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ARTICLE
Propagation and reflection of magneto-elastic plane waves at the free surface of a rotating micropolar fibre-reinforced medium with voids
1
COMSATS University Islamabad, Department of Mathematics, Islamabad
Submission date: 2019-01-27
Acceptance date: 2019-05-06
Online publication date: 2019-10-15
Publication date: 2019-10-15
Journal of Theoretical and Applied Mechanics 2019;57(4):869-881
KEYWORDS
ABSTRACT
This work investigates rotational effects on propagation and reflection of waves at the free
surface of a micropolar fibre-reinforced medium with voids under magnetic fields. When the
P-wave is incident on the free surface, there exist four coupled reflected plane waves traveling
in the medium; quasi-longitudinal displacement (qLD) wave, quasi-transverse displacement
(qTD) wave, quasi-transverse microrotational (qTM) wave and a wave due to voids. Normal
mode analysis is adopted in concomitant with Snell’s laws, and appropriate boundary
conditions in determination of the solution. Amplitude ratios which correspond to reflected
waves in vertical and horizontal components are presented analytically and graphically.
REFERENCES (27)
1.
Abd-Alla A.M., Abo-Dahab S. M., Khan A., 2017, Rotational effects on magneto-thermoelastic Stonely, Love, and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order, Computers, Materials and Continua, 53, 1, 49-72.
2.
Baljeet S., Sarva J.T., 2004, Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space, Sadhana, 29, 3, 249-257.
3.
Biswas P.K., Sengupta P.R., Debnath L., 1996, Axisymmetric Lamb’s problem in a semi-infinite micropolar viscoelastic medium, International Journal of Mathematics and Mathematical Scieences, 19, 4, 815-820.
4.
Chattopadhyay A., Choudhury S., 1990, Propagation, reflection and transmission of magneto elastic shear waves in a self-reinforced medium, International Journal of Engineering Science, 28, 6, 485-495.
5.
Chattopadhyay A., Venkateswarlu V.R.K., 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.
6.
Chaudhary S., Kaushik V.P., Tomar S. K., 2004, Reflection/transmission of plane SH wave through a self-reinforced elastic layer between two half-spaces, Acta Geophysica Polonica, 52, 2, 219-235.
7.
Cowin S.C., Nunziato J.W., 1979, A nonlinear theory of elastic materials with voids, Archives Rational Mechanics and Analysis, 72, 2, 175-291.
8.
Cowin S.C., Nunziato J.W., 1983, Linear elastic materials with voids', Journal of Elasticity, 13, 2, 125-147.
9.
Eringen A.C., 1967, Linear theory of micropolar viscoelasticity, International Journal of Engineering Science, 5, 2, 191-204.
10.
Hillion P., 2008, Harmonic plane wave propagation in anisotropic chiral media, International Journal of Applied Electromagnetics and Mechanics, 28, 3, 337-350.
11.
Khan A., Anya A.I., Kaneez H., 2015, Gravitational effects on surface waves in non-homogeneous rotating fibre-reinforced anisotropic elastic media with voids, International Journal of Applied Science and Engineering Research, 4, 5, 620-632.
12.
Kumar R., Gogna M.L., Debnath L., 1990, On Lamb’s plane problem in a micropolar viscoelastic half-space with stretch, International Journal of Mathematics and Mathematical Scieences, 13, 2, 363-372.
13.
Kumar R., Sharma K.D., Garg S.K., 2015, Reflection of plane waves in transversely isotropic micropolar viscothermoelastic solid, Materials Physics and Mechanics, 22, 1, 1-14.
14.
Lakes R.S., Benedict R.L., 1982, Noncentrosymmetry in micropolar elasticity, International Journal of Engineering Sciences, 20, 10, 1161-1167.
15.
Lata P., 2018, Reflection and refraction of plane waves in a layered nonlocal elastic and anisotropic thermoelastic medium, Structural Engineering and Mechanics, 66, 1, 113-124.
16.
McCarthy M.F., Eringen A.C., 1969, Micropolar viscoelastic waves, International Journal of Engineering Science, 7, 5, 447-458.
17.
Othman M.I.A., Lotfy Kh., 2013, The effect of magnetic field and rotation of the 2-D problem of a fiber-reinforced thermoelastic under three theories with influence of gravity, Mechanics of Materials, 60, 129-143.
18.
Puri P., Cowin S.C., 1985, Plane waves in linear elastic materials with voids, Journal of Elasticity, 15, 2, 167-183.
19.
Roy I., Acharya D.P., Acharya S., 2017, Propagation and reflection of plane waves in a rotating magneto-elastic fibre-reinforced semi space with surface stress, Mechanics and Mechanical Engineering, 21, 4, 1043-1061.
20.
Schoenberg M., Censor D., 1973, Elastic waves in rotating media, Quarterly of Applied Mathematics, 31, 1, 115-125.
21.
Sengupta P.R., Nath S., 2001, Surface waves in fibre-reinforced anisotropic elastic media, Sadhana, 26, 4, 363-370.
22.
Singh B., 2000, Reflection and transmission of plane harmonic waves at the interface between a liquid and micropolar viscoelastic solid with stretch, Sadhana – Academy Proceedings in Engineering Sciences, 25, 6, 589-600.
23.
Singh B., 2017, Reflection of elastic waves from plane surface of a half-space with impedance boundary conditions, Geosciences Research, 2, 4, 242-253.
24.
Singh B., Kumar R., 1998, Reflection and refraction of plane waves at an interface between micropolar elastic solid and viscoelastic solid, International Journal of Engineering Science, 36, 2, 119-135.
25.
Sinha M., Bera R.K., 2003, Eigenvalue approach to study the effect of rotation and relaxation time in generalized thermoelasticity, Computers and Mathematics with Applications, 46, 783-792.
26.
Sunita D., Suresh K.S., Kapil K.K., 2019, Reflection at the free surface of fibre-reinforced thermoelastic rotating medium with two temperature and phase-lag, Applied Mathematics Modelling, 65, 106-119.
27.
Tauchert T.R., 1971, Thermal stresses in micropolar elastic solids, Acta Mechanica, 11, 3, 155-169.
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| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
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