Frequency Response Analysis of a Capacitive Micro-beam Resonator Considering Residual and Axial Stresses and Temperature Changes Effects

This paper presents a study on the frequency response of a capacitive micro-beam resonator under various applied stresses. The governing equation whose solution holds the answer to all our questions about the mechanical behavior is the nonlinear electrostatic equation. Due to the nonlinearity and complexity of the derived equation analytical solution are not generally available; therefore, the obtained differential equation has been solved by using a step by step linearization scheme and a Galerkin based reduced order model. The obtained static pull-in voltages have been validated by previous reports and a good agreement has been achieved. The dynamic behavior of the beam under residual, axial and thermal stresses has been investigated. It has been shown that applying the positive residual stress and negative temperature changes shifts right the frequency response and decrease the vibration amplitude and vice versa. Also, it has been shown that applying the bias DC voltage beside the exciting AC voltage decreases the stiffness of the system and so, shifts left the frequency response and increases the vibration amplitude.