Chapter 8 - Guided-wave excitation in aerospace composites

Abstract

This chapter covers guided-wave excitation 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. In the previous chapter, guided waves in aerospace composites via the semianalytical finite element method, the SAFE method was used to study the guided-wave modes and characteristic wavenumbers in the absence of external excitation. In this chapter, the SAFE method is used to model how and external excitation would induce guided waves in an aerospace composite. The chapter starts with extension of the variational principle to include external excitation which then followed by the FEM setup in which the excitation is resolved in the form of nodal forces applied to the FEM nodes. Excitation representation in the wavenumber–frequency domain is generally assumed. Normal-mode expansion in terms of the guided wave modes is assumed and the solution is sought in the form of wavenumber and frequency dependent modal participation factors. The solution is obtained first in the wavenumber–frequency domain and the returned through an inverse Fourier transform to the space–frequency domain using the residue theorem. A further inverse Fourier transform is applied to deal with the frequency spectrum of the excitation such that the space–time domain solution is eventually obtained. For straight-crested guided waves, the solution depends only on a single wavenumber and the application of the residue theorem yields a closed-form solution. For the arbitrarily-crested guided waves, the application of the residue theorem in the wavenumber–angle domain yields an angle-dependent integral that is evaluated in the far field using the stationary phase theorem. A substantial number of worked-out examples are presented. The chapter closes with problems exercises, and list of cited references and further-reading bibliography.