Abstract
The present article aims to unravel the propagation characteristics of a shear wave in the context of reinforcement and frictional bonding in a composite structure. The geometrical configuration of the composite structure is comprised with a fibre-reinforced layer and an isotropic homogeneous semi-infinite medium which are frictionally bonded to each other. An analytical technique is employed to find the complex form of the frequency equation which is separated into real and imaginary parts representing the dispersion and damping relation, respectively. As a particular case of the problem, the deduced results are matched with the classical Love equation. The numerical simulation is performed to graphically portray the analytical findings and to trace out the effect of reinforcement by a comparative study which is a major highlight of the study. The significant influence of reinforcement, frictional bonding, and spectral decay parameter on the phase, group, and damped velocities are revealed. The outcome of the present study may be helpful to gain deeper insight into the propagation characteristics of a shear wave in a frictionally bonded composite structure which may provide useful information in engineering applications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Cambridge University Press, Cambridge (1920)
Pandit, D.K., Kundu, S., Gupta, S.: Propagation of Love waves in a prestressed Voigt-type viscoelastic orthotropic functionally graded layer over a porous half-space. Acta Mech. 228(3), 871–880 (2017)
Anderson, D.L.: Elastic wave propagation in layered anisotropic media. J. Geophys. Res. 66(9), 2953–2963 (1961)
Galich, P.I., Slesarenko, V., Rudykh, S.: Shear wave propagation in finitely deformed 3D fiber-reinforced composites. Int. J. Solids Struct. 110, 294–304 (2017)
Chattopadhyay, A., Michel, V.: A model for spherical SH wave propagation in self-reinforced linearly elastic media. Arch. Appl. Mech. 75(2–3), 113–124 (2006)
Singh, A.K., Mistri, K.C., Das, A.: Propagation of SH-wave in a corrugated viscous sandy layer sandwiched between two elastic half-spaces. Waves Random Complex Media 27(2), 213–240 (2017)
Spencer, A.J.M.: Deformation of fibre-reinforced materials. Oxford University Press, London (1972)
Belfield, A.J., Rogers, T.G., Spencer, A.J.M.: Stress in elastic plates reinforced by fibres lying in concentric circles. J. Mech. Phys. Solids. 31(1), 25–54 (1983)
Chattopadhyay, A., Venkateswarlu, R.L.K., Chattopadhyay, A.: Reflection and refraction of quasi P and SV waves at the interface of fibre-reinforced media. Adv. Stud. Theor. Phys. 1, 57–73 (2007)
Chattopadhyay, A., Singh, A.K.: G-type seismic waves in fibre reinforced media. Meccanica 47(7), 1775–1785 (2012)
Mallick, P.K.: Fiber-Reinforced Composites: Materials, Manufacturing, and Design. CRC Press, Boca Raton (2007)
Uddin, N. (ed.): Developments in Fiber-Reinforced Polymer (FRP) Composites for Civil Engineering. Elsevier, Amsterdam (2013)
Miller, R.K.: An approximate method of analysis of the transmission of elastic waves through a frictional boundary. J. Appl. Mech. 44(4), 652–656 (1977)
Iwan, W.D.: A generalization of the concept of equivalent linearization. Int. J. Non-Linear Mech. 8(3), 279–287 (1973)
Murty, G.S.: A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely-bonded interface of elastic half-spaces. Phys. Earth Planet. Inter. 11, 65–79 (1975)
Miller, R.K.: An estimate of the properties of Love-type surface waves in a frictionally bonded layer. Bull. Seismol. Soc. Am. 69, 305–317 (1979)
Di Bartolomeo, M., Massi, F., Baillet, L., Culla, A., Fregolent, A., Berthier, Y.: Wave and rupture propagation at frictional bimaterial sliding interfaces: from local to global dynamics, from stick-slip to continuous sliding. Tribol. Int. 52, 117–131 (2012)
Loeb, J.: Attenuation des ondes sismiques dans les solides. Geophys. Prospect. 9, 370–381 (1961)
Sezawa, K., Kanai, K.: A fault surface or a block absorbs seismic wave energy, Bull. Earthquake Res. Inst., Tokyo Univ., 18, 465–482 (1940)
Kanai, K.: A new problem concerning surface waves. Bull. Earthq. Res. Inst. 39, 85–95 (1961)
Kozdon, J.E., Dunham, E.M., Nordström, J.: Interaction of waves with frictional interfaces using summation-by-parts difference operators: weak enforcement of nonlinear boundary conditions. J. Sci. Comput. 50(2), 341–367 (2012)
Graff, K.F.: Wave Motion in Elastic Solids. Dover, New York (1991)
Markham, M.F.: Measurement of elastic constants of fibre-reinforced by ultrasonic. Composites 1(3), 145–149 (1970)
Gubbins, D.: Seismology and Plate Tectonics. Cambridge University Press, Cambridge (1990)
Acknowledgements
The author Ms. Akanksha Srivastava conveys her sincere thanks to Indian Institute of Technology (Indian School of Mines) Dhanbad, India for providing Junior Research Fellowship and facilitating us with its best research facility. Authors express their sincere thanks to Science and Engineering Research Board, Department of Science and Technology, New Delhi for providing financial support through Project no. EMR/ 2017/000263. They are also thankful to the reviewers for their useful suggestions and valuable comments in the improvement of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chattopadhyay, A., Srivastava, A., Kumar, P. et al. Analysis of propagation characteristics of a shear wave in a frictionally bonded fibre-reinforced stratum. Acta Mech 229, 4229–4238 (2018). https://doi.org/10.1007/s00707-018-2219-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-018-2219-y