Nonlinear vibration analysis of a ┴-shaped mass attached to a clamped–clamped microbeam under electrostatic actuation

Abstract

This article studies the nonlinear vibration of a ┴-shaped mass attached to a clamped–clamped microbeam under electrostatic actuation considering the effect of stretching. The DC and AC electrostatic force is applied to the horizontal part of ┴-shaped mass. The dynamic solution is studied using two methods of modeling. In the first model, the ┴-shaped mass is considered as a rigid body between two flexible microbeams. Then, the discretized equation of motion is derived using Lagrange’s equation combined with assumed mode method. The vibration mode shape of linear system is used as the comparison functions. In the second model, the dynamical effect of ┴-shaped mass is modeled as a concentrated force and moment, and it is introduced in the equation of motion by the Dirac function. Afterwards, the equation of motion is discretized using Galerkin method. In both methods of modeling, the equations of motion are solved using two methods. The first method is approximate analytical perturbation and the other one is Runge–Kutta numerical method. The effect of geometrical dimension of ┴-shaped mass on the nonlinear shift of resonance frequency and dynamic pull-in voltage is studied. The efficiency and accuracy of the presented formulations is verified by comparing the obtained results by two methods of modeling and two methods of solution.