Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Dr. Dumitru Caruntu

Second Advisor

Dr. Dorina M. Chipara

Third Advisor

Dr. Javier Ortega


In this work the behavior of micro-electromechanical (MEMS) cantilever resonators is investigated. The cantilever resonators are electrostatically actuated with hard AC voltage resulting in nine distinct resonances cases including super and subharmonic resonances. The amplitude frequency and amplitude voltage bifurcation diagrams are obtained for each of the nine resonance cases. Reduced order models (ROMs) are developed to include one and two modes of vibration. Three different methods are used to solve the ROMs namely 1) the method of multiple scales (MMS), which is a perturbation method used for one mode of vibration, 2) the homotopy analysis method (HAM), which is an analytical method rooted in topology used for one mode of vibration, and 3) direct numerical integration using two modes of vibration (2T ROM) resulting in time responses of the tip of the MEMS cantilever resonator. The MMS and HAM solutions directly yield steady state solutions for the bifurcation diagrams while the 2T ROM is used to validate and demonstrate the limitations of these two methods. The effects of damping, fringe, voltage, and detuning frequency are investigated.


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