Hostname: page-component-cb9f654ff-rkzlw Total loading time: 0 Render date: 2025-08-22T22:21:47.922Z Has data issue: false hasContentIssue false
  • English
  • Français

The Effect of Rotation on Propagation of Rayleigh Wave in an Incompressible Monoclinic Elastic Solid

Published online by Cambridge University Press:  04 May 2020

Baljinder Kaur  and
Baljeet Singh Open the ORCID record for Baljeet Singh [Opens in a new window]
Baljinder Kaur
Affiliation:
Department of Mathematics, Panjab University, Chandigarh - 160014, India
Baljeet Singh*
Affiliation:
Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh - 160 011, India
*
*Corresponding author (bsinghgc11@gmail.com)
Get access

Abstract

In this paper, the Rayleigh wave propagation is investigated in rotating half-space of incompressible monoclinic elastic materials which are subjected to the impedance boundary conditions. In particular, the explicit secular equation of the Rayleigh wave is obtained. The main objective of this paper is to illustrate the dependence of dimensionless speed of Rayleigh wave on rotation, anisotropy and impedance parameters. An algorithm in MATLAB software is developed to solve the secular equation of Rayleigh wave. The speed of Rayleigh wave is plotted against rotation, anisotropy and impedance parameters.

Keywords

Rayleigh waveIncompressibilityMonoclinic materialSecular equation

Information

Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 4 , August 2020 , pp. 485 - 495
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Rayleigh, L., On waves propagating along the plane surface of an elastic solid, Proceedings of the Royal Society of London A, 17, pp. 4–11 (1885).Google Scholar
Sveklo, V.A., Plane waves and Rayleigh waves in anisotropic media (in Russian), Doklady Akademii Nauk SSSR, 59, pp. 871–874 (1948).Google Scholar
Stoneley, R., The propagation of surface waves in an elastic medium with orthorhombic symmetry, Geophysical Journal of the Royal Astronomical Society, 8, pp. 176–186 (1963).CrossRefGoogle Scholar
Royer, D. and Dieulesaint, E., Rayleigh wave velocity and displacement in orthorhombic tetragonal, hexagonal and cubic crystals, Journal of Acoustical Society of America, 6, pp. 1438–1444 (1984).CrossRefGoogle Scholar
Destrade, M., The explicit secular equation for surface acoustic waves in monoclinic crystals, Journal of Acoustical Society of America, 109, pp. 1398–1402 (2001).CrossRefGoogle Scholar
Destrade, M., Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds, Mechanics of Materials 35, pp. 931–939 (2003).10.1016/S0167-6636(02)00294-6CrossRefGoogle Scholar
Destrade, M., Martin, P.A. and Ting, T.C.T., The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics, Journal of the Mechanics and Physics of Solids, 50, pp. 1453–1468 (2002).CrossRefGoogle Scholar
Ogden, R.W. and Vinh, P.C., On Rayleigh waves in incompressible orthotropic elastic solids, Journal of Acoustical Society of America, 115, pp. 530–533 (2004).CrossRefGoogle ScholarPubMed
Vinh, P.C. and Ogden, R.W., Formulas for the Rayleigh wave speed in orthotropic elastic solids, Archive of Mechanics, 56, pp. 247–265 (2004).Google Scholar
Vinh, P.C. and Ogden, R.W., On the Rayleigh wave speed in orthotropic elastic solids, Meccanica, 40, pp. 147–161 (2005).10.1007/s11012-005-1603-6CrossRefGoogle Scholar
Ogden, R.W. and Singh, B., Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited, Journal of Mechanics of Materials and Structures, 6, pp. 453–477 (2011).CrossRefGoogle Scholar
Vinh, P.C., Merodio, J., Hue, T.T.T. and Nam, N.T., Non-principal Rayleigh waves in deformed transversely isotropic incompressible non-linearly elastic solids, IMA Journal of Applied Mathematics, 79, pp. 915–928 (2014).10.1093/imamat/hxu023CrossRefGoogle Scholar
Vinh, P.C., Aoudia, A. and Giang, P.T.H., Rayleigh waves in orthotropic fluid-saturated porous media, Wave Motion, 61, pp. 73–82 (2016).10.1016/j.wavemoti.2015.10.007CrossRefGoogle Scholar
Sudheer, G., Lakshmi, M.H. and Rao, Y.V., A note on formulas for the Rayleigh wave speed in elastic solids, Ultrasonics, 73, pp. 82–87 (2017).CrossRefGoogle ScholarPubMed
White, R.M., Acoustic sensors for physical, chemical and biochemical applications, Frequency Control Symposium, pp. 587–594 (1998).Google Scholar
Tiersten, H.F., Stevens, D.S. and Das, P.K., Acoustic surface wave accelerometer and rotation rate sensor, Ultrasonics Symposium, pp. 692–695 (1980).Google Scholar
