Study On Nonlinear Dynamics Of Functionally Gradient Conical Curved

Functionally graded material(FGM) is a new composite material compared to the traditional composite material, diatribution types of material components are graded in thickness direction according to the actural engineering needs. FGM usually made of corrosion resistance and good toughness material(metal) and heat resisting material(metal) which has good heat resistance and guarantee a high enough mechanical strength. Due to these excellent mechanical and physical properties of functionally graded material, it can be applied to high temperature environment, especially the situations that temperature on both sides of the material are great differences. In the field of aerospace, the circular conical panel structure will appear large amplitude nonlinear vibration which can lead to structural damage and even catastrophic accidents. Therefore, the research into the dynamics of functionally graded circular conical panel has important engineering significance and theoretical value.In this paper, considering the influence of thermal environment, based on First-Order Shear deformation theory and von-Karman type strain and displacement relationship, using the Hamilton’s principle to establish the nonlinear dynamic partial differential equations of functionally graded material circular conical panel. Then Galerkin’s method is utilized to discretize the partial differential equations of motion to the nonlinear ordinary differential dynamics system. Nonlinear dynamic behaviors of the FGM circular conical panel are investigated. The specific work including the four aspects.(1) Nonlinear dynamic behaviors of the initial imperfect FGM circular conical panel subjected to thermal and mechanical load are investigated. The two-degree-of-freedom ordinary differential equation of motions are derived by Galerkin’s method. Numerical simulations are performed to compare different imperfection parameters.(2) Nonlinear dynamic behaviors of the perfect FGM circular conical panel subjected to thermal and mechanical load are investigated. The nonlinear vibration response of different indexes of volume fraction for ceramic, temperatures and thickness-radius ratios are compared.(3) The averaged equations of the perfect FGM circular conical panel under the case of 1:2 internal resonance are obtained by using the method of multiple scales. The influence of in-plane excitation and damping on the amplitude-frequency characteristic, and the amplitude jump phenomenon under the in-plane load are researched. Runge-Kutta method is applied for numerical simulation.(4) Considering the aerodynamic force and aerodynamic heating, the six-degree-of-freedom flutter equations of perfect FGM circular conical panel with constants are obtained by Galerkin’s discrete. Newton iterative mothod and continuation method is applied to calculate the steady-state solution of the system and solve the eigenvalue problem, the flutter point can be obtained. The aero-thermo-elasticity flutter characteristics of the circular conical panel are analyzed by Runge-Kutta method.