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MULTIWAVE NONLINEAR COUPLINGS IN ELASTIC STRUCTURES

机译：弹性结构中的多波非线性耦合

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This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.
机译：这一简短贡献考虑了典型机械系统（例如，无限的直杆，圆环和平板）中非线性波属性的本质。发现在所有显示连续光谱和离散光谱的系统中都经历了非线性共振。讨论了多波相互作用和耦合模式关于小扰动的稳定性。重点放在机械现象上，例如应力放大，尽管与某些非线性光学系统的某些类比也很明显。选择基尔霍夫-洛夫（Kirchhoff-Love）近似范围内的板中的非线性共振耦合作为二维示例，该示例展示了丰富的共振波现象。最初使用Whitham的平均拉格朗日方法进行了检验。特别地，示出了在纵向，剪切和弯曲模式之间存在三个基本共振三单元组。其中一些必然会进入与小扰动下三重轴的某些模式分量的不稳定性有关的级联波过程。

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