Vibrations of functionally graded material conical panel subjected to instantaneous thermal shock using Chebyshev-Ritz route

Abstract

The present study deals with the phenomenon of thermally induced vibrations in a conical panel. The considered conical panel is made of functionally graded materials. All thermal and mechanical properties of the panel are distributed through the thickness direction. The properties of two constituents are considered to be temperature-dependent. A volumetric power law is used to express the volume fraction of ceramic and metal. Also, the rule of mixtures is employed to calculate each thermo-mechanical property. First, the one-dimensional heat transfer equation through the thickness of the shell is solved for different boundary conditions, including the states of constant temperature, surface flux, and insulation. Due to the dependence of the thermal conductivity on the temperature, the heat transfer equation will be nonlinear, which requires an appropriate numerical model to be solved. The heat transfer equation is discretized using the appropriate numerical method (finite element) and traced in time by the Crank-Nicolson method. Then, the equations of motion of the shell are derived using the first-order shell theory and solved in the spatial and time domains employing an appropriate numerical method (Ritz) and the Newmark method, respectively. The numerical method is suitable for various types of boundary conditions. Finally, the effects of inertia, mechanical and thermal boundary conditions, shell geometry, and temperature dependence of the responses are investigated.