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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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Elastic Waves in Multilayer Composites

Elastic Waves in Multilayer Composites

Chapter:
6 (p.225) Elastic Waves in Multilayer Composites
Source:
Physical Ultrasonics of Composites
Author(s):

Dale Chimenti

Stanislav Rokhlin

Peter Nagy

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195079609.003.0010

Expanding on the theme of bulk waves from the previous chapters, we will examine the problem of plane wave sound propagation in layered media. We assume we have an finite stack of planar layers with perfect, rigidly bonded planar interfaces, but infinite in their lateral extent. The problem has significant industrial interest. Most practical composite laminates are composed of layers of uniaxial fibers and plastic, i.e., plies, whose fiber orientation directions vary from ply to ply through the thickness of the laminate. The mechanical purpose of this directional variation is to render the product stiff and strong in all in-plane directions, much as plywood is layered in cross-grain fashion. Almost no practical composite would be fabricated as a uniaxial product, because of the low bending strength normal to the fiber direction. Instead, various types of layering have been devised to give either tailored stiffness for a specific purpose or approximate in-plane isotropy, also known colloquially as a “quasi-isotropic” laminate. In fact, the approximate isotropy is achieved only in the plane of the plies, because the out-of-plane direction still has significant and unavoidable stiffness differences, since it contains no fibers. The scale of the layering is also important. When the laminations are fine, i.e., when each directional lamina is no thicker than an individual ply as we go through the thickness, only acoustic waves of relatively short wavelength will be able to discern the effect of the layering. At longer wavelengths, the laminate may behave more like an effective medium, still anisotropic, but with averaged elastic properties. On the other hand, if each lamina contains multiple numbers of individual 1/8-mm plies, then the frequency at which an acoustic wavelength approaches the layer thickness will be proportionately lower. This is an important distinction, because it suggests the point at which the layering must be treated as a discrete substructure in order to develop an accurate description of waves in a layered medium. The situation is illustrated schematically in Fig. 6.1. The figure illustrates laminations for a quasi-isotropic composite.

Keywords:   Asymptotic stiffness matrix method, Bleeder cloths, Christoffel’s equation, Global matrix, Helmholtz’s theorem, Kronecker delta, Polarization vectors, Recursive stiffness matrix, Snell’s law, Stable stiffness matrix method, Transfer matrix

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