ORIGINAL PAPER
Fundamental solution of the steady oscillations equations in couple stress micropolar viscoelastic thermoelastic solid
 
More details
Hide details
1
Mathematics, Deenbandhu Chotu Ram University of Science and Technology, Murthal-131039, India
 
These authors had equal contribution to this work
 
 
Submission date: 2024-09-27
 
 
Final revision date: 2024-12-16
 
 
Acceptance date: 2025-03-07
 
 
Online publication date: 2025-06-13
 
 
Publication date: 2025-06-13
 
 
Corresponding author
Ravinder Kumar Sahrawat   

Mathematics, Deenbandhu Chotu Ram University of Science and Technology, Murthal-131039, India
 
 
International Journal of Applied Mechanics and Engineering 2025;30(2):140-160
 
KEYWORDS
TOPICS
ABSTRACT
In this article, we study case of steady oscillations to solve the system of differential equations by using elementary functions in the theory of microploar couple stress viscoelastic solid . Four waves were discovered: two coupled longitudinal waves and two coupled transverse waves that propagate at various wave speeds. The penetration depth, specific loss, attenuation coefficients, and phase velocity—all of which have been computed numerically and plotted graphically for the LS and GL models—are affected by couple stresses and viscous parameters. Specific cases are created and contrasted with the earlier outcomes.
REFERENCES (43)
1.
Voigt W. (1887):Theoretische Studien über die Elasticitätsverhältnisse der Krystalle.– Abhandlungen der Brau, vol.34, pp.3-52, http://eudml.org/doc/135896.
 
2.
Cosserat E. and Cosserat F. (1909): Theorie des Corps Deformables.– Hermann et Fils, Paris, http://jhir.library.jhu.edu/ha....
 
3.
Eringen A.C. and Suhubi E.S.(1964): Nonlinear theory of simple micro-elastic solids-I.– Int. J. of Eng. Sci., vol.2, No.4, pp.189-203,doi.org/10.1016/0020-7225(64)90004-7.
 
4.
Suhubi E.S. and Eringen A.C. (1964):Nonlinear theory of simple micro-elastic solids-II.– Int. J. of Eng. Sci., vol.2, No.4, pp.389-404. doi.org/10.1016/0020-7225(64)90017-5.
 
5.
Eringen A.C. (1966): Linear theory of micropolar elasticity.– J. of Math. and Mech., vol.15, No.6, pp.909-923, doi:org/10.1512/iumj.1966.15.15060.
 
6.
Eringen A.C. (1999): Microcontinum Field Theories-I.– Foundations and Solids, Springer-Verlag, Berlin, https://doi.org/10.1007/978-1-....
 
7.
Eringen A.C. (1970): Foundations of Micropolar Thermoelasticity.– Springer Briefs in Applied Sciences and Technology, pp.1-170, https://doi.org/10.1007/978-3-....
 
8.
Nowacki W. (1986): Theory of Asymmetric Elasticity.– Oxford, Pergamon, pp.383.
 
9.
Ciarletta M. (1999): A theory of micropolar thermoelasticity without energy dissipation.– Jour. of Thermal Str., vol.22, No.6, pp.581-594, DOI:10.1080/01495731003656907.
 
10.
Chandrasekhariah D.S.(1998): Hyperbolic thermoelasticity.– App. Mech. Rev.,vol.51, No.12, pp.705-729, doi.org/10.1115/1.3098984.
 
11.
Biot A.M. (1965): Mechanics of Incremental Deformations.– John Wiley & Sons, New York, doi: hal-01352219.
 
12.
Abouelregal A.E., Nasr M.E., Khalil K.A., Abouhawwash M. and Moaaz O. (2023): Effect of the concept of memory-dependent derivatives on a nanoscale thermoelastic micropolar material under varying pulsed heating flow.– Ir. J. of Sci. and Tech. Trans. of Mech. Eng., vol.47, No.12, pp.2003-2019, doi: 10.1007/s40997-023-00606-4.
 
