Nonlinear Dynamical Analysis Of Microresonators Considered Nonlinear Damping And Small-scale Effects

Micro-electro-mechanical systems involve interdisciplinary,in which can be applied and developed in natural and engineering fields.Micro-electro-mechanical systems are important development direction p ointed out clearly by the national plan for medium and long term scientific and Technological Development.This paper focuses on the microresonator with wide application prospects in Micro-electro-mechanical systems.The small-scale effect and nonlinear da mping have a significant effect on the nonlinear vibration of the microresonator,but the theoretical research on the small-scale effect and nonlinear damping is still not perfect and needs to be further deepened.We use the slender beam model including th e small-scale effect and nonlinear damping to investigate the nonlinear vibrations of the electrostatic resonators in the present paper.We apply the Galerkin method on a nonlinear partial differential equation to obtain the nonlinear ordinary differential equations for first and third modes.The two equations include constant terms.The multiple scale method are used to obtain the approximate analytical solutions of the two equations.Then,the approximate analytical solutions discover the effects of drivi ng electric field,small-scale effect,and nonlinear damping on structural vibrations.The results suggest the following:（1）The electrostatic force term leads to the constant term in the nonlinear differential equation.（2）In order to avoid the buckling of the beam caused by the axial force,it is necessary to limit the resonator parameters and the initial axial load.（3）Under the same excitation voltage,the amplitudes of the third mode are much smaller than these of the first mode.（4）The small-scale effect has a significant impact on both static loading and dynamic vibration.The nonlinear damping has a small effect on the vibration amplitude when the load’s frequency is less than the modal frequency.However,when the load’s frequency is greater than the modal frequency,nonlinear damping will change the jump points of the load.（5）Both direct current (V_DC) and alternating current(V_AC)have a significant effect on the vibration amplitude for the prima ry resonance.When the exciting frequency is greater than the modal frequency of the microbeam,the external excitation terms and the nonlinear damping terms cause the response curve to bend and result in the multi-value amplitude and jumping phenomena.The theoretical research in this paper reveals the laws of vibration of micro-beam resonators considering small-scale effects and nonlinear damping.These laws will help people better understand the nonlinear vibration behavior of micro-beam resonators.Further experimental research and theoretical exploration can be done according to these results.