Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever

Abstract

The paper deals with free small vibrations of a micro-cantilever near the deformed static position incorporating the electrostatic and intermolecular forces acting from the fixed electrode. First, the initial static deviation of the cantilever due to the external forces is determined using the approach based on the approximation of the resultant lateral forces by the linear or parabolic functions of the axial coordinate, the initial deflection being evaluated under the values of voltage and intermolecular forces less than the critical ones. To study free small vibrations of the initially deformed cantilever, we linearise the nonlinear differential equation in the neighbourhood of the deformed static position. The derived governing equation with variable coefficients is solved using both the asymptotic approach and the Runge – Kutta method. The effect of the applied voltage and the intermolecular forces, including the van der Waals and Casimir ones, is analysed.