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 Chipara

Third Advisor

Dr. Nazmul Islam


Two methods are used in the investigation, which are the Method of Multiple Scales (MMS) and the Reduced order Model (ROM) with up to 6 modes of vibration. The MMS is done in three ways, one based on soft excitation and the other models based on the usage of the bookkeeping parameter, ε, in the electrostatic term. These are referred to as the 1 term no ε, and the 2 term no ε, which allow it to model hard excitation. The influence of the number of terms in the Taylor expansion is explored.

These methods are used to investigate the effects of intermolecular forces such as Casimir or van der Waals, as well as the influence of voltage, the detuning parameter, and damping. This is done for both the amplitude-frequency responses, and the voltage-responses, for various frequencies such as primary, subharmonic and superharmonic resonances.


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