Experimental and theoretical investigations of linear and nonlinear wedge waves

• Applicant: Professor Dr. Andreas Mayer
• Subject Area: Experimental Condensed Matter Physics ; Theoretical Condensed Matter Physics
• Term: from 2012 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 207396191

• Final Report Year: 2021

Final Report Abstract

Guided acoustic waves have applications in various technical fields like non-destructive evaluation and devices in mobile communication, where nonlinear effects are receiving increased attention. In the framework of this project, the properties of acoustic waves were investigated that have displacements localized at the apex of elastic wedges, and of guided waves in composite wedge systems. In the case of homogeneous media and planar surfaces, waves localized at the ideal tip of a wedge are, like surface waves, non-dispersive, which favors nonlinear effects. In laser ultrasound experiments, which were carried out in the first period of the total project, Alexey Lomonosov demonstrated the tendency towards shock formation of acoustic pulses localized at a silicon edge. On the basis of an evolution equation following from nonlinear elasticity theory, it was shown that the frequency spectrum of the pulses tends to a power law. The elastic nonlinearity acts on wedge waves in an unusual way. In isotropic wedges, the second-order nonlinearity in the evolution equation for flexural wedge waves vanishes. Also, our calculations have shown that third-harmonic generation is strongly impeded in sharp-angle wedges. In the presence of second-order nonlinearity and weak dispersion, the non-integrable evolution equation possesses a one-parameter family of solitary pulse solutions. Simulations of pulse collisions and pulse evolution out of various initial conditions revealed behavior similar to that of Korteweg – de Vries solitons with characteristic differences. In spite of extensive efforts and the application of different laser-based excitation methods, we have so far not succeeded in confirming these solitary pulses experimentally. Anisotropy leads to the existence of leaky waves at crystal edges, which were excited by Alexey Lomonosov and Pavel Pupyrev via reflection of surface waves at the edge of a silicon crystal. With a laser pulse, an acoustic surface wave pulse was generated by the thermo-elastic effect. With an optical detection method, the reflection scenario could be visualized in detail. For the correct angle of incidence, a pulse is detected corresponding to the pseudo-wedge wave. Its change of shape, as it propagates along the edge, is well reproduced in numerical simulations. Our calculations have also shown that the excitation of the pseudo-wedge wave is associated with anomalous reflection and transmission of surface waves. In addition to homogeneous anisotropic wedges, composite wedge systems were investigated by numerical methods, and one-dimensionally guided waves and leaky waves were identified, which are expected to find applications in non-destructive evaluation and geophysics.

Publications

• “Laser-generated ultrasonic pulse shapes at elastic wedges,” Ultrasonics 70, 75–83 (2016)
  Pupyrev, Pavel D.; Lomonosov, Alexey M. & Mayer, Andreas P.
  
• “On the existence of guided acoustic waves at rectangular anisotropic edges,” Ultrasonics 71, 278–287 (2016)
  Pupyrev, Pavel D.; Lomonosov, Alexey M.; Nikodijevic, Aleksandar & Mayer, Andreas P.
  
• “Nonlinear acoustic wedge waves,” in “Generalized Models and Non-classical Approaches in Complex Materials 2”, eds. H. Altenbach, J. Pouget, M. Rousseau, B. Collet, and T. Michelitsch (Springer International Publishing, Basel 2018) chapter 8, pp. 161-184
  Pupyrev, Pavel D.; Lomonosov, Alexey M.; Sokolova, Elena S.; Kovalev, Alexander S. & Mayer, Andreas P.
  
• “Nonlinear effects of micro-cracks on acoustic surface and wedge waves,” Low Temperature Physics / Fizika Nizkikh Temperatur 44, 946– 953 (2018)
  Rjelka, M.; Pupyrev, P. D.; Koehler, B. & Mayer, A. P.
  
• “Guided acoustic waves at the intersection of interfaces and surfaces,” Ultrasonics 95, 52-62 (2019)
  Pupyrev, P.D.; Nedospasov, I.A. & Mayer, A.P.
  
• “Anomalous reflection and transmission of surface acoustic waves at a crystal edge via coupling to leaky wedge waves,” Appl. Phys. Lett. 119, 021902/1-5 (2021)
  Pupyrev, P. D.; Lomonosov, A. M.; Nedospasov, I. A. & Mayer, A. P.
  
• “Surface acoustic waves confined to a soft layer between two stiff elastic quarter-spaces,” Wave Motion 101, 102672/1-16 (2021)
  Pupyrev, P.D.; Nedospasov, I.A.; Sokolova, E.S. & Mayer, A.P.
  
• “Solitary acoustic pulses propagating at the tip of an elastic wedge,” Contribution to the Proceedings of the XLVIII International Summer School – Conference Advanced Problems in Mechanics, St. Petersburg, June 21–26, 2020
  Pupyrev, Pavel D.; Lomonosov, Alexey M. & Mayer, Andreas P.