Improved Mathematical Modeling of Thermal Effects in Flexural Microcantilever Resonators Dynamics

In a recent research the thermal dependency of material characteristics in dynamic response of microresonator systems is modeled using Lorentzian function and employing perturbation analysis. Thermal phenomena introduce two main effects: damping due to internal friction, and softening due to Young modulus-temperature relationship. The presented mathematical model provided effective equations to study the electrically actuated microbeam resonators. The mathematical model of thermal phenomena in microbeam vibration was introduced by Jazar (2009). In that analysis, using the Zener model, a positive frequency dependent damping and a negative frequency dependent stiffness terms were introduced to mode the effects of warming at resonance (Jazar 2009). In this investigation, the problem will be analyzed from a practical point of view. We introduce a better mathematical model by improving the presented model. The main difference would be including the strain distribution in the damping and stiffness model.