The Research On Multi-Nonlinear Coupled Dynamic Response Of Variable-Cross-Section Mems Switches

With Micro-Electro-Mechanical System(MEMS)technology has been one of the most important development directions in the 21 st century,MEMS dynamics is becoming a new research area and focus gradually.In order to meet the demands of MEMS,the researches on MEMS switches are developing towards high frequency,low driving voltage,low cost and large scale integration.Previous studies show that geometric nonlinearity caused by large deformation,loading nonlinearity from the electrostatic force and other factors jointly affect the vibrational and mechanical properties of MEMS switches,arising from the nonlinear dynamics problems has been academia extensive attention and has become one of the hotspots in the study of MEMS.At the same time,MEMS preparation materials such as monocrystalline silicon,polycrystalline silicon,silicon oxide,shape memory alloy,grapheme etc generally possess nonlinear elastic constitutive relationship belong to material nonlinear,and now theoretical research at home and abroad are only for approximate linear processing,which will to the applications of MEMS brings the problem of reliability and safety,so material nonlinearity should also be concerned and studied.In this paper geometric nonlinearity caused by large deformation,loading nonlinearity from the electrostatic force,size effect,fringing fields and the nonlinear elasticity constitutive relationship from the MEMS materials are comprehensively considered to systematically analyse the dynamic characteristics of variable-cross-section microcantilever switches,the main research contents and results are as follows:(1)Setting the variable-cross-section microcantilever as the research object,it’s the first time the influence of variable-cross-section on nonlinear vibration response of MEMS switches is studied.The change rules of the amplitude and the response cycle(frequency)of MEMS switches showed by numerical examples provide theoretical supports for shape design of MEMS switches and a reference for analysis of dynamic problems of variable-cross-section MEMS switches.(2)Setting the variable-cross-section microcantilever as the research object and taking into account the geometric nonlinearity,loading nonlinearity,size effect,fringing fields and material nonlinearity,the first time that the nonlinear equations governing the longitudinal-transverse motions and the corresponding initial-boundary conditions are derived by means of Hamilton’s principle in conjunction with the modified couple stress theory to research the influence of material nonlinearity on the dynamic response of a variable-cross-section MEMS switches.Through the analysis of examples,the amplitude and the response cycle(frequency)of the dynamic response of the variable-cross-section MEMS switches are defined under the material nonlinearity.The mathematical model can well reflect the characteristics of multi nonlinear coupling dynamics of MEMS,especially the influence of material nonlinearity on the dynamic characteristics of MEMS,makes the design of MEMS more reliable and more secure.(3)For the first time,the time-domain DQ method is used for the research on multi-nonlinear coupled dynamic response of variable-cross-section MEMS switches.By employing regular perturbation method,the nonlinear governing equation is transformed into a set of linear differential equations which are then solved by using time-domain DQ method step by step and then use MATLAB software to simulate time-displacement response of the MEMS switches.The analysis results show that time-domain DQ method is an effective method and the principle is simple and easy to program,the calculation accuracy is good,and the efficiency is high.Therefore,this method is an effective numerical method for solving nonlinear dynamic problems,and it is worth popularizing.