Bednarik Michal, Cervenka Milan
Czech Technical University in Prague--FEE, Technicka 2, 166 27 Prague, Czech Republic.
Ultrasonics. 2006 Dec 22;44 Suppl 1:e783-5. doi: 10.1016/j.ultras.2006.05.194. Epub 2006 Jun 9.
This work is dedicated to nonlinear interactions in elastic resonators. It is supposed that a resonator wall yields locally to the inner pressure. The elastic wall of the resonator induces strong dispersion and dissipation of acoustic energy. The dispersion can significantly influence studied nonlinear interactions which are ineffective because the synchronous conditions are not satisfied and hence a coherence length is too short. In the frame of this work conditions for generation of subharmonics are studied on the basis of topological and numerical analyze. For this reason the method of local stability is applied. For description of nonlinear standing wave is derived modified inhomogeneous Burgers equation and the inhomogeneous Korteweg-de Vries-Burgers equation. These equations take into account thermo-viscous losses of supposed fluids, boundary layer losses, wall losses and dispersion effects caused by both the resonator wall and the acoustic boundary layer. Number of numerical solutions of these model equations is shown and unsteady solitary waves are investigated.
这项工作致力于研究弹性谐振器中的非线性相互作用。假定谐振器壁会局部屈服于内部压力。谐振器的弹性壁会引起声能的强烈色散和耗散。这种色散会显著影响所研究的非线性相互作用，由于同步条件不满足，因此相干长度太短，这些非线性相互作用是无效的。在这项工作的框架内，基于拓扑和数值分析研究了亚谐波产生的条件。为此应用了局部稳定性方法。为了描述非线性驻波，推导了修正的非齐次伯格斯方程和非齐次科特韦格 - 德弗里斯 - 伯格斯方程。这些方程考虑了假定流体的热粘性损耗、边界层损耗、壁损耗以及由谐振器壁和声边界层引起的色散效应。展示了这些模型方程的一些数值解，并对非稳态孤立波进行了研究。
