Based on the Flügge’s shell theory, the vibration characteristics and stability of submergedfunctionally graded (FG) cylindrical shell under hydrostatic pressure is examined. By means of conversionswitch on axial wave number, the coupled frequency of submerged FG cylindrical shell with variousboundary conditions is obtained, using wave propagation method and Newton method. Then the criticalpressure of FG cylindrical shells is given by applying linear fitting method. Results are compared to knownsolutions, where these solutions exist. The natural frequency and critical pressure of FG cylindrical shell are illustrated. The effects of constituent materials, volume fraction, boundary condition and dimensions on the natural frequencies and critical pressures of submerged FG cylindrical shell are illustrated by examples.
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