Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method

The present study is concerned with the vibration analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The continuity conditions between layers of symmetric cross-ply laminated beams are satisfied by the use of the shape function incorporated into the theory which also unifies the 1D shear deformable beam theories developed previously. The governing equations are obtained by means of Hamiltonʹs principle. Six different combinations of free, clamped and simply supported edge boundary conditions are considered. The free vibration frequencies are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and lay-ups are presented and compared with results available in the literature.