Free vibrations of rectangular unsymmetrically laminated composite plates with internal line supports

Free vibrations of rectangular unsymmetrically laminated composite plates with internal line supports in one or two directions are studied. The static beam functions, which are the complete solutions of a unit width strip taken from the plate in the direction parallel to the edges of the plate and under a series of transverse static sinusoidal loads, are used as the trial functions of the transverse bending deflection of the plate. Besides, the vibrating bar functions are used as the trial functions of the in-plane stretching deformation of the plate. The Rayleigh–Ritz method is applied to arrive at the governing eigenfrequency equation in which the coupling effect of bending and stretching is contained. Different transverse boundary conditions combining with various in-plane constraints are considered in the analysis. The effects of fiber orientation angles and locations of internal line supports on eigenfrequencies of cross-ply and antisymmetric angle-ply laminated composite plates of two layers are investigated in detail. Convergence and comparison study show the correctness and effectiveness of the proposed method. Sets of valuable results are presented for the first time, which can serve as benchmarks for future reference.