Nonlinear Acoustic Waves in a Slender Wedge
Nonlinear Acoustic Waves in a Slender Wedge
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细长楔形物中的非线性声波
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
D. F. Parker
中科院分区：
文献类型：
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作者：
A. Mayer;V. G. Mozhaev;V. Krylov;D. F. Parker
这一贡献与位移场位于弹性楔体尖端的声波的非线性传播有关。与楔形波相关的能量被限制在两个维度。这意味着可以达到较高的能量密度，而且对于楔形声波，某些非线性效应应该比对于体波或表面波更明显。一维光波导中的楔形波和波的传播有两个重要的区别特征，引起了人们的特别关注。首先，楔形波非常慢。它们的速度必须小于瑞利波的速度，对于细长的楔形，它与楔形角度成正比。其次，理想弹性楔体是一个非色散系统，因为它的几何形状不涉及任何长度尺度，并且进入弹性理论方程的参数与频率无关。这对该系统中的非线性波传播具有重要的意义，因为它导致了不同谐波之间的共振相互作用。虽然线性楔形声波的存在很早就为人所知，但关于非线性对这些波的影响的研究还很少。
This contribution is concerned with the nonlinear propagation of acoustic waves that have displacement field localized at the tip of an elastic wedge. The energy associated with a wedge wave is confined in two dimensions. This means that high energy densities can be reached and certain nonlinear effects should be more pronounced for wedge acoustic waves than for bulk or surface waves. There are two important features which distinguish wedge acoustic waves from wave propagation in one-dimensional optical waveguides and attract particular attention. Firstly, wedge waves are very slow. Their velocity has to be smaller than that of Rayleigh waves, and for slender wedges, it is proportional to the wedge angle. Secondly, an ideal elastic wedge is a nondispersive system since the geometry does not involve any length scale and the parameters entering the equations of elasticity theory are independent of frequency. This has important implications on nonlinear wave propagation in this system since it leads to resonant interaction between different harmonics. While the existence of linear wedge acoustic waves has been known since a long time, only few investigations have yet been carried out on the influence of nonlinearity on these waves1, 2.