Geometrically nonlinear response of FGM joined conical–conical shells subjected to thermal shock

Abstract

Geometrically nonlinear thermally induced vibrations of functionally graded material (FGM) joined conical–conical shells is analyzed in the current research. Thermo-mechanical properties of the shell are assumed to be temperature and position dependent. The system of joined conical–conical shells is subjected to thermal shock on the ceramic-rich surface, whereas the metal-rich one is kept at reference temperature. The one-dimensional transient heat conduction equation is established and solved via the generalized differential quadrature (GDQ) and the Crank–Nicolson methods. This equation is nonlinear since the thermo-mechanical properties of the shell are temperature dependent. The total functional of the shell is obtained under the assumptions of uncoupled thermoelasticity laws, first order shear deformation shell theory, and the von Kármán type of geometrical non-linearity. Non-linear coupled equations of motion are solved via the iterative Picard method accompanied with the β-Newmark time approximation technique. Numerical results are well validated with the available results for the case of FGM single conical shell. Parametric studies are conducted to examine the influences of conical geometry, material composition, temperature dependence, in-plane and out-of-plane mechanical, various configuration of joined shell system, and thermal boundary conditions.