Vibrational Characteristics of Micro Beams

Several high frequency MEMS devices such as resonators and filters can be modeled as electrostatically driven micro-beams. While their static structural response depends solely on the magnitude of the applied voltage and their elastic stiffness, their dynamic response also depends on their mass, damping properties and the applied voltage frequency. In designing these devices, critical parameters must include the maximum voltage, voltage frequency and the natural frequency of the system. Even though the electrostatic force developed by the voltage is non-linear, the system can be modeled as a harmonic system due to the periodic nature of the response. Results from a non-linear structural-electrostatic dynamic model show the importance of the dynamic properties and the non-linear electrostatic force. The results show significantly lower limiting voltages, especially when the driving voltage is close to the natural frequency of the system. The effect of damping is also addressed.