Plane waves at an interface of thermoelastic and magneto-thermoelastic media
Abstract
This research examines the propagation of waves in a semi-infinite, isotropic magneto-thermoelastic solid, and a semi-infinite thermoelastic solid with welded contact. The study investigates the influence of a magnetic field on amplitude coefficients for the incidence of thermal, SV, and P waves in the magnetothermoelastic solid in a semi-infinite space. The incidence of these waves results in a total of six waves, including both refracted and reflected waves. The fluctuation of amplitude coefficients for various magnetic pressure values is explored for copper and aluminum as numerical constants. The study observes that the amplitude coefficients of seismic waves, occurring during the incidence of thermal, SV, and P waves in the magneto-thermoelastic solid semi-infinite space, are dependent on the incident angle, magnetic field, and material constants. Notably, the amplitude coefficients for the incidence of SV waves exhibit only a minor influence from the magnetic field. The implications of this research extend to applications in ocean acoustics, geophysics, acoustic devices, composite materials, and non-destructive testing.
Keyword : magnetic field, reflection, refraction, seismic waves, thermoelastic
How to Cite
Rani, A., Madan, D. K., Kumar, N., & Punia, M. (2024). Plane waves at an interface of thermoelastic and magneto-thermoelastic media. Mathematical Modelling and Analysis, 29(3), 493–508. https://doi.org/10.3846/mma.2024.18477
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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S.M. Abo-Dahab and A.M. Abd-Alla. Green Lindsay model on reflection and refraction of P- and SV-waves at interface between solid-liquid media presence in magnetic field and initial stress. Journal of Vibration and Control, 22(12):2885–2897, 2014. https://doi.org/10.1177/1077546314554637
S.M. Abo-Dahab, A. Jahangir and A.N. Abd-alla. Reflection of plane waves in thermoelastic microstructured materials under the influence of gravitation. Continuum Mechanics and Thermodynamics, 32(3):803–815, 2020. https://doi.org/10.1007/s00161-018-0739-2
M.A. Biot. Thermoelasticity and irreversible thermo-dynamics. Journal of Applied Physics, 27(3):240–253, 1956. https://doi.org/10.1063/1.1722351
N.C. Das, A. Lahiri, S. Sarkar and B. Basu. Reflection of generalized thermoelastic waves from isothermal and insulated boundaries of a halfspace. Computers and Mathematics with Applications, 56(11):2795–2805, 2008. https://doi.org/10.1016/j.camwa.2008.05.042
S. Deswal, B.S. Punia and K.K. Kalkal. Propagation of waves at an interface between a transversely isotropic rotating thermoelastic solid half space and a fiber-reinforced magneto-thermoelastic rotating solid half space. Acta Mechanica, 230:2669–2686, 2019. https://doi.org/10.1007/s00707-019-02418-7
M.A. Ezzat and A.A. El-Bary. Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories. Steel and Composite Structures, 24(3):297– 307, 2017. https://doi.org/10.12989/scs.2017.24.3.297
A.E. Green and A. Lindsay. Thermoelasticity. Journal of Elasticity, 2(1):1–7, 1972. https://doi.org/10.1007/BF00045689
I. Kaur, P. Lata and K. Singh. Reflection of plane harmonic wave in rotating media with fractional order heat transfer and two temperatures. Partial Differential Equations in Applied Mathematics, 4:100049, 2021. https://doi.org/10.1016/j.padiff.2021.100049
R. Kumar and T. Kansal. Reflection and refraction of plane harmonic waves at an interface between elastic solid and magneto-thermoelastic diffusion solid with voids. Computational Methods in Science Technology, 23(1):43–56, 2017. https://doi.org/10.12921/cmst.2016.0000036
R. Kumar and B. Singh. Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half space with stretch. Indian Journal of Pure and Applied Mathematics, 29(6):657–669, 1998.
P. Lata and S. Singh. Plane wave propagation in a nonlocal magneto-thermoelastic solid with two temperature and Hall current. Waves in Random and Complex Media, 32(4):1820–1846, 2022. https://doi.org/10.1080/17455030.2020.1838667
H.W. Lord and Y. Shulman. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5):299–309, 1967. https://doi.org/10.1016/0022-5096(67)90024-5
D.K. Madan and A. Rani. Propagation of love waves in prestressed orthotropic layer coated over a prestressed orthotropic semi-infinite space with irregular interface. South East Asian Journal of Mathematics and Mathematical Sciences, 18(1):409–418, 2022.
