A two-direction cross-iteration solution for in-plane vibrations of thin-walled composite plates with a simplified explicit vibration mechanical model

For the fine and high reliability design of advanced precision engineering structures, this work presents an analytically cross-iteration method for in-plane vibrations analysis of thin-walled composite plates, the single-layer and laminated structures both involved. The governing equations and corresponding boundary conditions are derived adopting Rayleigh’s principle, in which the governing partial differential equations are transferred into ordinary differential equations. The most important advantage of this method lies in the fact that the explicit eigenvalue equations and mode functions are obtained with only a series of four-by-four matrices by simplifying boundary conditions in the two-direction cross-iteration procedures. Accuracy of the present method is verified by comparison with the previous studies and the finite element method in natural characteristics solutions, and convergence analysis on the single-layer orthotropic plates and composite laminates reveals the high efficiency and stability. Finally, the effects of boundary conditions, ply orientation angles, stacking sequences, aspect ratios and stiffness ratios on the in-plane natural characteristics are investigated. The extensive results presented in this work for the first time can be taken as the benchmarks data compared with other methods.