Frequency analysis of microbeams with axial pretension

Erravelly, Indrasena Reddy and Pandey, Ashok Kumar (2019) Frequency analysis of microbeams with axial pretension. Masters thesis, Indian institute of technology Hyderabad.

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Abstract

Microstructures like beams, bars and membranes are being used in micro-electro-mechanical systems and few other microstructures - the microbeams made with traditional silicon-based materials, metals, polymers etc. Microbeams are designed based on some basic requirements like natural frequencies of the beams and deflection of the membranes. In this work, we investigate the frequency analysis of microbeams with an axial force using Eringen’s nonlocal elasticity theory. We employed the differential quadrature method and compared the obtained results with the analytical process. We also investigated the frequency analysis of microbeams using modified strain gradient theory, modified couple stress theory and the results compared with the classical elasticity theory. Numerical examples are given for the three end conditions of the microbeams, i.e. simply-supported beams, clamped-clamped beams and cantilever beams. The axial pretension is varied, and the effects of the force variation on frequencies and size effects are shown. The analysis is helpful where size effects are evident; our study is vital to obtain correct frequencies for beams with different end conditions. The analytical method presented in this work can be used for the analysis of micro-curved beams, and one can include the small scale effects by using MSGT, MCST or Nonlocal elasticity theory.

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