Mathematical modeling and simulation of thermal effects in flexural microcantilever resonator dynamics

摘要

The thermal dependency of material characteristics is an important phenomenon affecting the motion of microresonator systems. Thermal phenomena introduce two main effects: damping due to internal friction, and softening due to the Young's modulus-temperature relationship. Based on reported theoretical and experimental results, we qualitatively model the thermal phenomenon utilizing a Lorentzian function to describe its effect on restoring and damping forces. We present the mathematical modeling of microresonator dynamics and develop effective equations to study the electrically actuated microbeam resonators. In order to study the thermal effects, a linearized model of the microelectromechanical system is adapted. The response of the system at steady-state conditions is developed by employing the averaging perturbation method on the non-dimensionalized form of the equations. Frequency response, resonant frequency and peak amplitude are examined for variation of the dynamic parameters involved.