A computational multi-field mechanics model of composite micromechanical systems (MEMS) with piezoelectric actuation and sensing has been developed as a design tool for micro-resonators. These devices are to be used for filters and other signal processing applications. The developed dynamic model of MEMS resonators accounts for structural properties and the electromechanical coupling effect through finite element analysis. It is assumed that the deflection is large and that the geometric nonlinearity must be included. The mechanical strain is assumed to be small so that the linear constitutive relations are valid. The dynamic admittance model is derived by combining the linear piezoelectric constitutive equations with the modal transfer function of the micro-resonator structure. 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. In the development of the finite-element models, boundary conditions, electrodes shaping, and factors such as varying elastic modulus across the length of the beam for the multilayered structure are taken into account. The coupled model can be used to carry out sensitivity studies with respect to the following: i) resonator thickness and length; ii) influence of constant axial forces on the transverse vibrations of clamped-clamped micro-resonators; geometry of the drive and sense electrodes; and iii) imperfect boundary conditions due to mask imperfections and fabrication procedure. The developed model has been validated by comparing the predictions with results available in the literature for clamped-clamped resonators.
Forced oscillations of piezoelectric, micro-electromechanical (MEMS) resonators fabricated as clamped-clamped composite structures are studied in this effort. Piezoelectric actuation is used to excite these structures on the input side and piezoelectric sensing is carried out on the output side. Each resonator structure is modeled as an Euler-Bernoulli beam with axially varying properties across the length and distributed actuation. A nonlinear integro-partial differential system is derived to describe the micro-resonator. For weak damping and weak forcing, the method of multiple scales is used to obtain an approximate solution of the system about a post-buckling position. The different modeling assumptions are presented and discussed, and the analytical prediction is compared with experimental observation.