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A semi-analytical tool based on geometric nonlinearities for microresonator design

In this paper, a computational mechanics model specifically tailored for composite microresonators with piezoelectric actuation and piezoelectric sensing is developed and used as a design tool for these microresonators. The developed model accounts for the 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 dynamic admittance model is derived by combining the linear piezoelectric constitutive equations with the modal transfer function of the multi-layered microresonator structure. The resonator receptance matrix is constructed through modal summation by considering a limited number of dominant modes. The electromechanical coupling determination at the input and output ports makes use of converse and direct piezoelectric effects. In the development of the finite-element models, the boundary conditions, the shapes of electrodes and distributed parameters such as varying elastic modulus across the length of the structure have been taken into account. The developed semi-analytical tool can be used to carry out parametric 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 microresonators, (iii) the geometry of the drive and sense electrodes and (iv) imperfect boundary conditions due to mask imperfections and fabrication procedure. The semi-analytical development has been validated by comparing model predictions with prior results available in the literature for clamped–clamped resonators and experimental measurements. A detailed discussion of modeling considerations is also presented.