Chapter 6 - Bulk waves in aerospace composites

Abstract

This chapter deals with the study of bulk ultrasonic waves in anisotropic composites. The analysis of bulk-wave propagation in an infinite anisotropic composite medium is examined. First, the wavefront propagation is studied in terms of wavespeed (aka phase velocity), particle displacement polarization vector, wave phase, and wavefront. The attention is next focused on harmonic waves. Wavelength, wavenumber, wavevector, and polarization of harmonic waves are discussed. The directional dependence of wavespeed and polarization vector is analyzed in terms of Christoffel equation and acoustic tensor. Eigenvalue solution of the Christoffel equation is obtained as three angle-dependent fundamental wave modes. Polar and surface plots of wavespeed and slowness are presented and discussed. Conditions for pure-wave modes are discussed. The excitation of ultrasonic waves in anisotropic bulk composites is analyzed under various conditions. It is shown that finite-footprint excitation may result in skew wave beams that propagate at an angle with respect to the excitation direction. The concept of group velocity is introduced to account for this skew-propagation phenomenon. Expressions for calculating group velocity vector components are derived and the skew angle between group velocity and wavespeed is determined. Group velocity polar and surface plots are presented and discussed. The time-averaged wave energy and power flow are deduced. Expression for Poynting vector and energy velocity are attained. The energy velocity is shown to be equivalent to group velocity in nondissipative media. The relations between slowness surface, ray surface, wavenumber and group velocity are deduced and discussed. A large number of worked-out examples are presented in order to illustrate bulk-wave propagation in unidirectional and generally orthotropic carbon fiber reinforced polymer (CFRP) composites in comparison with isotropic aluminum. Problems and exercises as well as references and further-reading suggestions are given at the end of the chapter.