shows excellent agreement with experimental data from micromachined resonant silicon membranes.