Free vibration of layered cylindrical shells of variable thickness filled with fluid

Abstract

Free vibrational behavior of layered cylindrical shell filled with quiescent fluid is investigated. Cylindrical shell with variable thickness, made up of isotropic or specially orthotropic materials is studied using spline approximation. The thickness variations are assumed to be linear, exponential and sinusoidal along the radial direction. The equations of motion are derived by extending Love’s first approximation theory. Irrotational of an inviscid fluid are expressed as the wave equation. These two equations are coupled. The solutions of the displacement functions are assumed in a sep-arable form to obtain a system of coupled differential equations in terms of the displacement func-tions. The displacement functions are approximated by Bickley-type splines. A generalized eigen-value problem is obtained and solved numerically for the frequency parameter and an associated eigenvector of the spline coefficients. Two layered shells with different types of materials under Clamped-Clamped (C-C) boundary conditions are considered. The effect of relative layer thickness, length parameter, material properties, and coefficients of thickness variations on the frequency parameter is investigated.