Thermally Induced Vibrations of Temperature Dependent FGM Cylindrical Panel

Abstract

The current research deals with the rapid surface heating of cylindrical panels made of functionally graded materials (FGMs). The investigation encompasses the temperature-dependent nature of all thermo-mechanical properties within the FG media. Applying the uncoupled linear thermoelasticity theory establishes a one-dimensional transient heat conduction equation modelled by the Fourier type. Various distinct rapid heating boundary conditions are imposed on the top and bottom surfaces of the panel. First, the finite element method (FEM) is utilized to discretize the heat conduction equation across the panel thickness. As a result of the temperature dependence of the material properties, the heat conduction equation takes on a nonlinear form. Consequently, the time-dependent ordinary differential equations system is tackled through the iterative Crank–Nicolson time-stepping method. The thermal force and thermal moment outcomes acquired at each time increment from the temperature distribution are integrated into the equations of motion. The equations of motion are derived using the first-order shear deformation theory (FSDT). Due to the accuracy and suitable convergence rate , the Ritz method is used to discretize the equations of motion. The direct integration method based on the Newmark time marching scheme is employed to determine the unknown displacements at any given time. The accuracy of the formulation and solution method is verified through comparison investigations. Numerous examples are presented for functionally graded material consisting of SUS304 as the metal component and Si\(_3\)N\(_4\) as the ceramic component to examine the effects of various parameters such as power law index in the FGM formulation, temperature dependence, panel opening angle, in-plane and out-of-plane boundary conditions, and type of rapid heating on the thermally induced response of the FGM panel under thermal shock.