Analysis of Wave Propagation at an Imperfect Boundary between Micropolar Elastic Solid and Micropolar Porous Elastic Solid

Neelam Kumari; Pawan Kumar; Vinod Kaliraman

doi:https://doi.org/10.14445/22315373/IJMTT-V53P504

International Journal of Mathematics Trends and Technology

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Volume 53 | Number 1 | Year 2018 | Article Id. IJMTT-V53P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P504

Analysis of Wave Propagation at an Imperfect Boundary between Micropolar Elastic Solid and Micropolar Porous Elastic Solid

Neelam Kumari, Pawan Kumar, Vinod Kaliraman

Abstract

The purpose of the present paper is to represent a mathematical model to look into the propagation of the waves at an imperfect boundary between micropolar elastic solid and micropolar porous elastic solid. The variation of modulus of amplitudes ratios of various reflected and refracted waves against the angle of incidence are computed numerically for obliquely incident wave travelling at high frequency as well as at low frequency. Discussed the corresponding derivation for the normal force stiffness, transverse force stiffness and welded contact. Stiffness effects on the amplitude ratios with the angle of incidence has been observed and depicted graphically.

Keywords

Amplitude ratio, longitudinal wave, reflection, refraction, micropolar elastic solid, porous, frequency, normal force stiffness, transverse force stiffness.

References

1. A. Merkel and S. Luding, Enhance micropolar model for wave prorpagation in ordered granular materials. International Journal of Solids and structures, 106 – 107: 91- 105, 2017.
2. A.C. Eringen, Micropolar elastic solids with stretch. Ari. Kitabevi Matabaasi 24: 1-9.
3. A.C. Eringen and E.S. Suhubi, Nonlinear theory of simple micro-elastic solids I. International Journal of Engineering Science, 2: 189-203, 1964.
4. A.C. Eringen, Linear theory of micropolar viscoelasticity. Int. J. Eng. Sci., 5: 191-204, 1967.
5. A.C. Eringen, Theory of micropolar elasticity. Fracture (New York: Academic Press) 2: 1968.
6. B. Singh and R. Kumar, Wave reflection at viscoelastic-micropolar elastic interface. Applied Mathematics and Computation, 185: 421-431, 2007.
7. Chong Fu and P. J. Wei, The wave propagation through the imperfect interface between two micropolar solids. Advanced materials research, 803: 419-422, 2013.
8. D. Iesan and L. Nappa, Axially symmetric problems for a porous elastic solid. International Journal of Solids and Structures, 40: 5271-5286, 2003.
9. D. Singh and S. K. Tomar, Longitudinal waves at a micropolar fluid / solid interface. Journal of Applied Mathematics and Mechanics, 45: 225-244, 2008.
10. D. S. Chandrasekharaiah, Effect of surface stresses and voids on Rayleigh waves in an elastic solid. Int. J. Eng. Sci., 25: 205-211, 1987.
11. E.S. Suhubi and A.C. Eringen, Nonlinear theory of micro-elastic solids II. International Journal of Engineering Science, 2: 389-404, 1964.
12. F. R. Golamhesson, Propagation of waves in an elastic cylinder with voids. Science and Technology-Research Journal, University of Mauritius, Mauritius. 5: 43-52, 2000.
13. M. Ciarletta and M. A. Sumbatyan, Reflection of plane waves by the free boundary of a porous elastic half – space. Journal of Sound of Vibration, 259: 255-264, 2003.
14. N. Kumari, Plane wave propagation at solid-solid imperfect interface. International Journal of Mathematics And Its Applications, 2(3): 63-71, 2014.
15. P. Puri and S. C. Cowin, Plane waves in linear elastic material with voids. Journal of Elasticity, 15: 167-183, 1985.
16. P. Zhang, P. Wei and Y. Li, Reflection of longitudinal displacement wave at the viscoelastically supported boundary of micropolar half – space. Meccanica, 52:1641. doi:10.1007/S11012-016-0514-z, 2016.
17. R.D. Gautheir, Experimental investigations on micropolar media. Mechanics of micropolar media (eds) O Brulin, R K T Hsieh (World Scientific, Singapore), p.395, 1982.
18. R. Kumar and M. Singh, Effect of rotation and imperfection reflection and transmission of plane waves in anisotropic generalized thermoelastic media. Journal of Sound Vibration, 324: 773-793, 2009.
19. S. K. Tomar and J. Singh, Plane waves in micropolar porous elastic solid half-space. International Journal of Applied Mathematics and Mechanics, 2: 52-70, 2006.
20. S. K. Tomar and J. Singh, Transmission of longitudinal waves through a plane interface between two dissimilar porous elastic solid half-space. Applied Mathematics and Computation, 169: 672-688, 2005.
21. S. Shekhar and Imtiyaz A. Parvez, Wave propagation across the imperfectly bonded interface between cracked elastic solid and porous solid saturated with two immiscible viscous fluids. International Journal of Solids and Structures, 75-76: (1), 299-308, 2015.
22. T. W. Wright, Elastic wave propagation through a material with voids. Journal of Mechanics and Physics of Solids, 46: 2033-2047, 1998.
23. V.R. Parfitt and A.C. Eringen, Reflection of plane waves from the flat boundary of a micropolar elastic half space. J. Acoust. Soc. Am., 45: 1258-1272, 1969.
24. W. Nowacki, The Linear Theory of Micropolar Elasticity. International Centre for Mechanical Sciences. Springer, New York, 1974.

Citation :

Neelam Kumari, Pawan Kumar, Vinod Kaliraman, "Analysis of Wave Propagation at an Imperfect Boundary between Micropolar Elastic Solid and Micropolar Porous Elastic Solid," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 1, pp. 22-39, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P504