Large-amplitude vibration analysis of FG rectangular plates under rapid cooling

Abstract

In the present research, the large-amplitude vibration behavior of rectangular plates subjected to cooling shock is investigated based on a numerical solution approach. It is considered that the plates are made of functionally graded materials as a mixture of stainless steel and low-carbon steel. The thermoelastic properties are also considered temperature-dependent which are estimated based on available experimental data. According to the Mindlin plate theory, the nonlinear governing equations of motion together with corresponding boundary conditions are derived. The temperature profile is also obtained based on a one-dimensional Fourier-type transient heat conduction equation. Moreover, two time-dependent thermal loading scenarios for cooling shock on the plate’s top face are considered. To solve the problem numerically, the well-known generalized differential quadrature technique is used for discretization considering the Chebyshev–Gauss–Lobatto grid. In addition, the governing equations are traced in time by Newmark’s time integration scheme. After showing the validity of developed approach, a parametric study is presented to investigate the stress changes along the thickness and the effects of thermal load rapidity time, geometry, magnitude of thermal load, and material properties on the nonlinear vibrations of plates with various boundary conditions subjected to sudden decrease of temperature. It is concluded that the thermal load rapidity time has a significant role in the vibrational behavior and the stress distribution of the plate.