Free vibration of refined higher-order shear deformation composite laminated beams with general boundary conditions

In this paper, a unified formulation which is based on a general refined shear deformation beam theory is presented to conduct free vibration analysis of composite laminated beams subjected to general boundary conditions. In the refined theory model, the displacement fields are chosen by including the high-order variation of transverse shear strain through the thickness of the beam and meeting the stress-free boundary conditions on both the top and bottom surfaces. With considering the material couplings and the Poisson's effect, the governing equations and appropriate boundary conditions are derived from the Hamilton's principle. Exact solutions are obtained by employing the method of reverberation ray matrix (MRRM). In order to implement general boundary conditions, the artificial spring boundary technique is introduced in the MRRM to make it suitable for different boundary cases. The present solutions are compared with those available in the literature to confirm their validity. A systematic parameter study for composite beams with various boundary conditions, fiber orientations, lamina numbers and orthotropic ratios is also performed. New results for free vibration involving composite laminated beams with various boundary constraints are also presented for the first time and they may be served as benchmark for researchers in this field.