Dynamic stiffness method: New Levy's series for orthotropic plate elements with natural boundary conditions.

A novel Lévy series for developing a dynamic stiffness matrix for a completely free orthotropic Kirchhoff plate is presented in this paper. The bending behavior is based on the Kirchhoff–Love thin-plate theory. The dynamic stiffness matrix is derived using the new Lévy series without classical symmetry decomposition, simplifying the building procedure. Harmonic responses obtained by this method and the finite element method are compared to establish the rate of convergence and the degree of precision of the current formulation. [Display omitted] • We present new Lévy series for calculating the dynamic stiffness matrix of free orthotropic plates. • Free boundary conditions are required for plate assemblies. • Modal analysis and harmonic analysis are presented. • The numerical validation is achieved thanks to comparisons with FE results. [ABSTRACT FROM AUTHOR]