APPROXIMATIONS OF THE DISPERSION RELATION FOR AN ELASTIC PLATE COMPOSED OF STRONGLY ANISOTROPIC ELASTIC MATERIAL

✍ Scribed by G.A. ROGERSON; L.Y. KOSSOVITCH

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 330 KB
• Volume: 225
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2270

✦ Synopsis

In this paper approximations of the dispersion relation associated with harmonic waves propagating along the axis of transverse isotropy, parallel to the traction free surfaces, in a "bre-reinforced elastic plate are derived. High and low wave number expansions are derived which have potential applications to impact problems within plates and shells and acoustic scattering and radiation respectively. Plots of the associated group velocity curves are presented and a wave front travelling with a speed of the same order of magnitude as the Young's modulus along the "bre direction is observed. A particularly interesting feature of this front is that its formation arises through the cumulative e!ect of various harmonics in adjacent wave number regimes. The paper concludes with both a conjecture concerning the properties of this wave as the Young's modulus increases and the derivation of approximate solutions for the dispersion relation in the neighbourhood of the associated wave front.