Flow-Induced Vibration of Anisotropic Cylindrical Shells

This paper deals with the vibration analysis of anisotropic laminated cylindrical shells conveying fluid. We focus on the axi-symmetric (n=0) and lateral (beam-like, n=1) vibration modes of the anisotropic cylindrical shells. Particularly important in this study is to obtain the natural frequencies of the fluid-structure coupled system and also to estimate the critical flow velocity at which the structure loses its stability. The coupled equations between the shell and the fluid are derived from a refined shell theory by taking into account the shear deformation effects. The displacement functions are obtained from the exact solution of refined shell equations and therefore the mass and stiffness matrices of the shell are determined by precise analytical integration. The added mass, stiffness and damping matrices of the fluid are obtained by an analytical integration of the fluid pressure over the liquid element. Thereafter, these matrices are coupled with the dynamic equation of the empty shell. The natural frequencies obtained with the shell partially or completely filled with liquid are in good agreement with those obtained experimentally and from other theories. The stability of the shell subjected to a flowing fluid is also studied. The shell’s anisotropy is discussed.