Reflection of Three-Dimensional Plane Waves in a Self-Reinforced Medium under Initial Stresses
Publication: Journal of Engineering Mechanics
Volume 142, Issue 4
Abstract
The present paper deals with the reflection of three-dimensional plane waves at a traction-free boundary of a self-reinforced medium under initial stresses. The analytical expressions of all three phase velocities of quasi-compressional (qP), quasi-shear ( and ) waves in three dimensions under initial stresses have been obtained. The closed form expressions for the amplitude ratios of reflection coefficients of the three quasi waves in a self-reinforced medium in terms of the phase velocity, propagation vector, initial stresses, and the stiffness coefficients of the medium have also been obtained. The variations of reflected coefficients with the angle of incidence have been carried out numerically, and the results are given in the form of graphs.
Get full access to this article
View all available purchase options and get full access to this article.
References
Achenbach, J. D. (1973). Wave propagation in elastic solids, Elsevier, Amsterdam, Netherlands.
Akbarov, S. D., and Ozaydin, O. (2001). “The effect of initial stresses on harmonic stress fields within the stratified half plane.” Eur. J. Mech.-A/Solids, 20(3), 385–396.
Biot, M. A. (1940). “The influence of initial stress on elastic waves.” J. Appl. Phys., 11(8), 522–530.
Biot, M. A. (1963). “Surface instability in finite anisotropic elasticity under initial stress.” Proc. R. Soc. London, Series A, 273(1354), 329–339.
Biot, M. A. (1965). Mechanics of incremental deformations, Wiley, New York.
Borejko, P. (1996). “Reflection and transmission coefficients for three-dimensional plane waves in elastic media.” Wave Motion, 24(4), 371–393.
Chatterjee, M., Dhua, S., and Chattopadhyay, A. (2015). “Quasi-P and quasi-S waves in a self-reinforced medium under initial stresses and under gravity.” J. Vib. Control, in press.
Chatterjee, M., Dhua, S., Sahu, S. A., and Chattopadhyay, A. (2014). “Reflection in a highly anisotropic medium for three-dimensional plane waves under initial stresses.” Int. J. Eng. Sci., 85, 136–149.
Chattopadhyay, A. (2004). “Wave reflection and refraction in triclinic crystalline media.” Arch. Appl. Mech., 73(8), 568–579.
Chattopadhyay, A., Bose, S., and Chakraborty, M. (1982). “Reflection of elastic waves under initial stress at a free surface.” J. Acoust. Soc. Am., 72(1), 255–263.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Dhua, S. (2013). “Torsional surface waves in heterogeneous anisotropic half space under initial stress.” Arch. Appl. Mech., 83(3), 357–366.
Chattopadhyay, A., and Rogerson, G. A. (2001). “Wave reflection in slightly compressible finitely deformed elastic media.” Arch. Appl. Mech., 71(4–5), 307–316.
Chattopadhyay, A., Singh, A. K., and Dhua, S. (2014). “Effect of heterogeneity and reinforcement on propagation of a crack due to shear waves.” Int. J. Geomech., 04014013.
Chattopadhyay, A., Venkateswarlu, R. L. K., and Saha, S. (2002). “Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium.” Sadhana, 27(6), 613–630.
Crampin, S. (1975). “Distinctive particle motion of surface waves as a diagnostic of anisotropic layering.” Geophys. J. R. Astron. Soc., 40(2), 177–186.
Crampin, S. (1977). “A review of the effects of anisotropic layering on the propagation of surface waves.” Geophys. J. R. Astron. Soc., 49(1), 9–27.
Crampin, S., and Taylor, D. B. (1971). “The propagation of surface waves in anisotropic media.” Geophys. J. R. Astron. Soc., 25(1–3), 71–87.
Destrade, M., and Ogden, R. W. (2012). “On stress-dependent elastic moduli and wave speeds.” IMA J. Appl. Math., 78(5), 965–997.
Dhua, S., and Chattopadhyay, A. (2015). “Torsional wave in an initially stressed layer lying between two inhomogeneous media.” Meccanica, 50(7), 1775–1789.
Dhua, S., Chattopadhyay, A., and Sahu, S. A. (2015). “Propagation of surface wave in a fluid layer overlying a slightly compressible, finitely deformed elastic medium.” J. Vib. Control, 21(13), 2697–2704.
Dhua, S., Singh, A. K., and Chattopadhyay, A. (2015). “Propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half-space with initial stress.” J. Vib. Control, 21(10), 1987–1998.
Erbay, H. A., and Rogerson, G. A. (2000). “Effects of pre-stress on impact waves in an incompressible elastic plate.” Q. J. Mech. Appl. Math., 53(4), 531–550.
Hugues, D. S., and Kelly, J. L. (1953). “Second-order elastic deformation of solids.” Phys. Rev., 92(5), 1145–1149.
Keith, C. M., and Crampin, S. (1977a). “Seismic body waves in anisotropic media: Propagation through a layer.” Geophys. J. R. Astron. Soc., 49(1), 209–223.
Keith, C. M., and Crampin, S. (1977b). “Seismic body waves in anisotropic media: Reflection and refraction at a plane interface.” Geophys. J. R. Astron. Soc., 49(1), 181–208.
Keith, C. M., and Crampin, S. (1977c). “Seismic body waves in anisotropic media: Synthetic seismograms.” Geophys. J. R. Astron. Soc., 49(1), 225–243.
Knott, C. G. (1899). “Reflection and refraction of elastic waves with seismological applications.” Philos. Mag., 48(290), 64–97.
Markham, M. F. (1970). “Measurement of elastic constants of the fibre composites by ultrasonic.” Composites, 1(3), 145–149.
Musgrave, M. J. P. (1970). Crystal acoustics, Holden-Day, San Francisco.
Nayfeh, A. H. (1995). Wave propagation in layered anisotropic media with applications to composite, Elsevier, Amsterdam, Netherlands.
Norris, A. N. (1983). “Propagation of plane waves in a pre-stressed elastic media.” J. Acoust. Soc. Am., 74(5), 1642–1643.
Ogden, R. W., and Sotiropoulos, D. (1998). “Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space.” IMA J. Appl. Math., 61(1), 61–90.
Ogden, R. W., and Sotiropoulos, D. A. (1997). “The effect of pre-stress on the propagation and reflection of plane waves in incompressible elastic solids.” IMA J. Appl. Math., 59(1), 95–121.
Pal, A. K., and Chattopadhyay, A. (1984). “The reflection phenomena of plane waves at a free boundary in a pre-stressed elastic half-space.” J. Acoust. Soc. Am., 76(3), 924–925.
Shams, M., Destrade, M., and Ogden, R. W. (2011). “Initial stresses in elastic solids: Constitutive laws and acoustoelasticity.” Wave Motion, 48(7), 552–567.
Sharma, M. D. (2004). “3-D wave propagation in a general anisotropic poroelastic medium: Reflection and refraction at an interface with fluid.” Geophys. J. Int., 157(2), 947–958.
Spencer, A. J. M. (1974). “Boundary layers in highly anisotropic plane elasticity.” Int. J. Solids Struct., 10(10), 1103–1123.
Stillwell, J. (1989). Mathematics and its history, Springer, New York, 59–62.
Tolstoy, I. (1982). “On elastic waves in pre-stressed solids.” J. Geophys. Res., 87, 6823–6827.
Udias, A. (1999). Principles of seismology, Cambridge University Press, Cambridge, NY.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 142 • Issue 4 • April 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Apr 17, 2014
Accepted: Sep 14, 2015
Published online: Jan 8, 2016
Published in print: Apr 1, 2016
Discussion open until: Jun 8, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.