Experimental and theoretical investigations of linear and nonlinear wedge waves

应在实验和理论上研究由一维结构，特别是固体边缘引导的声波的线性和非线性特性。在这些一维波导中的波场的非常强的局部化导致显著的非线性效应，这是由理想的楔形色散的情况下增强。对于声波在晶体边缘的传播，各向异性起着重要的作用。它导致线性伪楔形波，这是在这个项目的框架中发现的，它使一个有效的二阶非线性，导致强烈的脉冲形状的演变与冲击形成的趋势。这一点已在项目第一阶段得到实验证明。现在，非线性，各向异性和弱色散之间的相互作用进行了研究，主要目标是实验验证孤立声脉冲在边缘和研究它们的属性。对于声脉冲的激发和检测，将使用泵浦-探测激光方法。基于这些方法获得的经验和早期的锐角楔形物理论工作，应证明三阶非线性效应，这发生在各向同性和高度对称的各向异性楔形物中，对称性禁止共振二阶非线性。对三阶非线性效应对脉冲传输的影响进行了定量的理论描述。这种描述是基于非线性弹性理论，并将用于数值模拟与激光超声实验进行比较。特别是在尖角楔形体中，预计会有大位移，因此会有高非线性，非线性对脉冲形状演变的特征效应问题，特别是孤立脉冲的特征效应问题，应予以澄清。样品的选择以及测量和模拟结果的解释将在理论和实验之间的密切相互作用中完成。

The linear and nonlinear properties of acoustic waves guided by one-dimensional structures, especially at edges of solids, shall be investigated experimentally and theoretically. The very strong localization of the wave-field in these one-dimensional waveguides leads to pronounced nonlinear effects, which are enhanced by the absence of dispersion in ideal wedges. For the propagation of acoustic waves at crystal edges, anisotropy plays an important role. It leads to linear pseudo-wedge waves which were discovered in the framework of this project, and it enables an efficient second-order nonlinearity which leads to strong pulse-shape evolution with a tendency to shock formation. This has been demonstrated experimentally in the first project phase. Now, the interplay between nonlinearity, anisotropy and weak dispersion shall be investigated with the main goal to verify experimentally solitary acoustic pulses at edges and to study their properties. For the excitation and detection of acoustic pulses, pump-probe laser methods will be used. Building on the experience gained with these methods and on earlier theoretical work for sharp-angle wedges, effects of third-order nonlinearity shall be demonstrated, which occur in isotropic and highly symmetric anisotropic wedges, where resonant second-order nonlinearity is forbidden by symmetry. A quantitative theoretical description is developed for the pulse propagation influenced by third-order nonlinearity. This description is based on nonlinear elasticity theory and will be used in numerical simulations for comparison with the laser-ultrasound experiments. Especially in sharp-angle wedges, where large displacements and therefore high nonlinearities are expected, the questions of characteristic effects of nonlinearity on pulse-shape evolution and, in particular, of solitary pulses shall be clarified. The choice of samples and the interpretation of measurement and simulation results will be done in a close interplay between theory and experiment.