Large Amplitude Nonlinear Heat-Induced Vibrations of Temperature-Dependent FGM Conical Panels

This research deals with the large amplitude vibrations in a conical panel under the action of sudden temperature elevation. The conical panel is made of functionally graded materials where properties vary through the thickness direction. All of the properties are considered to be temperature-dependent for the constituents. The one-dimensional heat conduction equation is established for the FGM panel and solved using the central finite difference scheme and Crank–Nicolson algorithm. First-order shear deformation theory of shell with Donnell type of kinematics and also von Karman type of geometrical nonlinearity are employed to extract the governing equations of the shell. These equations are discretized via the method of generalized differential quadrature and also are traced in time using the Newmark time marching method. Since the equations are nonlinear the method of Picard is applied to extract the solution. Results from this study are devoted to studying the impact of temperature dependency, thickness ratio, aspect ratio, thermal and mechanical boundary condition, opening angle and semi-vertex angle on the temporal evolution of shell deflection. It is shown that all of the mentioned parameters have a great impact on the response of the FGM conical shell subjected to thermal shock.