Dynamics of non-uniform beams for microelectromechanical systems

Singh, Sajal Sagar (2016) Dynamics of non-uniform beams for microelectromechanical systems. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

Microelectromechanical systems (MEMS) based cantilever beams have been widely used in various sensing applications. Most of the studies concerning these micro/nano resonators are centred around uniform cantilever beams. In this thesis, another class of micro-resonators consisting of non-uniform cantilever beams is investigated. Two classes of beams, one with increasing cross sectional area from the clamped edge (diverging beam) and other with decreasing cross sectional area from the clamped edge (converging beam) are studied. Within each class, beams with linear as well as quartic variation in width are investigated. Firstly, the Euler beam equation for non-uniform cantilever beams considering large deflection and their corresponding exact mode shapes from the linear equation are obtained. Subsequently, using the Galerkin method based on single mode approximation, static and dynamic modal equations for finding pull-in voltage and resonance frequency as a function of DC voltage, respectively are obtained. The research in this thesis is focused around investigating different characteristics including the pull-in voltage, resonance frequency at zero and finite DC voltage, mass sensitivity, size effects, etc. of non-uniform cantilever beams. The analysis is presented when these micro beams operate in the linear regime about different static equilibriums. In this thesis, we term this frequency as `linear frequency'. Calculation of the linear frequency is done at different static equilibriums corresponding to different DC voltages. It is found that linear frequency of converging beams increases with increase in non-uniform parameter (α) while those of diverging beams decreases with α. A similar trend is observed for pull-in voltage. Within the converging class, beams with quartic variation in width show significant increase in both frequency and pull-in voltage as compared to corresponding linearly tapered beams.

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