Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups

This study deals with the numerical evaluations of various higher-order shear deformation beam theories. Free vibration analysis of generally laminated composite beams with arbitrary boundary conditions is performed by using the spectral finite element method. A unified type of assumed displacement field is considered and the influences of shear deformation, rotary inertia and Poisson effect are included in the formulation. The spectral element matrix is derived by rigorous use of the analytical solutions of the governing differential equations of the laminated beam in free vibration. The application of the spectral element matrix to study the free vibration characteristics of the laminated beams is demonstrated by adopting the Wittrick–Williams algorithm. Numerical results for the natural frequencies of the illustrative examples, which are found by various higher-order shear deformation beam models, are compared with each other and with the available solutions in the literature.