Size Effect On The Pull-in Instability Of Electrostatically Actuated Micro-beam

The equipments of MEMS(Micro-Electro-Mechanical-Systems:MEMS)have been widely used in the fields of space exploration,intelligent control,biomedicine and other fields because of light weight,small size,short time response,low power.Due to the small size of the electrostatic actuator,the mechanical behaviors of the equipment are very different from those in the macroscopic state.At present,it has been proved by experiments that the mechanical behaviors show size effect phenomenon abviously.There is no material length scale parameter related to the size effect in the classical continuum theory,therefore,the classical continuum theory can not explain size effect phenomenon of the micro components above mentioned.However,the high-order strain gradient theory,such as couple stress theory,modified couple stress theory,strain gradient elasticity theory.The size effects of the mechanical properties of some parameters can be explained by drawing into one or more size parameters of the material related to the size effect in the constitutive equation.Because of the modified couple stress theory has only one additional material length scale parameter is comprised except two classical material constants,it has a great advantage to establish the theoretical model of micro components and to analyze the mechanical properties.In this paper,by considering the influence of Casimir force,the electrostatically actuated micro-beam model are established based on the modified couple stress theory.The high order nonlinear control equations are solved by the generalized differential quadrature method.The Pull-in voltage and dimensionless pull-in displacement of micro-beam with different geometrical parameters are analyzed.The specific research results are as follows:The pull-in voltage from the new model is larger than the value of classical theory of electrostatically actuated micro-beams when the thickness of microbeams equals to the material length scale parameter and the size effect is obvious.However,the size effect is almost diminishing as the thickness of microbeams is far greater than material length scale parameter.In addition,the pull-in voltage and the dimensionless pull-in displacement from the new model also increased during the ratio between the initial gap and the thickness increased.But the influence of the Casimir force can be neglected when the initial gap between the upper and lower paltes is much larger than the thickness of the microbeam.Furthermore,the Casimir force can reduce the pull-in voltage and the dimensionless pull-in displacement.Finally,A visual application platform is developed based on the MATLAB software to solve the nonlinear governing equations of the Pull-in characteristics of electrostatically actuated micro-beams.The visual application platform realizes the visualization of the characteristic size effect of electrostatically actuated micro-beams.