Axisymmetric vibrations of the composite orthotropic cylindrical shell with rigid weightless end disks

Abstract

A solution of the vibration problem for a composite orthotropic cylindrical shell with rigid weightless disks attached to its ends is presented in the paper. Using the Ritz method, the frequencies of the axisymmetric vibrations of the shell are determined. The clamped-clamped beam functions and their third derivatives are adopted as approximating functions for the shell deflection and axial displacement. Such an approximation satisfies the boundary conditions, according to which the shell deflections, angles of rotation, and axial reactive forces exerted on the end disks are zero. Based on this solution an analytical formula is derived for the calculations of the frequencies of axisymmetric vibrations. Using this formula, the vibration frequencies have been calculated for composite orthotropic shells with different lengths. The results were successfully verified by the finite element analyses. The effect of the fibre orientation on the vibration frequencies of the shell made of unidirectional carbon fibre reinforced plastic is investigated. Based on this analysis, the angles of the reinforcement orientation delivering the maximum and minimum values of the frequencies are determined. It is found that irrespective of the shell length, the high mode frequencies reach their maximum values for the shells reinforced in the hoop direction.