Chapter 7 - Guided waves in aerospace composites via the semi-analytical finite element method

Abstract

This chapter deals with the study of guided waves in aerospace composites. The analysis is performed with the semianalytical finite element (SAFE) method which performs finite element method (FEM) analysis of the vibration modes across the thickness while using analytical modeling of how these thickness vibration modes travel as guided waves. Straight-crested guided waves in composite plate are analyzed first. The elasticity relations are recalled and the variational formulation is introduced. The wave-propagation along the plate with an assumed frequency ω and wavenumber ξ is applied. FEM discretization is implemented and strains inside the elements are calculated. A discretized variational formula is developed and the elemental stiffness and mass matrices are derived. The FEM assembly procedure is applied and the ω-dependent FEM eigenvalue problem is developed. A range of ω is explored and the eigenvalues and eigenvectors are extracted for each ω value. Then, the SAFE analysis is extended to arbitrarily crested guided waves with the wavevector pointing in a generic direction θ. A θ-dependent SAFE formulation is developed where the resulting eigenvalues and eigenvectors depend on both direction θ and frequency ω.