Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Dr. Dumitru Caruntu

Second Advisor

Dr. Robert A. Freeman

Third Advisor

Dr. Dorina M. Chipara


The nonlinear dynamics of electrostatically actuated micro-electro-mechanical system (MEMS) cantilever resonators are investigated. The applied Alternating Current (AC) voltage is in the realm of superharmonic resonance of the second order (near one-fourth of the natural frequency of the resonator) and hard excitations. Method of Multiple Scales (MMS) and Reduced Order Models (ROMs) are used to solve the dimensionless partial differential equation (PDE) of motion along with boundary and initial conditions. MMS transforms the PDE of motion into zero-order and first-order problems. ROMs uses mode shapes of vibration for undamped cantilever resonator as a basis of functions. ROM is numerically integrated using AUTO 07P and MATLAB software to obtain the bifurcation diagrams as well as time responses. The bifurcation diagrams allow one to observe bifurcation and pull-in instabilities within the nonlinear system over a range of frequencies and range of voltages, respectively. The influences of dimensionless parameters, namely voltage, detuning frequency, fringe effect, and damping are investigated.


Copyright 2018 Martin Amador Botello. All Rights Reserved.