Free Vibrations of Laminated Anisotropic Cylindrical Shells

Abstract

The weak form of the equations of motion for laminated anisotropic composite shells are solved using the Ritz method for the problem of free vibration with various end conditions. Using a combination of power and Fourier series as the approximating functions for the three displacement components, the natural frequencies are evaluated for a number of geometric and material combinations. Because the full equations of elasticity are used in the formulation, no assumptions are required regarding the type of motion. The transverse shear strains, deformation of the normals, and all inertial terms are included in the formulation. The form of the approximating function assumes that the displacement components and their derivatives are continuous through the thickness of the shell. Several example geometries are considered, including a single‐layer isotropic shell, a three‐layer shell composed of dissimilar isotropic materials, a single‐layer anisotropic shell, and laminated shells composed of anisotropic materials with varying orientations. Comparisons are made with results of isotropic and anisotropic shell theories, with very good agreement being obtained.