Vibrational behavior investigation of axially functionally graded cylindrical shells under moving pressure

The current work presents an analytical procedure for the free vibration characteristics and dynamic response of an axisymmetric cylindrical shell that has finite length and it is made of functionally graded materials. The shell is subjected to a moving internal pressure. The material properties are assumed to vary along the axial direction according to an exponential law. The equations of motion are extracted based on the classical shell theory using Hamilton's principle. These equations, which are a system of coupled partial differential equations with variable coefficients, are solved analytically to find the natural frequencies and the responses of the structure. A sensitivity analysis is performed, and the effects of different parameters on the results are studied. The results are compared with the results available in the literature. Also, the results of the free vibration problem are compared with those of the finite element method.