Dynamic Analysis Of A Rotating Functionally Graded Material Microplate Under Temperature Field Conditions

Many structures can be simplified as hub-micro beams,micro plates,and micro shells in micro scale,such as micro turbines,micro rotor aircraft.nano engines and so on.Experiments have revealed that the classical continuum mechanics theory cannot correctly explain the mechanical properties of microstructures.In addition,the engineering structures often operate in high-temperature environments,while structures made of traditional materials have disadvantages such as poor insulation,poor corrosion resistance,and stress concentration.Therefore,it is necessary to study the dynamic characteristics of micro mechanical systems made of new composite materials.In this paper,the steady-state free vibration and transient dynamic response of functional gradient material rotating microplate systems in thermal environment are studied based on the rigid-flexible coupling dynamic modeling theory,the floating coordinate system method,the meshless radial point interpolation method,and the modified couple stress theory.The research work and main achievements of this article are as follows:1.Based on the modified couple stress theory,Mindlin plate theory,and von Karman geometric nonlinear theory,considering material heterogeneity and the higher-order terms of nonlinear coupling deformation which are ignored before,a meshless radial point interpolation method is used to describe the deformation field of a flexible plate,the higher-order rigidflexible coupled nonlinear dynamic model of a functionally graded material rotating microplate is established.2.Further considering the thermal effect,a one-dimensional steady-state heat conduction equation is introduced,and assuming that the temperature field gradient changes along a specified direction,a rigid-flexible coupled nonlinear dynamic model of functionally gradient material rotating microplates is established in thermal environment.3.The dynamic simulation of a functionally graded material rotating microplate system is performed.And the simulation results of the meshless method are compared with those of the traditional assumed mode method and the finite element method,which verifies the correctness of the meshless method.Numerical examples are presented for investigating the effects of temperature,functional gradient index,material length scale parameters,microplate geometric parameters and rotational laws on the dynamic behavior of microplate.It is revealed that the increase of non-dimensional material length scale parameter increases the stiffness of the microplate,which accordingly,results in an increase in natural frequencies and a decline of transient responses.The functionally graded index and angular velocity noticeably affect the natural frequencies and transient responses of rotating microplates.With the change of the rotation speed of the microplate,the microplate will occur frequency loci veering and mode shift phenomenon.