Study of Waves Propagating in Anisotropic Homogeneous Microstretch Elastic Medium




Microstretch, Microrotation, Phase velocity, Polarization, Coupled longitudinal waves, Coupled transverse waves


The present study deals with the plane waves moving in a solid medium qualifying for anisotropic, homogeneous, microstretch and elastic properties. Primarily, the Christoffel equations have been derived for propagation of waves (coupled longitudinal and coupled transverse) in the medium. A system of homogeneous equations has been established to study polarization of medium particles for wave motion, polarization of medium particles in microrotation and microstretch present in the medium. Condition of solvability for a system of homogeneous linear equations has been applied to derive an equation for determining phase velocities of coupled waves propagating in the medium. Using the software Mathematica and hypothetical values for parameters and elastic constants, numerical discussion has been carried out to see the possible number of waves propagating in arbitrarily chosen phase directions in the medium. Finally, a special case of anisotropic homogeneous elastic medium (absence of microstretch) has been discussed to support the results derived in the present study.


Download data is not yet available.


I. A. Abbas and R. Kumar, Interaction due to a mechanical source in transversely isotropic micropolar media, Journal of Vibration and Control 20(11) (2014), 1663 – 1670, DOI: 10.1177%2F1077546312475148.

I. Barsoum and J. Faleskog, Micromechanical analysis on the influence of the Lode parameter on void growth and coalescence, International Journal of Solids and Structures 48(6) (2011), 925 – 938, DOI: 10.1016/j.ijsolstr.2010.11.028.

S. Casolo, Macroscopic modelling of structured materials: Relationship between orthotropic Cosserat continuum and rigid elements, International Journal of Solids and Structures 43(3-4) (2006), 475 – 496, DOI: 10.1016/j.ijsolstr.2005.03.037.

A. C. Eringen, Microcontinuum Field Theories I: Foundations and Solids, Springer-Verlag, New York, xvi + 325 (1999), DOI: 10.1007/978-1-4612-0555-5.

A. C. Eringen, Microcontinuum Field Theories II: Fluent Media, Springer-Verlag, New York, xiv + 340 (2001), URL:

A. C. Eringen, Theory of thermo-microstretch elastic solids, International Journal of Engineering Science 28(12) (1990), 1291 – 1301, DOI: 10.1016/0020-7225(90)90076-U.

N. Garg, Effect of initial stress on harmonic plane homogeneous waves in viscoelastic anisotropic media, Journal of Sound and Vibration 303(3-5) (2007), 515 – 525, DOI: 10.1016/j.jsv.2007.01.013.

N. Garg, Existence of longitudinal waves in pre-stressed anisotropic elastic medium, Journal of Earth System Science 118(6) (2009), 677 – 687, DOI: 10.1007/s12040-009-0053-2.

R. R. Gupta and R. Kumar, Analysis of wave motion in a micropolar transversely isotropic medium, Journal of Solid Mechanics 1(4) (2009), 260 – 270, URL:

E. Inan and A. Kiris, 3-D vibration analysis of microstretch plates, in: Vibration Problems ICOVP-2007, E. Inan, D. Sengupta, M. Banerjee, B. Mukhopadhyay, H. Demiray (eds.), Springer Proceedings in Physics, Vol. 126, 189 – 200, Springer, Dordrecht (2008), DOI: 10.1007/978-1-4020-9100-1_19.

A. Kiris and E. Inan, On the identification of microstretch elastic moduli of materials by using vibration data of plates, International Journal of Engineering Science 46(6) (2008), 585 – 597, DOI: 10.1016/j.ijengsci.2008.01.001.

R. Kumar and R. Kumar, Analysis of wave motion at the boundary surface of orthotropic thermoelastic material with voids and isotropic elastic half-space, Journal of Engineering Physics and Thermophysics 84(2) (2011), 463 – 478, DOI: 10.1007/s10891-011-0493-9.

R. Kumar and R. R. Gupta, Plane waves reflection in micropolar transversely isotropic generalized thermoelastic half-space, Mathematical Sciences 6 (2012), Article number: 6, DOI: 10.1186/2251-7456-6-6.

K. Lotfy and M. I. A. Othman, Effect of rotation on plane waves in generalized thermo-microstretch elastic solid with a relaxation time, Meccanica 47 (2012), 1467 – 1486, DOI: 10.1007/s11012-011-9529-7.

M. Marin, I. Abbas and C. Cârstea, On continuous dependence for the mixed problem of microstretch bodies, Analele ¸stiin¸tifice ale Universit˘a¸tii "Ovidius" Constan¸ta. Seria Matematic˘a 25(1) (2017), 131 – 143, DOI: 10.1515/auom-2017-0011.

M. I. A. Othman and A. Jahangir, Plane waves on rotating microstretch elastic solid with temperature dependent elastic properties, Applied Mathematics & Information Sciences 9(6) (2015), 2963 – 2972, URL:

M. I. A. Othman and Kh. Lotfy, On the plane waves of generalized thermomicrostretch elastic half-space under three theories, International Communications in Heat and Mass Transfer 37(2) (2010), 192 – 200, DOI: 10.1016/j.icheatmasstransfer.2009.09.017.

M. I. A. Othman, S. M. Abo-Dahab and Kh. Lotfy, Gravitational effect and initial stress on generalized magneto-thermo-microstretch elastic solid for different theories, Applied Mathematics and Computation 230 (2014), 597 – 615, DOI: 10.1016/j.amc.2013.12.148.

R. A. Schapery, An engineering theory of nonlinear viscoelasticity with applications, International Journal of Solids and Structures 2(3) (1966), 407 – 425, DOI: 10.1016/0020-7683(66)90030-8.

M. D. Sharma, Existence of longitudinal and transverse waves in anisotropic thermoelastic media, Acta Mechanica 209(3) (2010), 275 – 283, DOI: 10.1007/s00707-009-0178-z.

S. Shaw and B. Mukhopadhyay, Electromagnetic effects on Rayleigh surface wave propagation in a homogeneous isotropic thermo-microstretch elastic half-space, Journal of Engineering Physics and Thermophysics 85 (2012), 229 – 238, DOI: 10.1007/s10891-012-0643-8.

B. Singh and M. Goyal, Wave propagation in a transversely isotropic microstretch elastic solid, Mechanics of Advanced Materials and Modern Processes 3 (2017), Article number: 8, DOI: 10.1186/s40759-017-0023-3.

S. K. Tomar and A. Khurana, Elastic waves in an electro-microelastic solid, International Journal of Solids and Structures 45(1) (2008), 276 – 302, DOI: 10.1016/j.ijsolstr.2007.08.014.

S. K. Tomar and D. Singh, Propagation of stoneley waves at an interface between two microstretch elastic half-spaces, Journal of Vibration and Control 12(9) (2006), 995 – 1009, DOI: 10.1177/1077546306068689.

Q.-L. Xiong and X.-G. Tian, Response of a semi-infinite microstretch homogeneous isotropic body under thermal shock, Journal of Applied Mechanics 78(4) (2011), 044503 (6 pages), DOI: 10.1115/1.4003429.




How to Cite

Rani, N., & Garg, S. (2023). Study of Waves Propagating in Anisotropic Homogeneous Microstretch Elastic Medium. Communications in Mathematics and Applications, 14(1), 37–48.



Research Article