Oscillations of Microscale Composite Structures with Applications to Microresonators
Mote, Clayton Daniel
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Free and forced oscillations of piezoelectric microelectromechanical resonators fabricated as clamped-clamped laminate structures are studied in this dissertation. Piezoelectric actuation is used to excite these structures on the input side, and piezoelectric sensing is carried out on the output side. A refined mechanics model is developed for composite beam structures and used for studying the nonlinear transverse vibrations of the microresonators. The model accounts for longitudinal extension due to transverse displacements, distributed actuation, and stepwise axially varying properties. Assuming a buckling induced non-flat equilibrium position, an approximation for the static equilibrium position is determined and the free vibration problem is solved. For weak damping and weak forcing, the method of multiple scales is used to obtain an approximate frequency-response solution. Following this work, a complete solution for the pre-buckling, critical-buckling, and post-buckling problem for axially elastic beams is developed from the nonlinear model. The analytical predictions are compared with experimental data and they are found to be in good agreement. The present work provides a means for determining the spatial and temporal response of microresonators and it can be used as a design tool for many microelectromechanical systems (MEMS). The present work provides the first evidence for buckling influenced dynamics in microresonators.