Free Vibration of Axisymmetric and Beam-Like Cylindrical Shells, Partially Filled with Liquid

摘要

A theory is presented for the determination of free vibration characteristics of anisotropic thin cylindrical shells, partially or completely filled with liquid for two circumferential wave numbers, n = 0 breathing and n = 1 beam-like. The method used was a hybrid one, based on the finite element method and supported by classical shell theories. The shell was subdivided into cylindrical finite elements and the displacement functions were obtained using the shell's equations. Expressions for the mass and stiffness matrices for a finite element and for the whole structure were obtained. Similarly, a finite element was developed for the liquid in cases of potential flow. The natural frequencies of the shell in vacuo and partially filled were obtained and compared with existing experiments and other theories.