A unified formulation for free vibration of laminated plate through Jacobi-Ritz method

In this research, an analytical Jacobi-Ritz method for the free vibration analysis of composite laminated rectangular plate subject to arbitrary boundary conditions is proposed. The theoretical model is constructed in the framework of the first-order shear deformation theory (FSDT), and the multi-segment partitioning strategy is introduced. The boundary condition as well as the interface continuity condition is dealt with through the artificial spring technique. The displacement functions for every separated plate segment are expanded in the way of Jacobi polynomials along both the length and width orientations. And all the undetermined coefficients are decided through the Ritz method. The solution exhibits excellent convergence performance and shows stable features. The reliability and precision of the proposed methodology are validated by comparison with results from literature, where general boundary conditions are taken into account. Furthermore, parameterized study of the composite laminated rectangular plate is conducted, the results of which can be benchmark results for the future study.