One-to-One and Three-to-One Internal Resonances in MEMS Shallow Arches

[+] Author and Article Information
Hassen M. Ouakad

Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, KSA

Hamid M. Sedighi

Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, IRI

Mohammad I. Younis

Mechanical Engineering Department, State University of New-York, Binghamton, 13850, NY, USAPhysical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, KSA

1Corresponding author.

ASME doi:10.1115/1.4036815 History: Received November 08, 2016; Revised May 16, 2017


The nonlinear modal coupling between the vibration modes of an arch shaped microstructure is an interesting phenomenon, which may have desirable features for numerous applications, such as vibration-based energy harvesters. This works presents an investigation into the potential nonlinear internal resonances of a Micro electro mechanical systems MEMS arch when excited by static (DC) and dynamic (AC) electric forces. The influences of initial rise and mid-plane stretching are considered in the governing equation. The cases of one-to-one and three-to-one internal resonances between the first and second modes and between the first and third modes are studied using the method of multiple scales and the direct attack of the partial differential equation of motion. It is interestingly shown that for distinct domain of actuation voltages, there exist three-to-one internal resonance between the first and third symmetric modes and one-to-one internal resonance case between the first symmetric and the second antisymmetric mode. These results can shed light on such interactions that are commonly found on micro and nano structures, such as carbon nano tubes.

Copyright (c) 2017 by ASME
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