Nonlinear large amplitude vibrations of higher-order functionally graded beams under cooling shock

In this paper, thermally induced vibrations of beams made of functionally graded materials (FGMs) subjected to cooling shocks are investigated. It is considered that the beam has been made of a mixture of stainless steel (SUS304) and low-carbon steel (AISI1020). To model the displacement field, the third-order beam theory, known as the Reddy beam theory (RBT), is used. Material properties depend on temperature and distribution of materials, and this dependence is modeled through the temperature and the location of materials along the thickness direction. Considering the uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and the equations of motion governing the higher-order beam are derived utilizing Hamilton's principle. Solving the equations is done numerically; the generalized differential quadrature method (GDQM) is employed to approximate the spatial derivatives, and the Newton-Raphson scheme is applied to linearize the equations. In addition, for approximation of the time derivatives, the Newmark method is utilized. Subsequently, the effects of various parameters on the nondimensional lateral deflection of the higher-order beam considering two different types of thermal loading are investigated. A comprehensive parametric study is conducted to study the effects of important parameters including beam thickness, thermal load rapidity time, the amount of applied load, and the FG parameter.