D.K. Madan and A. Rani. Reflection and refraction of a plane SV wave at an interface between two initially-stressed fiber-reinforced thermoelastic mediums. AIP Conference Proceedings, 2481(1), 2022. https://doi.org/10.1063/5.0103835
D.K. Madan, A. Rani and M.Punia. A note on the effect of rigidity and initial stress on the propagation of Rayleigh waves in pre-stressed orthotropic elastic layered medium. Proceedings of the Indian National Science Academy, 87(3):487–498, 2021. https://doi.org/10.1007/s43538-021-00044-3
A. Nayfeh and S.N. Nasser. Thermoelastic waves in solids with thermal relaxation. Acta Mechanica, 12(1):53–69, 1971. https://doi.org/10.1007/BF01178389
M.I.A. Othaman, Y.D. Elmaklizi and E.A.A. Ahmed. Effect of magnetic field on piezo-thermoelastic medium with three theories. Results in Physics, 7:3361– 3368, 2017. https://doi.org/10.1016/j.rinp.2017.08.058
M.I.A. Othman, S.M. Abo-Dahab and O.N.S. Alsebaey. Reflection of plane waves from a rotating magneto-thermoelastic mediums with two temperature and initial stress three theories. Mechanics and Mechanical Engineering, 21(2):217–232, 2017.
M.I.A. Othman and Y. Song. Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent moduli. Applied Mathematical Modelling, 32(4):483–500, 2008. https://doi.org/10.1016/j.apm.2007.01.001
A. Rani and D.K. Madan. Effect of initial stress and imperfect interface on love waves propagation in prestressed orthotropic layer coated over a prestressed orthotropic semi-infinite space. Journal of Rajasthan Academy of Physical Sciences, 20:219–228, 2021.
N. Sarkar, S.M. Abo-Dahab and S. Mondal. Reflection of magnetothermoelastic waves at a solid half-space under modified Green-Lindsay model with two temperatures. Journal of Thermal Stresses, 43(9):1083–1099, 2020. https://doi.org/10.1080/01495739.2020.1768991
H.H. Sherief and H.A. Saleh. A half-space problem in the theory of generalized thermoelastic diffusion. International Journal of Solids and Structures, 42(15):4484–4493, 2005. https://doi.org/10.1016/j.ijsolstr.2005.01.001
J. Singh and S.K. Tomar. Plane waves in thermo-elastic material with voids. Mechanics of Materials, 39(10):932–940, 2007. https://doi.org/10.1016/j.mechmat.2007.03.007
M.C. Singh and N. Chakraborty. Reflection of a plane magnetothermoelastic wave at the boundary of a solid half-space in presence of initial stress. Applied Mathematical Modelling, 39(5-6):1409–1421, 2015. https://doi.org/10.1016/j.apm.2014.09.013
A.N. Sinha and S.B. Sinha. Reflection of thermoelastic waves at a solid halfspace with thermal relaxation. Journal of Physics of the Earth, 22(2):237–244, 1974. https://doi.org/10.4294/jpe1952.22.237
S.M. Abo-Dahab. Reflection of P and SV waves from stress-free surface elastic half-space under influence of magnetic field and hydrostatic initial stress without energy dissipation. Journal of Vibration and Control, 17(14):2213–2221, 2011. https://doi.org/10.1177/1077546311400228
S.M. Abo-Dahab. Reflection of generalized magneto-thermoelastic waves with two temperatures under influence of thermal shock and initial stress. ASME Journal of Heat and Mass Transfer, 140(10):102005, 2018. https://doi.org/10.1115/1.4040258
S.M. Abo-Dahab and A.M. Abd-Alla. Green Lindsay model on reflection and refraction of P- and SV-waves at interface between solid-liquid media presence in magnetic field and initial stress. Journal of Vibration and Control, 22(12):2885–2897, 2014. https://doi.org/10.1177/1077546314554637
S.M. Abo-Dahab, A. Jahangir and A.N. Abd-alla. Reflection of plane waves in thermoelastic microstructured materials under the influence of gravitation. Continuum Mechanics and Thermodynamics, 32(3):803–815, 2020. https://doi.org/10.1007/s00161-018-0739-2
M.A. Biot. Thermoelasticity and irreversible thermo-dynamics. Journal of Applied Physics, 27(3):240–253, 1956. https://doi.org/10.1063/1.1722351
N.C. Das, A. Lahiri, S. Sarkar and B. Basu. Reflection of generalized thermoelastic waves from isothermal and insulated boundaries of a halfspace. Computers and Mathematics with Applications, 56(11):2795–2805, 2008. https://doi.org/10.1016/j.camwa.2008.05.042
S. Deswal, B.S. Punia and K.K. Kalkal. Propagation of waves at an interface between a transversely isotropic rotating thermoelastic solid half space and a fiber-reinforced magneto-thermoelastic rotating solid half space. Acta Mechanica, 230:2669–2686, 2019. https://doi.org/10.1007/s00707-019-02418-7
M.A. Ezzat and A.A. El-Bary. Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories. Steel and Composite Structures, 24(3):297– 307, 2017. https://doi.org/10.12989/scs.2017.24.3.297
A.E. Green and A. Lindsay. Thermoelasticity. Journal of Elasticity, 2(1):1–7, 1972. https://doi.org/10.1007/BF00045689
I. Kaur, P. Lata and K. Singh. Reflection of plane harmonic wave in rotating media with fractional order heat transfer and two temperatures. Partial Differential Equations in Applied Mathematics, 4:100049, 2021. https://doi.org/10.1016/j.padiff.2021.100049
R. Kumar and T. Kansal. Reflection and refraction of plane harmonic waves at an interface between elastic solid and magneto-thermoelastic diffusion solid with voids. Computational Methods in Science Technology, 23(1):43–56, 2017. https://doi.org/10.12921/cmst.2016.0000036
R. Kumar and B. Singh. Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half space with stretch. Indian Journal of Pure and Applied Mathematics, 29(6):657–669, 1998.
