Dynamic Characteristics of Electrostatically Actuated Shape Optimized Variable Geometry Microbeam - Sha Zhang; Wen-Ming Zhang; Zhi-Ke Peng; Guang Meng (Shock and Vibration)
We mainly analyze the dynamic characteristics of electrostatically actuated shape optimized variable geometry microbeam. A nonlinear dynamic model considering midplane stretching, electrostatic force, and electrical field fringing effects is developed. Firstly, we study the static responses of the optimized microbeams under DC polarization voltage. The generalized differential quadrature method (GDQM) is used. Secondly, the dynamic responses of the shape optimized microbeams driven by DC and AC voltages are investigated using GDQM in conjunction with Levenberg-Marquardt optimization method. The results show that the more gradual change in width, the larger the resonant frequency and the maximum amplitude at resonance. Then we further discuss in detail how do the maximum width, midsection width, and curvature of the width function affect the frequency response of the microbeams. We find that the amplitude and resonant frequency of the dynamic response are not monotonically increasing as the curvature of the width function increases and there exists a critical curvature. This analysis will be helpful in the optimal design of MEMS actuators. Finally, for more consideration, different residual stress, squeeze-film damping, and fringing effect models are introduced into the governing equation of motion and we compare the corresponding dynamic response.