Free Vibration of Layered Circular Cylindrical Shells of VariableThickness Using Spline Function Approximation

摘要

Free vibration of layered circular cylindrical shells of variable thickness is studiedusing spline function approximation by applying a point collocation method. The shell ismade up of uniform layers of isotropic or specially orthotropic materials. The equationsof motions in longitudinal, circumferential and transverse displacement components, arederived using extension of Love's first approximation theory. The coupled differentialequations are solved using Bickley-type splines of suitable order, which are cubic andquintic, by applying the point collocation method. This results in the generalizedeigenvalue problem by combining the suitable boundary conditions. The effect offrequency parameters and the corresponding mode shapes of vibration are studied withdifferent thickness variation coefficients, and other parameters. The thickness variationsare assumed to be linear, exponential, and sinusoidal along the axial direction. The resultsare given graphically and comparisons are made with those results obtained using finiteelement method.