Dynamic Response Of Functionally Graded Material Circular Plates With In-plane Vibration

Functionally graded material is a novel composite material invented in recent years.The components made by it have excellent mechanical properties different from those of the homogenous materials in high temperature environment.It is made through the reasonable combination of two or more metal or ceramic materials.Due to the superiority of its physical properties,FGM often be used in high-temperature environment in the need to withstand the aerospace,nuclear industry and chemical fields.Therefore,the mechanical properties of the functionally graded material plate s have become an active topic in the field of engineering applications.In this paper,we study the dynamic mechanical behavior of functionally graded material plates in considering in-plane vibration.The main research results and conclusions are summarized as follows: 1.Dynamic response of FGM circular plates with in-plane vibrationFirst,the Voigt's model is used to simulate the material gradient of the functionally graded material circular plates and the material properties are assumed to be graded in the thickness direction of circular plates and assume that the change form is in the form of a power function.Basing on the classical plate theory,considering the transverse vibration and the in-plane vibration,the kinematic differential equations of the linear dynamic response of the thin plate of the functionally graded material under the axisymmetric condition are deduced by the Hamilton 's principle and variational method.The equation is degraded into a general homogeneous plate,and its natural frequency is solved,and the result is very close to the relevant literature.Numerical results of thin FGM circular plates with different boundary are obtained by using shooting method.The numerical results are discussed and the influence of the in-plane vibration on the vibration of the FGM circular plate s is considered.2.Dynamic response of FGM circular plates with in-plane vibration on theWinkler elastic foundationBasing on the vibration of FGM plates on the Winkler elastic foundation,the dynamic response of functionally graded circular plates under two boundary conditions are studied considering the in-plane vibration.We apply the most basic classical board theory,considering the small deformation problem,ignoring the inertia moment,the control equation of the vibration of the FGM circular plates on the Winkler foundation under the axisymmetric condition is obtained.Assuming that the vibration of the FGM circular plates are the harmonic response mode,the partial differential equation is transformed into the ordinary differential equation.The dynamic response of the FGM thin plates are solved by using the shooting method.The influence of elastic foundation parameters and in-plane vibration on the dynamic response of FGM circular plates are analyzed by numerical results.The research of this paper enriches the research results of the dynamic mechanical behavior of FGM circular plate s,and draws references for the study of the vibration characteristics of FGM circular plate structure,which is of great significance to the application of FGM circular plate s in engineering practice.