A variational formulation for dynamic analysis of composite laminated beams based on a general higher-order shear deformation theory

This paper presents a general formulation for free and transient vibration analyses of composite laminated beams with arbitrary lay-ups and any boundary conditions. A modified variational principle combined with a multi-segment partitioning technique is employed to derive the formulation based on a general higher-order shear deformation theory. The material couplings of bending-stretching, bending-twist, and stretching-twist as well as the Poisson’s effect are taken into account. A considerable number of free and transient vibration solutions are presented for cross- and angle-ply laminated beams with various geometric and material parameters. Different combinations of free, simply-supported, pinned, clamped and elastic-supported boundary conditions are examined. The validity of the formulation is confirmed by comparing the present solutions with analytical and experimental results available in the literature and the ones obtained from finite element analyses. The accuracy of several higher-order shear deformable beam theories for predicting the vibrations of laminated beams has been ascertained. Results of parametric studies for composite beams with different orthotropic ratios, fiber orientations, layer numbers and boundary conditions are also discussed. The present formulation is versatile in the sense that it is capable of accommodating a variety of beam theories available in the literature, and allows the use of different polynomials as admissible functions for composite beams, such as the Chebyshev and Legendre orthogonal polynomials, and the ordinary power polynomials. Moreover, it permits to deal with the linear vibration problems for thin and thick beams subjected to dynamic loads and boundary conditions of arbitrary type.