Determination of material properties of orthotropic plates with general boundary conditions using Inverse method and Fourier series

摘要

Determination of material properties of orthotropic plates with general elastic boundary supports using the Inverse method is presented in this paper. The material properties were identified through updating four parameters in the governing equation of a symmetrically laminated thin plate. The sum of the squared difference of the natural frequencies obtained from modal testing was minimized using the Forward method. The displacement function was expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series. A classical solution was derived by letting the series exactly satisfy the governing differential equation and all the boundary conditions at every field and boundary point. In the Inverse method, the series expansions for all the relevant derivatives of the eigen frequencies were obtained through term-by-term differentiations of the displacements. Many simulations were done but one numerical example is presented to demonstrate the accuracy and convergence of the solutions.