A nonlinear elastic material with weakly inhomogeneous properties is considered. The counter-propagation and interaction of two waves are studied. The perturbative analytical solution is derived to describe an initial stage of the propagation, interaction, and reflection of waves. The phenomenon of interaction resonance is captured numerically. Numerical analysis clarifies the character of wave interaction resonances versus the parameters of a weakly inhomogeneous material.
1. Bhardwaj, M. C. Fundamental developments in ultasonics for advanced NDC. In Non-Destructive Testing of High-Performance Ceramics. Conference Proceedings, August 25–27, 1987, Boston, MA. American Ceramic Society, Inc., Westville, Ohio, 1987, 472–497.
2. Bland, D. R. Nonlinear Dynamic Elasticity. Waltham, Massachusetts, 1969.
3. Ravasoo, A. Nonlinear waves in characterization of inhomogeneous elastic material. Mech. Mater., 1999, 31, 205–213.
https://doi.org/10.1016/S0167-6636(98)00061-1
4. Braunbrück, A. and Ravasoo, A. Wave interaction resonance in weakly inhomogeneous nonlinear elastic material. Wave Motion, 2006, 43/3, 277–285.
https://doi.org/10.1016/j.wavemoti.2005.11.001
5. Guyer, R. A. and Johnson, P. A. Nonlinear mesoscopic elasticity: evidence for a new class of materials. Physics Today, 1999, 4, 30–36.
https://doi.org/10.1063/1.882648
6. Schneider, E. Untersuchung der materialspezifischen Einflüsse und verfahrenstechnische Entwicklungen der Ultraschallverfahren zur Spannungsanalyse an Bauteilen. Diss. RWTH Aachen, Fraunhofer IRB Verlag, 1999.
