On wave propagation in a random micropolar thermoelastic medium, second moments, and associated Green’s tensor. (English) Zbl 1397.74012
Summary: The couple stress theory developed by Eringen comprises granular materials as also composite fibrous materials. As such, micropolar materials present an inclusive model of composite materials. This article endeavors to study aspects of wave propagation in a random weakly thermal micropolar elastic medium. The smooth perturbation technique has been employed. The classical thermoelasticity has been used. Six different types of waves have been observed to propagate in the random interacting medium. Dispersion equations have been derived. The effects due to random variations of micropolar elastic and thermal parameters have been observed. Change of phase speed occurs on account of randomness. Attenuation coefficients for high-frequency waves have been computed. Second moment properties have been discussed with application to wave propagation in the random micropolar elastic medium. 36 + 1 components of the associated Green’s tensor have been computed. Integrals involving correlation functions have been transformed to radial forms. A special type of correlation function has been used to approximately measure effects of random variations of parameters.
MSC:
| 74A40 | Random materials and composite materials |
| 74F15 | Electromagnetic effects in solid mechanics |
References:
| [1] | Eringen AC. Linear theory of micropolar elasticity. J. Math. Mech. 1966;15:909-922. · Zbl 0145.21302 |
| [2] | Eringen AC. Theory of thermo-microstretch fluids and bubbly liquids. Int. J. Eng. Sci. 1990;28:133-143.10.1016/0020-7225(90)90063-O · Zbl 0709.76015 |
| [3] | Keller JB. Stochastic equations and wave propagation in random media. Proc. Symp. App. Math. 1964;16:145-170. · Zbl 0202.46703 |
| [4] | Eringen AC. Microcontinuum field theories. New York (NY): Springer-Science, Business Media; 1999.10.1007/978-1-4612-0555-5 · Zbl 0953.74002 |
| [5] | Kumar R. Wave propagation in micropolar viscoelastic generalized thermoelastic solid. Int. J. Eng. Sci. 2000;38:1377-1395.10.1016/S0020-7225(99)00057-9 |
| [6] | Kumar R, Singh B. Wave propagation in a micropolar generalized thermoelastic body with stretch. Proc. Math. Sci. 1996;106:183-199.10.1007/BF02837172 · Zbl 0858.73018 |
| [7] | Majewswski E. Seismic Rotation Waves: Spin and Twist Solitons. In: Teisseyre R, Takeo M, Majewski E, editors. Earthquake source asymmetry, structural media and rotation effects. Berlin: Springer; 2006. Chapter 19, p. 255. |
| [8] | Mitra M, Bhattacharyya RK. Wave propagation in a random micropolar elastic medium, extended abstracts. Second International Conference on Mathematical and Numerical Aspects of Wave Propagation; 1993 Jun 7-10; Delaware: University of Delaware. p.72-74. |
| [9] | Ignaczak J, Ostoja-Starzewski M. Thermoelasticity with finite wave speeds. New York (NY): Oxford University Press; 2010. Chapter 6, p. 111. · Zbl 1183.80001 |
| [10] | Karal FC, Keller JB. Elastic, electromagnetic, and other waves in a random medium. J. Math. Phys. 1964;5:537-547.10.1063/1.1704145 · Zbl 0118.13302 |
| [11] | Chow PL. Thermoelastic wave propagation in a random medium and some related problems. Int. J. Eng. Sci. 1973;11:953-971.10.1016/0020-7225(73)90010-4 · Zbl 0263.73007 |
| [12] | Chen YM, Tien CL. Penetration of temperature waves in a random medium. J. Math. Phys. 1967;XLVI:188-194. · Zbl 0164.29701 |
| [13] | Bhattacharyya RK. On wave propagation in a random magneto-thermo-viscoelastic medium. Indian J. Pure Appl. Math. 1986;17:705-725. · Zbl 0586.73030 |
| [14] | Bhattacharyya RK. On reflection of waves from the boundary of a random elastic semi-infinite medium. Pure App. Geophys. (PAGEOPH). 1996;146:677-688. |
| [15] | Bera RK. Propagation of waves in random rotating infinite magneto-thermo-visco-elastic medium. Comput. Math. App. 1998;36:85-102.10.1016/S0898-1221(98)00194-1 · Zbl 0952.74032 |
| [16] | Chernov LA. Wave propagation in a random medium. New York (NY): McGraw Hill Book Co; 1960;XXVIII:245-258. |
| [17] | Beran MJ, McCoy JJ. Mean field variation in random media. Q. App. Math. 1970. · Zbl 0207.09301 |
| [18] | Beran MJ, Frankenthal S, Deshmukh V, et al. Propagation of radiation in time-dependent three-dimensional random media. Waves Random Complex Media. 2008;18:435-460. · Zbl 1271.78015 |
| [19] | Sobczyk K, Wedrychowicz S, Spencer Jr BF. Dynamics of structural systems with spatial randomness. Int. J. Solids Struct. 1996;33:1651-1669. · Zbl 0903.73037 |
| [20] | Frankenthal S, Beran MJ. Propagation in one-dimensionally stratified time-independent scattering media. Waves Random Complex Media. 2007;17:189-212. · Zbl 1191.35195 |
| [21] | Uscinski BJ. Intensity fluctuations in a moving random medium. Waves Random Complex Media. 2005;15:437-450. · Zbl 1191.35198 |
| [22] | Frisch U. Wave propagation in random media. In: Bharucha-Reid AT, editor. Probabilistic methods in applied mathematics. Vol. I. New York(NY): Academic Press; 1968. p. 76-198. |
| [23] | Lavoine J. Methods De Calcul II, Calcul Symbolique, Distributions et Pseudo-Fonctions. Paris: Centre National De La Recherche, Scientifique; 1959. · Zbl 0092.11904 |
| [24] | Keller JB, Karal FC. Effective dielectric constant, permeability, and conductivity of a random medium and the velocity and attenuation coefficient of coherent waves. J. Math. Phys. 1966;7:661-670.10.1063/1.1704979 |
| [25] | Eringen AC. Theory of micropolar elasticity. In: Liebowitz H, editor. Fracture, an advanced treatise. Vol. II. New York (NY): Academic Press; 1968. Chapter VII. · Zbl 0266.73004 |
| [26] | Schiff LT. Quantum mechanics. Auckland: McGraw-Hill Book Company Inc; 1949. |
| [27] | Bhattacharyya RK. A note on determination of Green’s tensor. Indian J. Mech. Math. 1982;XX:34-39 (Jadavpur University, Calcutta). · Zbl 0561.73094 |
| [28] | Chattopadhyay G, Bhattacharyya RK. Determination of Green’s tensor for a conducting magneto-viscoelastic medium. In: Cohen GC, Heikkola EH, Joly P, Neittaanmaki P, editors. Proceedings of Mathematical & Numerical Aspects of Wave Propagation. WAVES 2003 Conference; Jyvaskyla, Finland (INRIA-FRANCE); 2003Jun 30-Jul 4; Springer. p. 298-303. · Zbl 1075.74039 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
