Experimental and theoretical investigations of linear and nonlinear wedge waves

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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.