13.
Abouelregal A.E. and Ali F. Rashid (2024): Deformation in a micropolar material under the influence of hall current and initial stress fields in the context of a double-temperature thermoelastic theory involving phase lag and higher orders.– Acta. Mech., vol.235, pp.4311-4337, doi.org/10.1007/s00707-024-03922-1.
 
14.
Yadav A.K. (2016): Reflection of plane wave in a micropolar thermoelastic solid half-space with diffusion.– J. of Therm. Str., vol.39, No.11, pp.1378-1388, doi.org/10.1080/17455030.2021.1956014.
 
15.
Yadav A.K. (2021): Thermoelastic waves in a fractional-order initially stressed micropolar diffusive porous medium.– J. of Ocean Eng. and Sci., vol.6, No.11, pp.376-388, doi.org.10.1016/j.joes.2021.04.001.
 
16.
Yadav A.K, Carrera E. and Schnack E. (2023): Effects of memory response and impedance barrier on reflection of plane waves in a nonlocal micropolar porous thermo-diffusive medium.– Mech. and Adv. Mat. and Str., vol.31, No.22, pp.5564-5580, doi.org/10.1080/15376494.2023.2217556.
 
17.
Yadav A.K. (2024): Reflection of plane waves in a micropolar thermo-diffusion porous medium.– Waves in Rand. Coml. Media, vol. 34, No.4, pp.2319-2341, doi:10.1080/17455030.2021.1956014.
 
18.
Singh B., Yadav A.K. and Gupta D. (2019): Reflection of plane waves from a micropolar thermoelastic solid half-space with impedance boundary conditions.– J. of Ocean Eng. and Sci., vol.4, No.2, pp.122-131, https://doi.org/10.1016/j.joes....
 
19.
Singh B. and Yadav A.K. (2021): The effect of diffusion on propagation and reflection of waves in a thermo microstretch solid half-space.– Comput. Math. Model., vol.32, No.5, pp.221-234, doi.org/10.1007/s10598-021-09527.
 
20.
Hetnarski R.B. and Ignaczak J. (1996): Solution like wave in a low temperature nonlinear thermoelastic solid.– Int. Jour. of Eng. Sci., vol.34, No.15, pp.1767-1787, doi.org/10.1016/S0020-7225(96)00046-8.
 
21.
Lord H. and Shulman Y. (1967): A generalised dynamical theory of thermoelasticity.– Jour. of Mech. and Phy. of Sol., vol.15, No.5, pp.299-309, doi: org/10.1016/0022-5096(67)90024-5.
 
22.
Green A.E. and Lindsay K.A. (1972): Thermoelasticity.– Jour. of Elast., vol.2, No.1, pp.1-7.
 
23.
Abouelregal A.E. (2024): A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature.– Math. and Mech. of Solids, vol.29, No.8, pp.1564-1590, https://doi.org/10.1177/108128....
 
24.
Abouelregal A.E. (2024): Effect of non‐local modified couple stress theory on the responses of axially moving thermoelastic nano‐beams.– J. of App. Math. And Mech., vol.104, No.4, doi:10.1002/zamm.202200233.
 
25.
Yadav A.K. (2021): Reflection of plane waves from the free surface of a rotating orthotropic magneto thermoelastic solid half-space with diffusion.– J. of Therm. Stress., vol.44, No.1, pp.86-106, doi.org/10.1080/ 01495739. 2020.1842273.
 
26.
Yadav A.K. (2022): Reflection of plane waves from the impedance boundary of a magneto-thermo microstretch solid with diffusion in a fractional order theory of thermoelasticity.– Waves in Rand. and Comp. Media, vol.32, No.5, pp.2416-2444, doi.org/10.1080/ 17455030. 2020.1854489.
 
27.
Yadav A.K, Carrera E., Marin M. and Othman M.I.A. (2024): Reflection of hygrothermal waves in a nonlocal theory of coupled thermo-elasticity.– Mech. of Ad. Mat. and Str., vol.31, No.5, pp.1083-1096, doi.org/10.1080/15376494.2022.2130484.
 
