A practical method for calculating eigenfrequencies of a cantilever microbeam with the attached tip mass

Abstract

This paper is concerned with the free vibration of cantilever microbeams with attached tip mass in a systematical manner. Small size effects on the vibrations of the microbeam are taken into consideration by introducing a scale parameter. A Fourier sine series is used to represent the lateral displacement function. Stokes' transformation is applied in the present formulation and corresponding derivatives are presented explicitly. The present formulations can be readily reduced to those for others classical elasticity models by setting corresponding small scale parameter to zero. Several parametric studies are performed to validate the present solutions and the effects of various important physical parameters (scale parameter, tip mass) are investigated.