Nonlinear Analysis of Mechanical Behavior of Electrostatically Actuated Step Bilayer Cantilever Microbeam Considering Variable Width for Second Layer

The present paper is aimed to analyze static deformation, natural frequency and subharmonic resonance of a bilayer cantilever microbeam, the second layer of which has a variable width and is located on a point along the microbeam's length. Electrostatic actuation is induced by applying the voltage between the microbeam and its opposite electrode. The importance of such configuration is revealed particularly in mass and pollutants micro-sensors. First, the nonlinear equation of motion, which has been extracted in previous studies using Hamilton's principle and considering the bending neutral axis shortening assumption, was rewritten for a microbeam with variable-width second layer. Then differential equations governing the static deflection and free vibration equation around the stability point are solved using Galerkin method. Three mode shapes of a doubled stepped-microbeam are employed as the comparison function. The shapes such as triangular, parabolic, symmetric parabolic and hyperbolic are considered for the second layer. In order to find the optimal length and thickness for the selected form, the relevant diagrams were plotted for static deformation and natural frequency at constant volume and different lengths and thicknesses, and then were analyzed and investigated. The discretized equations are solved by the perturbation theory. The excitation frequency is tuned near twice the fundamental natural frequencies (subharmonic excitation). The results show that system behavior depends on the size, position and width of the coated layer. The results of this paper can be used for optimum design of microsystems such as microswitches and mass and pollutant microsensors.