Analytic Rayleigh Wave Speed Formula in Non-Linear Orthotropic Material

A. Rehman*, Maqsood-Ul-Hassan**
*-** Department of Mathematics, National College of Business Administration & Economics, Punjab, Pakistan.
Periodicity:January - June'2022
DOI : https://doi.org/10.26634/jmat.11.1.18469

Abstract

Analytic Rayleigh wave speed formula in nonlinear orthotropic medium is determined. Speed of Rayleigh waves in iodic acid, a specimen of non-linear orthotropic materials, is calculated and is compared with that of the speed in linear orthotropic iodic acid. In linear iodic acid, three distinct Rayleigh waves propagate with speeds 53.44 km/s, 80.94 km/s, and 125.37 km/s, respectively. While, in nonlinear iodic acid these three waves become coincident and only one Rayleigh wave seem to propagate with velocity 63.68 km/s.

Keywords

Rayleigh Waves, Linear, Non-Linear, Orthotropic Material, Elasticity, Hooke's Law, Strain, Stress.

How to Cite this Article?

Rehman, A., and Maqsood-Ul-Hassan. (2022). Analytic Rayleigh Wave Speed Formula in Non-Linear Orthotropic Material. i-manager’s Journal on Mathematics, 11(1), 12-19. https://doi.org/10.26634/jmat.11.1.18469

References

[1]. Acharya, D. P., & Mondal, A. K. (2006). Effect of magnetic field on the propagation of quasi-transverse waves in a nonhomogeneous conducting medium under the theory of nonlinear elasticity. Sadhana, 31(3), 199-211. https://doi.org/10.1007/BF02703376
[2]. Chi Vinh, P., & Ogden, R. W. (2004). Formulas for the Rayleigh wave speed in orthotropic elastic solids. Archives of Mechanics, 56(3), 247-265.
[3]. Kaur, I., & Lata, P. (2019). Rayleigh wave propagation in transversely isotropic magneto-thermoelastic medium with three-phase-lag heat transfer and diffusion. International Journal of Mechanical and Materials Engineering, 14(1), 1-11. https://doi.org/10.1186/s40712-019-0108-3
[4]. Malischewsky, P. G. (2000). Comment to “A new formula for the velocity of Rayleigh waves” by D. Nkemzi [Wave Motion 26 (1997) 199–205]. Wave Motion, 31(1), 93-96. https://doi.org/10.1016/S0165-2125(99)00025-6
[5]. Nkemzi, D. (1997). A new formula for the velocity of Rayleigh waves. Wave Motion, 26(2), 199-205. https://doi.org/10.1016/S0165-2125(97)00004-8
[6]. Pichugin, A.V. (2008). Approximation of the Rayleigh Wave Speed (Unpublished paper). Department of Mathematics, Brunel University, London, UK.
[7]. Rahman, M., & Barber, J. R. (1995). Exact expressions for the roots of the secular equation for Rayleigh waves. ASME Journal of Applied Mechanics, 62(1), 250-252. https://doi.org/10.1115/1.2895917
[8]. Rayleigh, L. (1885). On waves propagated along the plane surface of an elastic solid. Proceedings of the London Mathematical Society, 1(1), 4-11. https://doi.org/10.1112/plms/s1-17.1.4
[9]. Rehman, A., Khan, A., & Ali, A. (2007a). Rayleigh waves in a rotating transversely isotropic materials. Electronic Journal Technical Acoustics, 5.
[10]. Rehman, A., Khan, A., & Ali, A. (2007b). Rotational effects on Rayleigh wave speed in orthotropic medium. Punjab University Journal of Mathematics, 39, 29-33.
[11]. Rehman, A., & Shahid, I. (2017). Speed of plane harmonic elastic waves in homogeneous and non-homogeneous orthorhombic material. Journal of Advances in Civil Engineering, 4(1), 14-18. https://doi.org/10.18831/djcivil.org/2018011004
[12]. Stoneley, R. (1963). The propagation of surface waves in an elastic medium with orthorhombic symmetry. Geophysical Journal International, 8(2), 176-186. https://doi.org/10.1111/j.1365-246X.1963.tb06281.x
[13]. Xia, J., Miller, R. D., Park, C. B., & Tian, G. (2002). Determining Q of near-surface materials from Rayleigh waves. Journal of Applied Geophysics, 51(2-4), 121-129. https://doi.org/10.1016/S0926-9851(02)00228-8
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.