Tiersten, H.F., Stevens, D.S. and Das, P.K., Circulating flexural wave rotation rate sensor, Ultrasonics Symposium, pp. 163–166 (1981).Google Scholar
Wren, T. and Burdess, J.S., Surface waves perturbed by rotation, Journal of Applied Mechanics, 54, pp. 464–468 (1987).10.1115/1.3173043CrossRefGoogle Scholar
Schoenberg, M. and Censor, D., Elastic waves in rotating media, Quarterly of Applied Mathematics, 31, pp. 115–125 (1973).CrossRefGoogle Scholar
Censor, D. and Schoenberg, M., Two dimensional wave problems in rotating elastic media, Applied Scientific Research, 27, pp. 401–414 (1973).CrossRefGoogle Scholar
Auriault, J.-L., Body wave propagation in rotating elastic media, Mechanics Research Communications, 31, pp. 21–27 (2004).10.1016/j.mechrescom.2003.07.002CrossRefGoogle Scholar
Clarke, N.S. and Burdess, J.S., A rotation rate sensor based upon a Rayleigh resonator, Journal of Applied Mechanics, 61, pp. 139–143 (1994).CrossRefGoogle Scholar
Clarke, N.S. and Burdess, J.S., Rayleigh waves on a rotating surface, Journal of Applied Mechanics, 61, pp. 724–726 (1994).CrossRefGoogle Scholar
Wauer, J., Waves in rotating conducting piezoelectric media, The Journal of the Acoustical Society of America, 106, pp. 626–636 (1999).CrossRefGoogle Scholar
Fang, H., Yang, J. and Jiang, Q., Rotation perturbed surface acoustic waves propagating in piezoelectric crystals, International Journal of Solids and Structures, 37, pp. 4933–4947 (2000).CrossRefGoogle Scholar
Destrade, M., Surface acoustic waves in rotating orthorhombic crystals, Proceedings of the Royal Society of London A, 460, pp. 653–665 (2003).CrossRefGoogle Scholar
Destrade, M., Rayleigh waves in anisotropic crystals rotating about the normal to a symmetry plane, Journal of Applied Mechanics, 71, pp. 516–520 (2004).CrossRefGoogle Scholar
Ting, T.C.T., Surface waves in a rotating anisotropic elastic half-space, Wave Motion, 40, pp. 329–346 (2004).CrossRefGoogle Scholar
Tomar, S.K. and Ogden, R.W., Two dimensional wave propagation in a rotating elastic solid with voids, Journal of Sound and Vibration, 333, pp. 1945–1952 (2014).10.1016/j.jsv.2013.11.043CrossRefGoogle Scholar
Ogden, R.W. and Singh, B., The effect of rotation and initial stress on the propagation of waves in a transversely isotropic elastic solid, Wave Motion, 51, pp. 1108–1126 (2014).10.1016/j.wavemoti.2014.05.004CrossRefGoogle Scholar
Tiersten, H.F., Elastic surface waves guided by thin films, Journal of Applied Physics, 46, pp. 770–789 (1969).10.1063/1.1657463CrossRefGoogle Scholar
Malischewsky, P.G., Surface waves and discontinuities, Elsevier, Amsterdam (1987).Google Scholar
Godoy, E., Durn, M. and Ndlec, J.-C., On the existence of the surface waves in an elastic half-space with impedance boundary conditions, Wave Motion, 49, pp. 585–594 (2012).CrossRefGoogle Scholar
Vinh, P.C. and Hue, T.T.T., Rayleigh waves with impedance boundary conditions in incompressible anisotropic half-spaces, International Journal of Engineering Science, 85, pp. 175–185 (2014).CrossRefGoogle Scholar
Vinh, P.C. and Hue, T.T.T., Rayleigh waves with impedance boundary conditions in anisotropic solids, Wave Motion, 51, pp. 1082–1092 (2014).CrossRefGoogle Scholar
Vinh, P.C. and Xuan, N.Q., Rayleigh waves with impedance boundary condition: Formula for the velocity, existence and uniqueness, European Journal of Mechanics-A/Solids, 61, pp. 180–185 (2017).CrossRefGoogle Scholar
Singh, B., Rayleigh waves in an incompressible fibre-reinforced elastic solid with impedance boundary conditions, Journal of the Mechanical Behavior of Materials, 24, pp. 183–186 (2015).CrossRefGoogle Scholar
Singh, B. and Kaur, B., Propagation of Rayleigh waves in an incompressible rotating orthotropic elastic solid half-space with impedance boundary conditions, Journal of the Mechanical Behavior of Materials, 26, pp. 73–78 (2017).CrossRefGoogle Scholar
Nair, S. and Sotiropoulos, D.A., Interfacial waves in incompressible monoclinic materials with an interlayer, Mechanics of Materials, 31, pp. 225–233 (1999).CrossRefGoogle Scholar
Stroh, A.N., Steady state problems in anisotropic elasticity, Journal of Mathematical Physics, 41, pp. 77–103 (1962).CrossRefGoogle Scholar
Ting, T.C.T., The polarization vector and secular equation for surface waves in an anisotropic elastic half-space, International Journal of Solids and Structures, 41, pp. 2065–2083 (2004).CrossRefGoogle Scholar