Thermally Induced Vibrations of Functionally Graded Shallow Spherical Shells Under Cooling Shock

Abstract

Based on the first-order shear deformation theory (FSDT), the large-amplitude vibration behavior of shallow spherical shells made of functionally graded materials (FGMs) due to the rapid decrease of temperature (cooling shock) is investigated. FGM is assumed to be a mixture of stainless steel and low-carbon steel whose properties are considered temperature dependent and are estimated based on the power-law model. According to FSDT and von Kármán assumptions, the governing equations of motion in conjunction with corresponding boundary conditions are obtained using Hamilton’s principle. The temperature distribution is also achieved by means of the 1D Fourier transient heat conduction equation, considering two time-dependent thermal loading scenarios. The considered thermal boundary conditions allow that a temperature difference is created with a time delay for the structure under cooling shock. Also, the results of recent experiments are employed to estimate the temperature-dependent properties of structures. In the solution approach, the generalized differential quadrature method and the Newmark-beta integration scheme are utilized. Selected numerical results are presented to study the effects of thermal load rapidity time, geometry, magnitude of thermal load, and material gradient index on the thermally induced vibrations of spherical shells. Stresses generated in the shell due to the thermally induced vibrations are also investigated.