Thermal Modal Analysis Of Functionally Graded Plate

Functionally gradient material(FGM)is a new type of composite material.Its composition,structure or physical parameters are constantly changing to adapt to different environments,so as to realize a particular function.Pneumatic thermoelastic research is focused on thermal vibration and thermal flutter problem,and the emphasis of the research on the thermal elasticity is the thermal vibration and the thermal flutter.Therefore,it is very important to analyze and study the thermal mode problems of functionally graded materials.In this paper,the thermal mode of a new type of FGM composed by ZrO2 and Al1100 are analyzed by using finite element method.and the correctness of this method has have been proved.The influence of the porosity,displacement boundary conditions and the center hole on FGM thermal modal are discussed.In this paper,the thermal load of FGM plate under the action of thermal stress calculation formula is derived based on the finite element method,and use the principle of minimum potential energy,the heat load of the structure is deduced under the condition of equivalent thermal load.And then expounded the related theory of thermal vibration,the initial displacement stiffness matrix and the initial stress stiffness matrix expression are deduced in detail.Then,based on the variational principle,the initial displacement stiffness matrix and the initial stress stiffness matrix of the nonlinear plate element are derived in detail.At last,based on the classical thin plate theory,the thermal model of a functionally graded material plate with fixed boundary conditions and simply supported boundary conditions is analyzed by means of ABAQUS's two development of Python.The results of numerical examples show that:With the increase of the temperature of the thin plate,the natural frequency of the FGM thin plate will decrease when the condition that porosity parameter Az is certain,when the FGM control parameters are constant,and the temperature of FGM thin plate is fixed,the natural frequency of the FGM plate will increase with the increase of the porosity control parameter Az.when the temperature and porosity control parameters Az of the FGM plate are certain,hole will have a great impact on the natural frequency of the FGM plate,and with the increase of plate hole radius r,the natural frequency of the FGM plate will increase;when the temperature and hole radius r of FGM plate are certain,the natural frequency of FGM the perforated plate increases with increasing porosity control parameters Az of the FGM plate;when the porosity control parameters Az and hole radius r are certain,with the increase of the temperature of the FGM plate,the natural frequency of FGM plates with holes will continue to decrease.When the FGM plate temperature,porosity control parameters and center hole radius are the same,the natural frequency of the FGM plate with displacement boundary condition is higher than the natural frequency of the FGM plate with simply supported.This study provides a basis for the dynamic analysis of functionally graded materials at elevated temperatures.