Nonlinear dynamic snap-through and vibrations of temperature-dependent FGM deep arch under sudden thermal shock

Abstract

In this paper, nonlinear thermally induced vibrations of deep arches made of functionally graded material (FGM) are investigated. The two surfaces of the arch have different thermal conditions, one surface is under thermal shock and the other is maintained at the reference temperature. The properties of FGM depend on temperature. Using the Crank–Nicolson and the central finite difference methods, the one-dimensional heat conduction equation is solved through the thickness of the arch, and the temperature profile can be obtained according to the uncoupled thermoelasticity theory. The equations of motion of the arch are extracted by combining the linear thermoelastic equation, assumptions of uncoupled thermoelasticity laws, and kinematic assumptions of a deep arch with geometrical nonlinearity. The equations of motion are discretized by using the Ritz method with polynomial shape functions and then solved with the help of the β−Newmark time marching scheme and Newton–Raphson linearization technique. The effects of various parameters such as opening angle, slenderness ratio, and arch power law index have been analyzed. Moreover, the Budiansky and other criteria are used to obtain the dynamic buckling temperature.