An efficient methodology for modelling nonlinear deflection of thin cantilever beams for microelectromechanical systems
This paper presents an effective approach to estimate the nonlinear deflection of thin cantilever beams, which are the building blocks of micro and nano electromechanical systems, fabricated with micro and nanosized characteristic lengths. Based on the large deflection Euler-Bernoulli equation, mathematical expressions for the vertical and horizontal deflections are generated. These equations are inherently nonlinear and cannot be solved easily, but numerically or using elliptical integrals. The later is adopted here to obtain theoretical deflections, which are compared with experimental results in order to identify empirical deflection models based on quintic polynomials. Theoretical and experimental results are presented to validate the deflection models and to demonstrate the efficacy of the models in order to estimate the nonlinear deflection of the cantilever beams. The methodology proposed in this study is offered to model and estimate deflection of micro and nanosized cantilever beams, and use these models to estimate their, otherwise difficult to measure parameters such as the modulus of elasticity.