28.
Hetnarski R.B. (1964): The fundamental solution of the coupled thermoelastic problem for small times.– Archiwum Mechaniki Stosowanej, vol.16, No.2, pp.23-31.
 
29.
Iesan D. (1998): On the theory of thermoelasticity without energy dissipation.– Jour. of Thermal Str., vol.21, No.4, pp.295-307, doi:10.1080/01495739808956148.
 
30.
Svanadze M. (2004): Fundamental solutions of the equations of the theory thermoelasticity with microtemperatures.– J. of Therm. Str., vol.27, No.2, pp.151-170, doi:10.1080/01495730490264277.
 
31.
Svanadze M., Tibullo V. and Zampoli V. (2006): Fundamental solution in the theory of micropolar thermoelasticity without energy dissipation.– J. of Thermal Str., vol.29, No.1, pp.57-66, doi.org/10.1080/01495730500257417.
 
32.
Hörmander L. (1969): Linear Partial Differential Operators.– Springer-Verlag, Berlin, Göttingen, Heidelberg, doi:10.1007/978-3-662-30722-9.
 
33.
Hörmander L. (1983): The analysis of linear partial differential operators II: diffrential operators with constant coefficients.– Springer-Verlag, Berlin, Heidelberg, New-York, Tokyo, doi:10.1007/978-3-642-96750-4.
 
34.
Kumar R., Kumar K. and Nautiyal R.C. (2014): Plane wave and fundamental solution in a couple stress generalized thermoelastic solid.– Afrika Matematika, vol.24, No.3, pp.591-603, doi:10.1007/s13370-013-0136-8.
 
35.
Sahrawat R.K., Poonam and K. Kumar (2020): Plane wave and fundamental solution in non-local couple stress micropolar thermoelastic solid without energy dissipation.– J. of Thermal Str., vol.44, pp.1-20, doi.10.1080/01495739.2020.1860728.
 
36.
Poonam and Sahrawat R.K. (2021): Reflection-refraction coefficients and energy ratios in couple stress microploar thermoviscous elastic solid.– Int. Jour. of Applied Mech. and Eng, vol.26, No.2, pp.47-69, doi: https://doi.org/10.2478/ijame-....
 
37.
Baksi A., Roy B.K. and Bera R.K. (2006): Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension.– Math. Comput. Model, vol.44, No.11-12, pp.1069-1079, doi.org/10.1016/j.mcm.2006.03.010.
 
38.
Eringen A.C. (1967): Mechanics of Continua.– John Wiley & Sons, Inc., New York.
 
39.
Eringen A.C. (2002): Nonlocal Continuum Field Theories.– Springer-Verlag, New York, doi: 10.1007/b97697.
 
40.
Kumar R. and Sharma N. (2008): Propagation of waves in micropolar viscoelastic generalized thermoelastic solids having interficial imperfections.– Theoretical and Applied Fracture Mechanics, vol.50, No.3, pp.226-234, doi.org/10.1016/j.tafmec.2008.07.010.
 
41.
Kumar B., Kumar R. and Kaushal S. (2017): Viscosity effect on reflection and transmission coefficients between two micropolar viscothermoelastic half spaces with three-phase legs.– Int. J. of Eng. Sci. and Res. Tech., vol.6, No.11, pp.51-71, doi.org/10.5281/zenodo.1042076.
 
42.
Kumar R. (2000): Wave propagation in micropolar viscoelastic generalized thermoelastic solid.– Journal of Engineering Science, vol.38, No.12, pp.1377-1395, doi:10.1016/S0020-7225(99)00057-9.
 
43.
Singh B. (2015): Wave propagation in an incopmressible transversely isotropic thermoelastic solid.– Meccanica, vol.50, No.7, pp.1817-1825, doi.org/10.1007/s11012-015-0126.
 
eISSN:2353-9003
ISSN:1734-4492
Journals System - logo
Scroll to top