Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

  • Kim, No-Hyu (Department of Mechatronic Engineering, Korea University of Technology and Education) ;
  • Yang, Seung-Yong (Department of Mechanical Engineering, Korea University of Technology and Education)
  • Published : 2007.12.30

Abstract

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness.

References

  1. Biwa, S., Hiraiwa, S. and Matsumoto, E. (2006) Experimental and Theoretical Study of Harmonic Generation at Contacting Interface, Ultrasonics, Vol. 44, pp. 1319-1322 https://doi.org/10.1016/j.ultras.2006.05.010
  2. Biwa, S., Suzuki, A. and Ohno, N. (2005) Evaluation of Interface Wave Velocity, Reflection Coefficients and Interfacial Stiffnesses of Contacting Surfaces, Ultrasonics, Vol. 43, pp. 495-502 https://doi.org/10.1016/j.ultras.2004.09.003
  3. Delsanto, P. P., Sigrun Hirsekorn, V. Agostini, Loparco, and Koka, A. (2002) Modeling the Propagation of Ultrasonic Waves in the Interface Region Between Two Bonded Elements, Ultrasonics, Vol. 40, pp. 605-610 https://doi.org/10.1016/S0041-624X(02)00183-X
  4. Kim, J. Y., Baltazar, A., Hu, J. W., and Rokhlin, S. I. (2006) Hysteretic linear and Nonlinear Acoustic Responses from Pressed Interfaces, International Journal of Solids and Structures, Vol. 43, pp. 6436-6452 https://doi.org/10.1016/j.ijsolstr.2005.11.006
  5. Kim, J. Y., Baltazar, A. and Rokhlin, S. I. (2004) Ultrasonic Assessment of Rough Surface Contact Between Solids from Elasto-Plastic Loading-Unloading Hysteresis Cycle, Journal of the Mechanics and Physics of Solids, Vol. 52, pp. 1911-1934 https://doi.org/10.1016/j.jmps.2004.01.006
  6. Nihei, K. T, Gu, 8., Myer, L. R., L. J. Pyrak-Nolte and Cook, N. G. (1995) Elastic Interface Wave Propagation Along a Fracture, International Congress on Rock Mechanics, Vol. 3, pp. 1151-1157
  7. Pyrak-Nolte, L. J. and Cook, N. G. W. (1987) Elastic Interface Waves Along a Fracture, Geophys. Res. Lett. 14, pp. 1107-1110 https://doi.org/10.1029/GL014i011p01107
  8. Pyrak-Nolte, L. J., Xu, J. and Hayley, G. M. (1992) Elastic Interface Waves Along a Fracture: Theory and Experiment, Rock Mechanics Proceedings of the 33rd U.S. Symposium. New Mexico, USA, pp. 999-1007
  9. Roy, S. and Pyrak-Nolte, L. J. (1995) Interface Waves Propagating Along Tensile Fractures in Dolomite, Geophys. Res. Lett. 22 (20), pp. 2773­-2776 https://doi.org/10.1029/95GL02660