Waveguides of a Composite Plate by using the Spectral Finite Element Approach

Abstract

This work presents the extension of an existing procedure for evaluating the waveguides and the dispersion curves of a laminate made up of thin orthotropic composite plates arbitrarily oriented. The adopted approach is based on one-dimensional finite-element mesh throughout the thickness. Stiffness and mass matrices available in the literature for isotropic material are reported in full expanded form for the selected problem. The aim of the work is the development of a tool for the simulation of the most common composite materials. The knowledge of the wave characteristics in a plate allows correct sizing of the numerical mesh for the frequency-dependent analysis. The development of new stiffness matrices and the analysis for different heading angles are detailed to take into account the general anisotropic nature of the composite. The procedure concerns a standard polynomial eigenvalue problem in the wavenumber variable and is focused on the evaluation of the dispersion curves for all the propagating waves within the materials. A comparison with an analytical approach is also shown in the results using the classical laminate plate theory (CLPT). However, limits of CLPT are outlined and spectral finite element method can be successfully used to overcome such limitations.