Free Vibration And Stability Analysis Of Variable Thickness FGM Circular Plates Considering Temperature-dependent Material Properies

Functionally graded material(FGM)is a new type of composite material.It is widely used in aerospace,nuclear industry,machinery manufacturing and other fields,through reasonable design to make its physical properties superior to conventional uniform materials.In recent years,the deformation and dynamics of functionally graded components under thermal loading have become one of the hot issues in mechanical research.In this paper,the numerical solution method is used to analyze the free vibration of FGM variable-thickness circular plates in different thermal environments and the stability problems in different temperature fields.1.Based on the first-order shear plate theory,the governing differential equation of free vibration of FGM variable-thickness circular plate under two-parameter elastic foundation is established by using Hamilton’s principle.The first order transverse shear deformation and the temperature dependence of material property parameters are fully considered in research.The vibration governing equations and boundary conditions of the circular plate are dimensionless and discretized.Differential quadrature method(DQM)was used to numerically solve the control equation.The results of homogeneous plate degenerated into the same working condition were compared with the existing literature data to verify the effectiveness of the method.Then the influence of thickness change on the vibration frequency of homogeneous circular plate under different boundary conditions was discussed in detail.2.The free vibration response of FGM variable-thickness circular plate without thermal load is numerically solved by DQM method,and the relation curve of natural frequency of FGM circular plate with material gradient index and thickness to diameter ratio under different boundary conditions was obtained,and the results were analyzed.The vibration frequencies of FGM variable-thickness circular plates under different boundary conditions in the field of uniform temperature rise and non-uniform temperature rise were emphatically researched.The correlation curves and charts of vibration frequencies and physical parameters in different temperature fields were made,and the effects of different temperature fields on vibration frequencies were compared quantitatively.3.The stability of FGM plate under thermal loading is researched.The dynamic equation of FGM circular plate is degenerated into the static equilibrium equation of FGM circular plate,and the dynamic equation is obtained by substituting bendingmoment and shear force,The influence of material properties and first order shear deformation on the stability of circular plate is considered.The relation curve between the critical buckling load and the gradient index of the circular plate in the field of uniform and non-uniform temperature rise is obtained by using the shooting method.The influence of two temperature fields on critical buckling load is analyzed,and the influence of gradient index and thick-diameter ratio on critical temperature parameters in different non-uniform heating fields is discussed quantitatively.The research results of this paper can provide theoretical basis and effective numerical results for the research of the vibration characteristics and stability of functionally graded materials under thermal load.