Nonlinear vibrations of functionally graded cylindrical shell by using numerical analysis in the wave propagation method

Functionally graded materials (FGMs) are materials that show different properties in different areas due to the gradual change of chemical composition, distribution, and orientation, or the size of the reinforcing phase in one or more dimensions. In this paper, the free vibrations of a thin cylindrical shell made of FGM is investigated. In order to investigate this problem, the first-order shear theory is used, by using relations related to the propagation of waves and fluid-structure interaction. Also, due to the rotational iner tia of first-order shear deformation and the fluid velocity potential, dynamic equation of functionally graded cylinder shell, containing current is obtained. Convergence of the solutions obtained from this method in different modes of boundary conditions as well as different geometric characteristics for the submerged cylinder and results of other studies and articles is showed. Also the effects of different parameters on the FGM cylindrical shell frequencies for the classical boundary conditions (compositions of simple, clamped, and free boundary conditions) are investigated against the ratio of length to the radius and the ratio of thickness to radius for different values of exponential power (exponential order) of FGM material. The results show that if the more density of the fluid in which the cylinder is submerged is lower, then the frequency values will be higher. Also, by examining the different fluid velocities, it can be seen that the effect of thickness change so that increas ing thickness causes the increase of effect of speed on the natural frequency reduction, especially in higher modes.