Free vibrations of thick, layered cylinders having finite length with various boundary conditions

Abstract

On the basis of the three-dimensional, linear, small deflection theory of elasticity, a finite layer method of solution is presented for free vibrations of thick laminated finite cylinders with various end conditions. In the analysis, the cylinder is divided into a number of layers while for each layer the material can be isotropic or orthotropic. A Rayleigh-Ritz type formulation is used, a displacement field being assumed in the form Σ Σ φ(θ) ψ(z) Ξ(x), in which φ(θ) is a trigonometric function of the circumferential angle, ψ(z) is a polynomial in the radial direction and the functions Ξ(x) are eigenfunctions which satisfy various boundary conditions. As a result, the stiffness and consistent mass matrices can be formed and they lead to an eigenvalue problem which is solved to yield mode shapes and frequencies. The method is applicable to various homogeneous cylindrical surface conditions. However, the example problems treated are for the cases where the cylinders are bounded by traction-free surfaces. The numerical solutions compare favorably with previous results available to the authors. © 1972.