Vibrational responses of antisymmetric angle-ply laminated conical shell by the methods of polynomial based differential quadrature and Fourier expansion based differential quadrature

Vibrational response of antisymmetric angle-ply laminated conical shell based on transverse shear deformation theory is analyzed in this research. The equilibrium and corresponding boundary equations including the extension-coupling terms are derived in terms of displacement and rotational components. Two types of differential quadrature methods (DQM) including polynomial based differential quadrature (PDQ) and Fourier expansion based differential quadrature (FDQ) are applied to convert the existing differential equations to algebraic equations. After discretization of existing differential equations, the eigenvalue equation system for the functional value in the whole domain is established and solved. A series of numerical tests are carried out to validate the present approach that highly accurate results are obtained only few grid points. Finally, the parametric studies are performed to illustrate the effects of different boundary conditions, fiber angle and number of layers and also various aspect ratio of the shell including thickness to radius ratio length to radius on the frequency parameter.