Vibration And Buckling Analysis Of Functional Graded Material Axisymmetric Circular Plate Based On Levinson Theory

Functional graded material is a new type of non-uniform composite material,because of its excellent performance has attracted the attention of experts and scholars at home and abroad.The material properties of the functionally graded material vary continuously in one or more directions,and the inherent material properties are not uniform,which brings great difficulties to the mechanical analysis.In the past,mechanical concepts,theories and experimental methods for the introduction and development of homogeneous materials have many applications that are no longer applicable to functional gradient materials and require exploration and innovation.In-depth study of these mechanical problems is to promote the use of functional gradient material premise,but also to promote the development of nonuniform media mechanics.The main work of this paper includes the following three parts.Firstly,the governing equations of the general form of functionally graded circular plates under Levinson third-order shear theory are obtained by Hamilton principle.The governing equations of the general form of the functionally graded material circular plate under the Levinson third-order shear theory are deduced to the equilibrium equation of free vibration and buckling problem.By selecting the appropriate coordinate plane,the coupled equilibrium equation is partially decoupled to obtain a motion equation with only deflection.The solution of FGM circular plate free vibration and buckling problem under different boundary conditions under Levinson's theory is obtained by using the series method.Based on the verification of the results,the convergence of the series is studied,and the pitch radius and modal characteristics of the vibration modes are given.Finally,the influence of gradient coefficient and plate thickness on free vibration frequency and critical load is studied.Secondly,on the basis of the analytical solution,the free vibration problem and the buckling problem are regarded as the eigenvalue problem.By using the load equivalent and the similarity of the problem in mathematical,the relationship between functionally gradient Levinson axisymmetric circular plate and the uniform Kirchhoff axisymmetric circular plate is obtained.In this way,as long as the critical load and natural frequency of a uniform Kirchhoff axisymmetric circular plate with the same boundary condition are known,the critical buckling load and the natural frequency of the FGM plate under the Levinson theory can be obtained by using the transformation relation,thus avoiding the complex solutions of coupled differential equation.Moreover,the influence of the no shear deformation theory on the free vibration frequency and the critical load is further discussed.Finally,the physical model of FGM axisymmetric circular plate with various materials is constructed.The mechanical properties of the symmetrical circular plate composed of multi-layer materials are studied.A general representation of the material properties of a symmetrical circular plate within the material is given.This is applicable to any FGM axisymmetric circular plate of any number of materials.The free vibration frequency and critical load of the three-layer FGM axisymmetric circular plate are calculated.The influence of the new material on the mechanical properties of the FGM axisymmetric circular plate is studied,providing a new idea for the research of the functionally graded material.