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Physical Ultrasonics of Composites$
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Dale Chimenti, Stanislav Rokhlin, and Peter Nagy

Print publication date: 2011

Print ISBN-13: 9780195079609

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195079609.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 19 October 2021

Elastic Waves in Anisotropic Media

Elastic Waves in Anisotropic Media

Chapter:
2 (p.35) Elastic Waves in Anisotropic Media
Source:
Physical Ultrasonics of Composites
Author(s):

Dale Chimenti

Stanislav Rokhlin

Peter Nagy

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195079609.003.0006

In this chapter, we provide a brief introduction to ultrasonic wave propagation in unbounded anisotropic solids with emphases on examples suitable for ultrasonics of composites. Many excellent books are relevant to the subject addressed in this chapter. Some of them broadly discuss elastic waves in anisotropic solids, including waves in layered anisotropic media. In-depth theoretical description of elastic waves in anisotropic media is given in classical texts, which have influenced and provided guidance to our treatment of some aspects of the theory. Beautiful visualization of ultrasonic waves in crystals (often obtained by laser excitation) is given in reference. The equations of motion for the vibration of an elastic medium are extensions of Newton’s second law for particles. Treating the elastic continuum as a collection of particles, each of which is assumed to obey Newton’s laws, leads to a particularly straightforward argument. We begin by considering a short segment of a bar with length Δx and cross-sectional area S0 as is illustrated in Fig. 2.1. The material is assumed to be linear and elastic, and its deformations can be described by constitutive equations derived in the previous chapter. For simplicity, we assume only uniaxial stress in the x-direction of the continuum.

Keywords:   Action function, Crystal acoustics, Dispersive media, Energy flow velocity, Gauss’ theorem, Hamilton’s principle, Isotropic symmetry, Lagrangian density, Newton’s second law, Phase velocity vector

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