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The Comparison Between Effects of Regular and Irregular Nonlinear Elastic Layers Overlying a Rigid Substratum on Bright Solitary-Like SH Waves

Year 2024, Volume: 7 Issue: 1.addition 2, 17 - 24, 29.02.2024

Abstract

The influences of planar and corrugated free surfaces on bright solitary-like shear horizontal (SH) waves
propagating on a nonlinear elastic layer over a rigid substratum are compared. The amplitude of irregularity of the
free surface is co nsidered as small compared to the average thickness of the layer. The layers consist of
compressible, homogeneous and isotropic materials. A generalized nonlinear Schrödinger (GNLS) equation for
the nonlinear modulation of SH waves is obtained via an asymptotic perturbation method. A comparative study
between the influences of regular and irregular layers on the bright solitary-like SH waves is presented graphically.

References

  • [1] Achenbach, J.D., 1973, Wave Propagation in Elastic Solids. North Holland Publ. Co., Amsterdam. [2] Ewing, W.M., Jardetsky, W.S., 1957, Elastic Waves in Layered Media. McGraw-Hill, New York .
  • [3] Boxberger, T., Picozzi, M. and Parolai, S., 2011 Shallow geology characterization using Rayleigh and Love wave dispersion curves derived from seismic noise array measurements. Journal of Applied Geophysics, 75(2), 3 [4] Kuznetsov, S. V., 2010, Love waves in nondestructive diagnostics of layered composites. Survey. Acoustical Physics 56(6), 877-892.
  • [5] Chattaraj, R., Samal, S. K. and Mahanti, N. C., 2013, Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress. International Journal of Geomechanics 13(4), 402-408.
  • [6] Chattaraj, R., and Samal, S. K., 2016, On dispersion of Love type surface wave in anisotropic porous layer with periodic non uniform boundary surface. Meccanica 51(9), 2215-2224.
  • [7] Pandit, D. K., Kundu, S. and Gupta, S., 2017, Analysis of dispersion and absorption characteristics of shear waves in sinusoidally corrugated elastic medium with void pores. Royal Society open science, 4(2), 160511.
  • [8] Ahmetolan, S., Peker-Dobie, A., Deliktas-Ozdemir, E., & Caglayan, E., 2023, Propagation of Lamb waves in an elastic layer with irregular surfaces. Wave Motion, 119, 103136.
  • [9] Noyer, J.,1961, The effect of variations in layer thickness on Love waves. Bull. Seismol. Soc. Am. 51, 227–235.
  • [10] Deliktas-Ozdemir, E., & Teymür, M., 2022, Nonlinear surface SH waves in a half-space covered by an irregular layer. Zeitschrift für angewandte Mathematik und Physik, 73(4), 145.
  • [11] Demirkuş, D., Teymür, M., 2017, Shear horizontal waves in a nonlinear elastic layer overlying a rigid substratum. Hacettepe Journal of Mathematics and Statistics, 46(5), 801-815.
  • [12] Serkin, V.N., Hasegawa, A., 2002, Exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion. IEEE J. Sel. Top. Quantum Electron. 8(3), 418–431.
  • [13] Yang, J., 2010, Nonlinear Waves in Integrable and Nonintegrable Systems. Society for Industrial and Applied Mathematics, Philadelphia . 45-354 .
Year 2024, Volume: 7 Issue: 1.addition 2, 17 - 24, 29.02.2024

Abstract

References

  • [1] Achenbach, J.D., 1973, Wave Propagation in Elastic Solids. North Holland Publ. Co., Amsterdam. [2] Ewing, W.M., Jardetsky, W.S., 1957, Elastic Waves in Layered Media. McGraw-Hill, New York .
  • [3] Boxberger, T., Picozzi, M. and Parolai, S., 2011 Shallow geology characterization using Rayleigh and Love wave dispersion curves derived from seismic noise array measurements. Journal of Applied Geophysics, 75(2), 3 [4] Kuznetsov, S. V., 2010, Love waves in nondestructive diagnostics of layered composites. Survey. Acoustical Physics 56(6), 877-892.
  • [5] Chattaraj, R., Samal, S. K. and Mahanti, N. C., 2013, Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress. International Journal of Geomechanics 13(4), 402-408.
  • [6] Chattaraj, R., and Samal, S. K., 2016, On dispersion of Love type surface wave in anisotropic porous layer with periodic non uniform boundary surface. Meccanica 51(9), 2215-2224.
  • [7] Pandit, D. K., Kundu, S. and Gupta, S., 2017, Analysis of dispersion and absorption characteristics of shear waves in sinusoidally corrugated elastic medium with void pores. Royal Society open science, 4(2), 160511.
  • [8] Ahmetolan, S., Peker-Dobie, A., Deliktas-Ozdemir, E., & Caglayan, E., 2023, Propagation of Lamb waves in an elastic layer with irregular surfaces. Wave Motion, 119, 103136.
  • [9] Noyer, J.,1961, The effect of variations in layer thickness on Love waves. Bull. Seismol. Soc. Am. 51, 227–235.
  • [10] Deliktas-Ozdemir, E., & Teymür, M., 2022, Nonlinear surface SH waves in a half-space covered by an irregular layer. Zeitschrift für angewandte Mathematik und Physik, 73(4), 145.
  • [11] Demirkuş, D., Teymür, M., 2017, Shear horizontal waves in a nonlinear elastic layer overlying a rigid substratum. Hacettepe Journal of Mathematics and Statistics, 46(5), 801-815.
  • [12] Serkin, V.N., Hasegawa, A., 2002, Exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion. IEEE J. Sel. Top. Quantum Electron. 8(3), 418–431.
  • [13] Yang, J., 2010, Nonlinear Waves in Integrable and Nonintegrable Systems. Society for Industrial and Applied Mathematics, Philadelphia . 45-354 .
There are 11 citations in total.

Details

Primary Language English
Subjects Topology, Mathematical Methods and Special Functions, Applied Mathematics (Other)
Journal Section The Comparison B etween E ffects of Regular and Irregular N onlinear E lastic L ayer s O verlying a R igid Substratum on B right S olitary Like SH W aves
Authors

Ekin Deliktaş-özdemir 0000-0001-7890-6521

Early Pub Date February 28, 2024
Publication Date February 29, 2024
Submission Date February 18, 2024
Acceptance Date February 21, 2024
Published in Issue Year 2024 Volume: 7 Issue: 1.addition 2

Cite

APA Deliktaş-özdemir, E. (2024). The Comparison Between Effects of Regular and Irregular Nonlinear Elastic Layers Overlying a Rigid Substratum on Bright Solitary-Like SH Waves. Journal of Advanced Mathematics and Mathematics Education, 7(1.addition 2), 17-24.