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.

PACS 03.65.Sq -Semi-classical theories and applications PACS 07.10.Cm -Micromechanical devices and systems PACS 85.85.+j -Micro-and nano-electromechanical systems (MEMS/NEMS) and devices Abstract -Applying an external electric field on a graphene surface is an important way to improve the molecular adsorption capability of graphene, thus pull-in instability of suspended graphene sensors becomes a critical issue. Incorporating residual built-in strains, fringing fields and intermolecular forces, an electromechanical model is developed to characterize the nonlinear pull-in behaviors of suspended graphene-based sensors. The obtained results of pull-in voltages agree well with the reported experimental data. Moreover, the fracture failure of graphene sensors is initially compared to the pull-in failure. To avoid pull-in instability and fracture failure, critical formulas of axial pre-stress for zigzag-oriented and armchair-oriented graphene sensors are derived. It is demonstrated that axial pre-stress is an effective and controllable way to improve the pull-in stability of graphene sensors.

Optical gradient force, as a novel type of actuation force for nano-resonators, has recently attracted a lot of attention. In this paper, the inherent nonlinear characteristics of the optical gradient force are analyzed. A nonlinear dynamic model of the ring and spoke resonant system driven by optical gradient force is proposed. The influences of optical input power and geometric parameters on the nonlinear dynamic responses of the system are investigated. The results show that the optical gradient force can cause stiffness to soften. The amplitude increases and the resonance frequency shifts as the input optical power increases. Moreover, the amplitude and resonance frequency of the nano-resonator decrease as the initial gap of the rings increases. Therefore, the resonance frequency can be adjusted by changing the optical input power. This work can be useful for the further design and performance prediction of nano-resonators driven by the optical gradient force.