Nonlinear free and forced oscillations of piezoelectric microresonators

Free and forced oscillations of piezoelectric, microelectromechanical 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. A refined integro-partial differential model is developed for a clamped-clamped composite beam structure and used for studying the nonlinear transverse vibrations of these resonators. This model accounts for the longitudinal extension due to transverse vibrations, distributed actuation and axially varying properties across the length of the structure. Free oscillations about a post-buckled position are studied, and for weak damping and weak forcing, the method of multiple scales is used to obtain an approximate solution for the response to a harmonic forcing. Analytical predictions are also compared with experimental observations. The model development and the analysis can serve as a basis for analysing the responses of other composite microresonators.