Study On Nonlinear Dynamics Of Functionally Graded Conical Shells Under Complex Load

Functionally gradet material (referred to as FGM), as a non-homogeneous composite,have a continuous variation of material properties along the thickness direction from onesurface to another. In the field of aerospace, the conical shell often need to work togetherby the aerodynamic loads and mechanical loads, these will lead to big vibration in thesystem, often can produce a lot of noise and even a serious fault. Therefore, the researchinto the dynamics of functionally graded conical shell is very important.In this paper, considering the influence of thermal stress, based on First-Order Sheardeformation theory and von-Karman type nonlinear strain-displacement relationshipcombined with Hamilton’s principle, the nonlinear partial differential equations of motionof FGM truncated conical shells are obtained. Galerkin’s method is utilized to discretizethe partial equations to the ordinary differential equations. Nonlinear dynamic behaviors ofthe FGM truncated conical shell subjected to complex loads are investigated. The mainresearch content includes the following four aspects.(1) The influences of in plane load on the nonlinear vibration are studied, when theFGM truncated conical shell subjected to thermal load. And the comparison of theinfluences of different temperature field on nonlinear vibration is given.(2) The influences of the material gradient index, aerodynamic load, the semi-vertexangle and in plane load of the FGM truncated conical shell subjected to aerodynamic loadand mechanical load on the nonlinear dynamics are studied.(3) under the case of the FGM truncated conical shell subjected to aerodynamic loadand mechanical load, the averaged equations of the system are obtained under the case of1:1internal resonance by using the method of multiple scales. The influences of machnumber and in plane load on amplitude-frequency characteristic and vibration.(4) Considering aerodynamic force with the curvature correction term and theaerodynamic heating, the flutter equations of the FGM truncated conical shell are deduced.The aero-thermo-elasticity flutter characteristics of the FGM truncated conical shell werestudied by solving system of eigenvalue problem and Runge Kutta method.