摘要：Micromechanical systems (MEMS) that employ active piezoelectric materials,
typically in thin-film form, show promise for a variety of applications and
are currently the subject of research in a number of laboratories. The
development of increasingly complex devices demands sophisticated simulation
techniques for design and optimization. MEMS devices typically involve multiple
coupled energy domains and media that can be modeled by using a set of
partial differential equations, including spatial and time variables. In this
work, a computational multi-field mechanics model of a micro-structure with
piezoelectric actuation and piezoelectric sensing has been developed as a
design tool for micro-resonators and micro-resonator arrays. Although linear
models of electrostatically actuated microresonator arrays have been
developed in the literature, such models have not been developed for
piezoelectrically driven resonator arrays. The developed dynamic model of
MEMS resonator array accounts for structural properties and electromechanical
coupling effect through finite element analysis. In the simulations, a beam
element was used for the structural modeling. We assume that the deflection
is large and account for the geometric nonlinearity. The mechanical
strain, however, is assumed to be small so that the linear constitutive
relations are still valid. The admittance model is derived by combining the
linear piezoelectric constitutive equations with the modal transfer function
of the resonator structure. The overall transfer function describing the
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