Vibration Response Of Shearable Gradient Porous Circular Plate In Thermal Environment

Gradient porous material is a new kind of engineering material which combines the characteristics of both functional gradient material and porous material.Gradient porous materials have both functional and structural properties.Compared with the general dense metal material,it has the advantages of lighter mass,larger specific surface area,stronger specific strength,specific stiffness and energy absorption.Compared with homogeneous materials,graded porous materials can achieve better mechanical performance in one or several aspects through specific design and preparation.Due to the characteristics and advantages of the above gradient porous materials,the gradient porous materials are widely used in lightweight,multifunctional and high-strength structures in aerospace and navigation now and have broad prospects for development in the future.It is great practical value for engineers to study its vibration response,because circular plate is one of the most common basic components in engineering and mechanical structures.Therefore,this paper takes Mindlin circular plate as the research object and gradient porous material as the structural material to carry out the following research:1.This paper introduced the relevant research background,significance and status,and summarizes the physical properties of gradient porous materials,the classification according to pore density,material preparation and future applications,as well as the basic knowledge of Mindlin plate theory and numerical analysis by differential quadrature method.2.In this paper,the governing equation of free vibration of shearing gradient porous circular plate is studied in thermal environment.Based on the Mindlin plate theory and the concept of physical middle plane,a mechanical model of circular plate was established.And the physical parameters of gradient porous materials with two kinds of porosity density distributions is listed.According to the Hamiltonian principle,the motion differential governing equation of the studied circular plate is derived from the displacement function,geometric equation and physical equation of the Mindlin circular plate under the first-order shear deformation condition.For the convenience of numerical simulation,it also derived the differential equation of motion in displacement-strain form,the differential governing equation of motion in mode function form and the differential governing equation of motion in dimensionless form.3.Basing on the motion differential governing equation of the free vibration of the shearing gradient porous circular plate,the dynamic responses of the shearing gradient porous circular plate under various influence conditions in thermal environment are obtained by using the differential quadrature method.Influencing conditions include: Non-thermal environment and Thermal environment;Peripheral fixation and Peripheral simple support;Variable porosity coefficient;Symmetric porosity density distribution model and Asymmetric porosity density distribution model.In this paper,the change degree and characteristics are analyzed in detail by using table data and graph changes about the free vibration frequency of the shearable porous circular plate under the above influence conditions.The results of this study can provide theoretical support and numerical reference for future researches on shearable gradient porous circular plates in thermal environment.