Lamb quasi–modes in curved plates

D. Gridin, R. Craster
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引用次数: 11

Abstract

Wave propagation in slowly varying elastic waveguides is analysed in terms of mutually uncoupled quasi–modes. These are a generalization of the Lamb modes that exist in a uniform guide to a weakly non–uniform guide. Quasi–modal propagation is dependent upon the wavelength and two geometrical length–scales, that of the longitudinal variations and the guide thickness. By changing these length–scales one enters different asymptotic regimes. In this paper the emphasis is on the mid–frequency regime, where only a few propagating modes can exist. Our aim is to present an asymptotic theory for quasi–modal propagation in a canonical geometry, an arbitrarily curved two–dimensional plate of constant thickness. We derive practically useful asymptotic expressions of the quasi–modes of a weakly curved plate; these are particularly important since an adiabatic approximation for this problem coincides with the expression for the Lamb modes of a flat plate of the same thickness.
弯曲板中的Lamb准模态
从相互不耦合准模的角度分析了波在慢变弹性波导中的传播。这是将存在于均匀波导中的兰姆模推广到弱非均匀波导中的兰姆模。准模态传播依赖于波长和两个几何长度尺度,即纵向变化和波导厚度。通过改变这些长度尺度,可以进入不同的渐近状态。本文的重点是在只有几种传播模式可以存在的中频区域。我们的目的是提出一个正则几何中准模态传播的渐近理论,这是一个任意弯曲的等厚度二维板。导出了弱弯曲板拟模态的实用渐近表达式;这些是特别重要的,因为这个问题的绝热近似与相同厚度的平板的兰姆模态的表达式一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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期刊介绍: Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.
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