Size-Dependent Nonlinear Vibration Analysis of Electrostatically Excited Bi-directional Functionally Graded Microbeam Mass Sensor

Functionally graded (FG) materials are widely used in several micro-scale systems mainly due to their property tailoring ability. The current study examines the dynamic response of a bi-directional functionally graded microbeam mass sensor in the presence of electrostatic forces and squeezes film damping and attached mass forces. The resonator beam is analyzed by Euler beam theory with modified couple stress theory (MCST) by considering geometrical nonlinearity. The equations of motion are formulated and the Galerkin’s method is employed to obtain the approximate solution. The FG resonator with doubly clamped end condition, central electrostatic load with fringing field effect, squeeze film damping and tip mass are considered for illustration. The present analysis is validated through direct comparisons with available results. In order to investigate the influences of material grading indices, length scale parameters and air-damping factor, the vibration response of the homogeneous and FG microbeam mass sensors is analyzed parametrically. It is observed that there is a remarkable effect of these key factors on the dynamic deflection.