Computational Multi-Field Mechanics Model Of Piezoelectric Microresonator Arrays.

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 admittance between a driven input and a sense output of a micro-resonator array is obtained in the frequency domain. The resonator receptance matrix is constructed through modal summation by considering only a limited number of dominant modes. The electromechanical coupling determination at the input and output ports makes use of the converse and direct piezoelectric effects. The coupled model can be used to carry out sensitivity studies with respect to the following: (i) the resonator beam thickness and length; (ii) the influence of constant axial forces on the transverse vibrations of clamped-clamped microresonator arrays; (iii) geometry of the drive and sense electrodes; and (iv) imperfect boundary conditions due to mask imperfections and fabrication procedure. For micromechanical resonators, these modeling uncertainties come in large part from manufacturing tolerance, residual stresses, irregular surface topology, and material property variations, among others. The developed model has been validated by comparing with results available in the literature for single clamped-clamped resonators.