Love-Type Wave Propagation in an Irregular Prestressed Composite Sandwiched Layer
Publication: International Journal of Geomechanics
Volume 16, Issue 2
Abstract
The present problem analytically investigates the possibility of Love-type wave propagation in a prestressed irregular composite layer lying between an upper prestressed heterogeneous isotropic layer of finite width and a lower prestressed isotropic half-space. The closed-form expression of dispersion relation has been deduced and matched with the classical Love wave equation as a special case of the problem for its authenticity. The effects of size of irregularity, heterogeneity parameter of the uppermost layer, width ratio of layers, and horizontal prestresses, present in each of the media, on the dispersion curve are the prime outcome of the study. A comparative study made between the case in which a composite medium is present as an irregular sandwiched layer and the case in which an isotropic medium is present as an irregular sandwiched layer is one of the major highlights of the problem. Moreover, numerical computations have been carried out and are depicted by means of graphs.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors acknowledge all the necessary support furnished by Indian School of Mines, Dhanbad.
References
Achenbach, J. D. (1975). Wave propagation in elastic solids, North Holland, New York.
Anderson, D. L. (1962). “Love wave dispersion in heterogeneous anisotropic media.” Geophysics, 27(4), 445–454.
Babich, S. Y. (1978). “Propagation of surface waves in an initially stressed body with a cylindrical cavity.” Prikl. Mekh., 14(2), 122–125.
Belfield, A. J., Rogers, T. G., and Spencer, A. J. M. (1983). “Stress in elastic plates reinforced by fibres lying in concentric circles.” J. Mech. Phys. Solids, 31(1), 25–54.
Bhattacharya, J. (1969). “The possibility of the propagation of Love type waves in an intermediate heterogeneous layer lying between two semi-infinite isotropic homogeneous elastic layers.” Pure Appl. Geophys., 72(2), 61–71.
Biot, M. A. (1965). Mechanics of incremental deformations, John Wiley & Sons, New York.
Bouchon, M., Campillo, M., and Gaffet, S. (1989). “A boundary integral equation-discrete wavenumber representation method to study wave propagation in multilayered media having irregular interfaces.” Geophysics, 54(9), 1134–1140.
Chattaraj, R., Samal, S., and Mahanti, N. (2013). “Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress.” Int. J. Geomech., 402–408.
Chattopadhyay, A. (1975). “On the dispersion equation for Love wave due to irregularity in the thickness of non-homogeneous crustal layer.” Acta Geophys. Pol., 23, 307–317.
Chattopadhyay, A., Chakraborty, M., and Pal, A. K. (1983). “Effects of irregularity on the propagation of guided SH waves.” J. Mech Theor. Appl., 2(2), 215–225.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2010). “Dispersion of shear waves in an irregular magnetoelastic self-reinforced layer sandwiched between two isotropic half-spaces.” Int. J. Theor. Appl. Mech., 5(1), 27–45.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2011). “Dispersion equation of magnetoelastic shear waves in an irregular monoclinic layer.” Appl. Math. Mech., 32(5), 571–586.
Chattopadhyay, A., Gupta, S., Sahu, S., and Singh, A. (2012). “Torsional surface waves in a self-reinforced medium over a heterogeneous half-space.” Int. J. Geomech., 193–197.
Chattopadhyay, A., Gupta, S., Samal, S., and Sharma, V. (2009). “Torsional waves in self-reinforced medium.” Int. J. Geomech., 9–13.
Chattopadhyay, A, Kumari, P., and Sharma, V. (2013). “Reflection and transmission of three dimensional plane qP wave through layered fluid medium between two distinct triclinic half-spaces.” Int. J. Geomech., 182–190.
Chattopadhyay, A., and Singh, A. K. (2011). “G-type seismic waves in fibre-reinforced media.” Meccanica, 47(7), 1775–1785.
Chattopadhyay, A., and Singh, A. K. (2012). “Propagation of magnetoelastic shear waves in an irregular self-reinforced layer.” J. Eng. Math., 75(1), 139–155.
Chen, X. F. (2007). “Generation and propagation of seismic SH waves in multi-layered media with irregular interfaces.” Adv. Geophys., 48, 191–264.
Dey, S., Gupta, A. K., and Gupta, S. (1996). “Torsional surface waves in nonhomogeneous and anisotropic medium.” J. Acoust. Soc. Am., 99(5), 2737–2741.
Dey, S., Gupta, S., Gupta, A., and Prasad, A. (2001). “Propagation of torsional surface waves in a heterogeneous half-space under a rigid layer.” Acta Geophys. Pol., 49(1), 113–118.
Du, J., Jin, X., and Wang, J. (2007). “Love wave propagation in layered magneto-electro-elastic structures with initial stress.” Acta Mech., 192(1–4), 169–189.
Eringen, A. C., and Samuels, C. J. (1959). “Impact and moving loads on a slightly curved elastic half-space.” J. Appl. Mech., 26, 491–498.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge University Press, Cambridge, U.K.
Guz, A. N. (2002). “Elastic waves in bodies with initial (residual) stresses.” Int. Appl. Mech., 38(1), 23–59.
Hool, G. A., and Kinne, W. S. (1924). Reinforced concrete and masonry structure, McGraw-Hill, New York.
Howell, J., and Benjamin, F. (2005). An introduction to seismological research: History and development, Cambridge University Press, Cambridge, U.K.
Kundu, S., Gupta, S., Vaishnav, P. K., and Manna, S. (2014). “Propagation of Love waves in a heterogeneous medium over an inhomogeneous half-space under the effect of point source.” J. Vib. Control,.
Love, A. E. H. (1911). A treatise on the mathematical theory of elasticity, Cambridge University Press, Cambridge, U.K.
Markham, M. F. (1969). “Measurement of the elastic constants of fibre composites by ultrasonics.” Composites, 1(2), 145–149.
Sahu, S. A., Saroj, P. K., and Dewangan, N. (2013). “SH-waves in viscoelastic heterogeneous layer over half-space with self-weight.” Arch. Appl. Mech., 84(2), 1–11.
Sahu, S. A., Saroj, P. K., and Paswan, B. (2014). “Shear waves in a heterogeneous fiber-reinforced layer over a half-space under gravity.” Int. J. Geomech., 04014048.
Sato, Y. (1952). “Love waves propagated upon heterogeneous medium.” Bull. Earthquake Res. Inst., 30, 1–12.
Singh, A. K., Kumar, S., and Chattopadhyay, A. (2015). “Love-type wave propagation in a piezoelectric structure with irregularity.” Int. J. Eng. Sci., 89, 35–60.
Sun, C. T., and Chen, J. K. (1985). “On the impact of initially stressed composite laminates.” J. Compos. Mater., 19(6), 90–504.
Tiersten, H. F. (1969). Linear piezoelectric plate vibrations, Plenum Press, New York.
Tranter, C. J. (1966). Integral transform in mathematical physics, Methuen and Co., London.
Upadhyay, S. K. (1970). “Love wave propagation in multilayered anisotropic inhomogeneous media.” Pure Appl. Geophys., 81(1), 51–63.
Verma, P. D. S. (1986). “Magnetoelastic shear waves in self-reinforced bodies.” Int. J. Eng. Sci., 24(7), 1067–1073.
Willis, H. F. (1948). “A formula for expanding an integral as series.” Philos. Mag., 39(293), 455–459.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 16 • Issue 2 • April 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jun 8, 2014
Accepted: Apr 13, 2015
Published online: Sep 28, 2015
Discussion open until: Feb 28, 2016
Published in print: Apr 1, 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.