P. Lata and S. Singh. Plane wave propagation in a nonlocal magneto-thermoelastic solid with two temperature and Hall current. Waves in Random and Complex Media, 32(4):1820–1846, 2022. https://doi.org/10.1080/17455030.2020.1838667
H.W. Lord and Y. Shulman. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5):299–309, 1967. https://doi.org/10.1016/0022-5096(67)90024-5
D.K. Madan and A. Rani. Propagation of love waves in prestressed orthotropic layer coated over a prestressed orthotropic semi-infinite space with irregular interface. South East Asian Journal of Mathematics and Mathematical Sciences, 18(1):409–418, 2022.
D.K. Madan and A. Rani. Reflection and refraction of a plane SV wave at an interface between two initially-stressed fiber-reinforced thermoelastic mediums. AIP Conference Proceedings, 2481(1), 2022. https://doi.org/10.1063/5.0103835
D.K. Madan, A. Rani and M.Punia. A note on the effect of rigidity and initial stress on the propagation of Rayleigh waves in pre-stressed orthotropic elastic layered medium. Proceedings of the Indian National Science Academy, 87(3):487–498, 2021. https://doi.org/10.1007/s43538-021-00044-3
A. Nayfeh and S.N. Nasser. Thermoelastic waves in solids with thermal relaxation. Acta Mechanica, 12(1):53–69, 1971. https://doi.org/10.1007/BF01178389
M.I.A. Othaman, Y.D. Elmaklizi and E.A.A. Ahmed. Effect of magnetic field on piezo-thermoelastic medium with three theories. Results in Physics, 7:3361– 3368, 2017. https://doi.org/10.1016/j.rinp.2017.08.058
M.I.A. Othman, S.M. Abo-Dahab and O.N.S. Alsebaey. Reflection of plane waves from a rotating magneto-thermoelastic mediums with two temperature and initial stress three theories. Mechanics and Mechanical Engineering, 21(2):217–232, 2017.
M.I.A. Othman and Y. Song. Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent moduli. Applied Mathematical Modelling, 32(4):483–500, 2008. https://doi.org/10.1016/j.apm.2007.01.001
A. Rani and D.K. Madan. Effect of initial stress and imperfect interface on love waves propagation in prestressed orthotropic layer coated over a prestressed orthotropic semi-infinite space. Journal of Rajasthan Academy of Physical Sciences, 20:219–228, 2021.
N. Sarkar, S.M. Abo-Dahab and S. Mondal. Reflection of magnetothermoelastic waves at a solid half-space under modified Green-Lindsay model with two temperatures. Journal of Thermal Stresses, 43(9):1083–1099, 2020. https://doi.org/10.1080/01495739.2020.1768991
H.H. Sherief and H.A. Saleh. A half-space problem in the theory of generalized thermoelastic diffusion. International Journal of Solids and Structures, 42(15):4484–4493, 2005. https://doi.org/10.1016/j.ijsolstr.2005.01.001
J. Singh and S.K. Tomar. Plane waves in thermo-elastic material with voids. Mechanics of Materials, 39(10):932–940, 2007. https://doi.org/10.1016/j.mechmat.2007.03.007
M.C. Singh and N. Chakraborty. Reflection of a plane magnetothermoelastic wave at the boundary of a solid half-space in presence of initial stress. Applied Mathematical Modelling, 39(5-6):1409–1421, 2015. https://doi.org/10.1016/j.apm.2014.09.013
A.N. Sinha and S.B. Sinha. Reflection of thermoelastic waves at a solid halfspace with thermal relaxation. Journal of Physics of the Earth, 22(2):237–244, 1974. https://doi.org/10.4294/jpe1952.22.237