Free vibration of symmetric angle-ply laminated truncated conical shells using spline function

Abstract

Free vibration of symmetric angle-ply laminated truncated conical shells using spline function technique is studied. The equations of motion for conical shells can be obtained by deriving and substituting the proper Lamé parameters of conical shells in the general shell equations. The displacements are assumed in the separable form. Since no closed form solutions are generally possible, a numerical solution procedure is adopted in which the displacement functions are approximated by cubic and quintic splines. A generalized eigenvalue problem is obtained which is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. Parametric studies are made to investigate the effect of circumferential mode number, length ratio and cone angle using different number of layers with different ply orientations on the frequency parameter under two different boundary conditions.