A unified formulation for vibration analysis of composite laminated shells of revolution including shear deformation and rotary inertia

Abstract

This paper introduces a variational formulation for predicting the free, steady-state and transient vibrations of composite laminated shells of revolution subjected to various combinations of classical and non-classical boundary conditions. A modified variational principle in conjunction with a multi-segment partitioning technique is employed to derive the formulation based on the first-order shear deformation theory. Double mixed series, i.e., Fourier series and polynomials, are used as admissible functions for each shell segment. The versatility of the formulation is illustrated through the application of four sets of polynomials, i.e., the Chebyshev orthogonal polynomials of first and second kind, the Legendre orthogonal polynomials of first kind and the ordinary power polynomials. A considerable number of numerical examples are given for the free vibrations of cross-ply and angle-ply laminated cylindrical, conical and spherical shells with various geometric and material parameters. Different combinations of free, shear-diaphragm, simply-supported, clamped and elastic-supported boundary conditions are considered. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. With regard to the steady-state and transient vibration analyses, laminated hemispherical and annular spherical shells subjected to different external forces are examined. Effects of structural damping, shell thickness, layer number, stacking sequence, and boundary conditions on the forced vibration responses of the composite spherical shells are also discussed. The present formulation is general in the sense that it allows to apply any linearly independent and complete polynomials as admissible functions for composite shells of revolution, and permits to analyze most of the linear vibration problems for shells having arbitrary boundary conditions and dynamic loads.