Hostname: page-component-77c78cf97d-7dld4 Total loading time: 0 Render date: 2026-04-24T16:09:52.632Z Has data issue: false hasContentIssue false
  • English
  • Français

Propagation of Love-Type Wave in a Corrugated Fibre-Reinforced Layer

Published online by Cambridge University Press:  17 June 2016

A. K. Singh ,
K. C. Mistri  and
A. Das
A. K. Singh
Affiliation:
Department of Applied Mathematics Indian School of Mines Dhanbad, India
K. C. Mistri*
Affiliation:
Department of Applied Mathematics Indian School of Mines Dhanbad, India
A. Das
Affiliation:
Department of Applied Mathematics Indian School of Mines Dhanbad, India
*
*Corresponding author (kchmistri@gmail.com)
Get access

Abstract

The present paper investigates the propagation of Love-type waves in an initially stressed heterogeneous fibre-reinforced layer with corrugated boundary surfaces, lying over a viscoelastic half-space under hydrostatic state of stress. The dispersion relation is obtained in closed form and found to be in well-agreement with the classical Love wave equation. The substantial effect of reinforcement, position and undulation parameters (i.e. corrugation), heterogeneity, horizontal initial stress and hydrostatic state of stress are discussed briefly. It is established through comparative study that reinforced layer supports more to phase velocity of Love-type wave as compare to reinforced free layer.

Keywords

Corrugated boundariesFibre-reinforcedLove-type wavesViscoelastic

Information

Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 6 , December 2016 , pp. 693 - 708
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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

1. Singh, A. K., Das, A., Kumar, S. and Chattopadhyay, A., “Influence of Corrugated Boundary Surfaces, Reinforcement, Hydrostatic Stress, Heterogeneity and Anisotropy on Love-Type Wave Propagation,” Meccanica, 50, pp. 2977–2994 (2015).CrossRefGoogle Scholar
2. Gupta, S. and Pramanik, A., “Torsional Surface Waves in an Inhomogeneous Layer over a Fluid Saturated Porous Half-Space,” Journal of Mechanics, 32, pp. 113–121 (2016).Google Scholar
3. Spencer, A. J. M., Deformations of Fibre-Reinforced Materials, Oxford University Press, New York (1972).Google Scholar
4. Belfield, A. J., Rogers, T. G. and Spencer, A. J. M., “Stress in Elastic Plates Reinforced by Fibres Lying in Concentric Circles,” Journal of the Mechanics and Physics of Solids, 31, pp. 25–54 (1983).Google Scholar
5. Chattopadhyay, A., Gupta, S. and Singh, A. K., “The Dispersion of Shear Wave in Multi-Layered Magnetoelastic Self-Reinforced Media,” International Journal of Solids and Structure, 47, pp. 1317–1324 (2010).CrossRefGoogle Scholar
6. Chattopadhyay, A., Gupta, S., Sahu, S. A. and Singh, A. K., “Dispersion of Horizontally Polarized Shear Waves in an Irregular Non-Homogeneous Self-Reinforced Crustal Layer over a Semi-Infinite Self-Reinforced Medium,” Journal of Vibration and Control, 19, pp. 109–119 (2013).CrossRefGoogle Scholar
7. Pradhan, P. M., Maskey, R. K. and Pradhan, P. L., “Stiffness Behavior and Shear Effect in Partially Infilled Reinforced Concrete Frame,” Journal of Earthquake Engineering, 18, pp. 580–588 (2014).Google Scholar
8. Hadigheh, S. A., Mahini, S. S. and Maheri, M. R., “Seismic Behavior of FRP-Retrofitted Reinforced Concrete Frames,” Journal of Earthquake Engineering, 18, pp. 1171–1197 (2014).Google Scholar
9. Biot, M. A., Mechanics of Incremental Deformations, Wiley, New York (1965).Google Scholar
10. Chattopadhyay, A., “Propagation of SH Waves in a Visco-Elastic Medium Due to Irregularity in the Crustal Layer,” Bulletin of Calcutta Mathematical Society, 70, pp. 303–316 (1978).Google Scholar
11. Kumari, P. and Sharma, V. K., “Propagation of Torsional Waves in a Viscoelastic Layer over an Inhomogeneous Half Space,” Acta Mechanica, 225, pp. 1673–1684 (2014).Google Scholar
12. Acharya, D. P., Roy, I. and Sengupta, S., “Effect of Magnetic Field and Initial Stress on the Propagation of Interface Waves in Transversely Isotropic Perfectly Conducting Media,” Acta Mechanica, 202, pp. 35–45 (2009).Google Scholar
13. Singh, B. and Yadav, A. K., “Reflection of Plane Waves in an Initially Stressed Perfectly Conducting Transversely Isotropic Solid Half-Space,” Journal of Earth System and Science, 122, pp. 1045–1053 (2013).CrossRefGoogle Scholar
14. Kaur, J., Tomar, S. K. and Kaushik, V. P., “Reflection and Refraction of SH-Waves at a Corrugated Interface Between Two Laterally and Vertically Heterogeneous Viscoelastic Solid Half-Spaces,” International Journal of Solids and Structures, 42, pp. 3621–3643 (2005).CrossRefGoogle Scholar
15. Kundu, S., Manna, S. and Gupta, S., “Love Wave Dispersion in Pre-Stressed Homogeneous Medium over a Porous Half-Space with Irregular Boundary Surfaces,” International Journal of Solids and Structures, 51, pp. 3689–3697 (2014).CrossRefGoogle Scholar
16. Singh, A. K., Das, A., Chattopadhyay, A. and Dhua, S., “Dispersion of Shear Wave Propagating in Vertically Heterogeneous Double Layers Overlying an Initially Stressed Isotropic Half-Space,” Soil Dynamics and Earthquake Engineering, 69, pp. 16–27 (2015).Google Scholar
17. Singh, S. S., “Love Wave at a Layer Medium Bounded by Irregular Boundary Surfaces,” Journal of Vibration and Control, 17, pp. 789–795 (2011).CrossRefGoogle Scholar
18. Asano, S., “Reflection and Refraction of Elastic Waves at a Corrugated Interface,” Bulletin of the Seismological Society of America, 56, pp. 201–221 (1966).Google Scholar
19. Ewing, W. M., Jardetzky, W. S. and Press, F., Elastic Wave in Layered Media, McGraw-Hill, New York (1957).CrossRefGoogle Scholar
20. Markham, M. F., “Measurements of Elastic Constants of Fibre Composites,” Ultrasonics, 1, pp. 145–149 (1970).Google Scholar
21. Caloi, P., “Comportement Des Ondes De Rayleigh Dans Un Milieu Firmoélastique Indéfini,” Publications Du Bureau Central Séismologique International, 17, pp. 89–108 (1950) (in French).Google Scholar
22. Gubbins, D., Seismology and Plate Tectonics, Cambridge University press, Cambridge, p. 170 (1990).Google Scholar