Free vibration of symmetric angly-plane layered truncated conical shells under classical theory

Truncated conical shell finds wide ranging of engineering applications. They are used in space crafts, robots, shelters, domes, tanks, nozzles and in machinery devices. Thus, the study of their vibrational characteristics has long been of interest for the designers. The use of the lamination for the structures leads to design with the maximum reliability and minimum weight. Moreover, the study of free vibration of laminated conical shells has been treated by a number of researchers. Irie et al. (1982) studied free vibration of conical shells with variable thickness using Rayleigh-Ritz method of solution. Wu and Wu (2000) provided 3D elasticity solutions for the free vibration analysis of laminated conical shells by an asymptotic approach. Wu and Lee (2001) studied the natural frequencies of laminated conical shells with variable stiffness using the differential quadrature method under first-order shear deformation theory (FSDT). Tripathi et al. (2007) studied the free vibration of composite conical shells with random material properties of the finite element method. Civalek (2007) used the Discrete Singular Convolution (DSC) to investigate the frequency response of orthotropic conical and cylindrical shells. Sofiyez et al. (2009) studied the vibrations of orthotropic non-homogeneous conical shells with free boundary conditions. Ghasemi et al. (2012) presented their study of free vibration of composite conical shells which was investigated under various boundary conditions using the solution of beam function and Galerkin method. Viswanathan et al. (2007, 2011) studied free vibration of laminated cross-ply plates, including shear deformation, symmetric angle-ply laminated cylindrical shells of variable thickness with shear deformation theory using the spline collocation method. In the present work, free vibration of symmetric angle-ply laminated truncated conical shells is analyzed and displacement functions are approximated using cubic and quantic spline and collocation procedure is applied to obtain a set of field equations. The field equations along with the equations of boundary conditions yield a system of homogeneous simultaneous algebraic equations on the assumed spline coefficients which resulting to the generalized eigenvalue problem. This eigenvalue problem is solved using eigensolution technique to get as many eigenfrequencies as required. The effect of circumferential mode number, length ratio, cone angle, ply angles and number of layers under two boundary conditions on the frequency parameter is studied for three- and five- layered conical shells consisting of two types of layered materials.