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This article is concerned with thermal vibration behaviors of the functionally graded material–stepped cylindrical shell coupled with annular plate, including free vibration, transient response, and steady state response. The stepped cylindrical shell is divided into N  s  segments at locations of thickness and radius variations, which is coupled with N  p  annular plates. The boundary and coupling conditions are achieved by introducing the artificial virtual spring technology. Under the framework of FSDT, the displacement function of arbitrary shell segment and annular plate is expanded with Chebyshev polynomials and Fourier series for circumferential direction. Compared with results obtained by the finite element method and the references, a series of numerical examples and validations are presented to verify the convergence and accuracy of the current method. The effects of the relevant parameters containing the geometric parameters, boundary conditions, various loadings, and the thermal environment are investigated in detail.

Investigation on vibration of the functionally graded material–stepped cylindrical shell coupled with annular plate in thermal environment