Analysis of Effects of Different Changes on the Frequency of a Micro-beam Resonator

This paper deals with the analysis of eigen frequency in a fixed-fixed micro-beam resonator considering effects of the tensile or compressive residual stresses, axial stress and temperature changes. Non linear governing differential equations of static deflection of the micro-beam using Euler-Bernouli beam theory has been derived, and linearized using a step by step linearization method. The obtained linearized differential equation has been discretized using a Galerkin weighted residual method. The equation of small oscillations about statically deflected position has been derived and solved using a Galerkin based reduced order model. The results show that owing to different applied voltage, residual stress and axial stress and temperature changes, the resonance frequency of the resonator is changed. Obtained results show that negative temperature changes and tensile residual stresses increase the first natural frequency and compressive residual stresses and positive temperature changes viceversa. Axial stress increases the first resonant frequency and its effect is more considerable when the applied DC voltage is close to the pull-in voltage.