Wave propagation in context of Moore–Gibson–Thompson thermoelasticity with Klein–Gordon nonlocality
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https://doi.org/10.15625/0866-7136/19728Keywords:
plane waves, Rayleigh wave, Moore–Gibson–Thompson thermoelasticity, secular equation, wave speed, nonlocality parameters, conductivity rate parameterAbstract
Understanding plane and surface waves in elastic materials is crucial in various fields, including geophysics, seismology, and materials science, as they provide valuable information about the properties of the materials they travel through and can help in earthquake detection and analysis. In the present paper, the governing equations of Moore–Gibson–Thompson (MGT) thermoelasticity are modified in context of Klein–Gordon (KG) nonlocality. For linear, homogeneous and isotropic case, the governing equations in two-dimensions are solved to obtain the dispersion relations for possible plane waves. It is found that there exists one transverse and two coupled longitudinal waves in a two-dimensional model of MGT weakly nonlocal thermoelastic medium and the speeds of these plane waves are found to be dependent on KG nonlocal parameters. The coupled longitudinal waves are also found to be dependent on conductivity rate parameter. For linear, homogeneous and isotropic case, the governing equations in two-dimensions are also solved to obtain a Rayleigh wave secular equation at thermally insulated surface. For a numerical example of aluminium material, the speeds of transverse wave, coupled longitudinal waves and the Rayleigh wave are computed and graphically illustrated to visualize the effects of KG nonlocality parameters, conductivity rate parameter and the angular frequency on the wave speeds.
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References
M. A. Biot. Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27,(1956), pp. 240–253. DOI: https://doi.org/10.1063/1.1722351
A. E. Green and K. A. Lindsay. Thermoelasticity. Journal of Elasticity, 2, (1972), pp. 1–7. DOI: https://doi.org/10.1007/BF00045689
H. W. Lord and Y. Shulman. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15, (1967), pp. 299–309. DOI: https://doi.org/10.1016/0022-5096(67)90024-5
J. Ignaczak and M. Ostoja-Starzewski. Thermoelasticity with finite wave speeds. Oxford University Press, (2009). DOI: https://doi.org/10.1093/acprof:oso/9780199541645.001.0001
R. B. Hetnarski and J. Ignaczak. Generalized thermoelasticity. Journal of Thermal Stresses, 22, (4-5), (1999), pp. 451–476. DOI: https://doi.org/10.1080/014957399280832
R. Quintanilla. Moore–Gibson–Thompson thermoelasticity. Mathematics and Mechanics of Solids, 24, (2019), pp. 4020–4031. DOI: https://doi.org/10.1177/1081286519862007
L. Rayleigh. On waves propagated along the plane surface of an elastic solid. Proceedings of the London Mathematical Society, s1-17, (1885), pp. 4–11. DOI: https://doi.org/10.1112/plms/s1-17.1.4
J. N. Flavin. Thermo-elastic Rayleigh waves in a prestressed medium. Mathematical Proceedings of the Cambridge Philosophical Society, 58, (1962), pp. 532–538. DOI: https://doi.org/10.1017/S0305004100036811
P. Chadwick and D. W. Windle. Propagation of Rayleigh waves along isothermal and insulated boundaries. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 280, (1380), (1964), pp. 47–71. DOI: https://doi.org/10.1098/rspa.1964.0130
T. P. Ivanov. On the propagation of thermoelastic Rayleigh waves. Wave Motion, 10, (1988), pp. 73–82. DOI: https://doi.org/10.1016/0165-2125(88)90007-8
A. E. Abouelregal. Rayleigh waves in a thermoelastic solid half space using dualphase-lag model. International Journal of Engineering Science, 49, (2011), pp. 781–791. DOI: https://doi.org/10.1016/j.ijengsci.2011.03.007
S. Chiriţă. On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space. Acta Mechanica, 224, (2012), pp. 657–674. DOI: https://doi.org/10.1007/s00707-012-0776-z
A. V. Bucur, F. Passarella, and V. Tibullo. Rayleigh surface waves in the theory of thermoelastic materials with voids. Meccanica, 49, (2013), pp. 2069–2078. DOI: https://doi.org/10.1007/s11012-013-9850-4
B. Singh. Rayleigh wave in a thermoelastic solid half-space with impedance boundary conditions. Meccanica, 51, (2015), pp. 1135–1139. DOI: https://doi.org/10.1007/s11012-015-0269-y
B. Singh and S. Verma. On propagation of Rayleigh type surface wave in five different theories of thermoelasticity. International Journal of Applied Mechanics and Engineering, 24, (2019), pp. 661–673. DOI: https://doi.org/10.2478/ijame-2019-0041
F. Passarella, V. Tibullo, and G. Viccione. Rayleigh waves in isotropic strongly elliptic thermoelastic materials with microtemperatures. Meccanica, 52, (2016), pp. 3033–3041. DOI: https://doi.org/10.1007/s11012-016-0591-z
A. C. Eringen. Nonlocal continuum field theories, Vol. 56. Springer Verlag, New York, (2001).
D. G. B. Edelen and N. Laws. On the thermodynamics of systems with nonlocality. Archive for Rational Mechanics and Analysis, 43, (1971), pp. 24–35. DOI: https://doi.org/10.1007/BF00251543
D. G. B. Edelen, A. E. Green, and N. Laws. Nonlocal continuum mechanics. Archive for Rational Mechanics and Analysis, 43, (1971), pp. 36–44. DOI: https://doi.org/10.1007/BF00251544
A. C. Eringen and D. G. B. Edelen. On nonlocal elasticity. International Journal of Engineering Science, 10, (1972), pp. 233–248. DOI: https://doi.org/10.1016/0020-7225(72)90039-0
S. Chirita. Nonlocal effects on the stress distribution in an elastic half space. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche,Matematiche e Naturali. Rendiconti, Serie 8, 60, (6), (1976), pp. 802–807.
D. Ieşan. Reciprocal theorems and variational theorems in nonlocal elastodynamics. International Journal of Engineering Science, 15, (1977), pp. 693–699. DOI: https://doi.org/10.1016/0020-7225(77)90019-2
A. C. Eringen. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54, (1983), pp. 4703–4710. DOI: https://doi.org/10.1063/1.332803
B. S. Altan. Uniqueness in linear theory of nonlocal elasticity. Bulletin of the Technical University of Istanbul, 37, (1984), pp. 373–385.
J. L. Nowinski. On a three-dimensional Kelvin problem for an elastic nonlocal medium. Acta Mechanica, 84, (1990), pp. 77–87. DOI: https://doi.org/10.1007/BF01176089
B. Cracium. On nonlocal thermoelasticity. Analele Stiintifice ale Universitatii Ovidius Constanta, 5, (1996), pp. 29–36.
A. C. Eringen. Linear theory of nonlocal elasticity and dispersion of plane waves. International Journal of Engineering Science, 10, (1972), pp. 425–435. DOI: https://doi.org/10.1016/0020-7225(72)90050-X
D. Singh, G. Kaur, and S. K. Tomar. Waves in nonlocal elastic solid with voids. Journal of Elasticity, 128, (2017), pp. 85–114. DOI: https://doi.org/10.1007/s10659-016-9618-x
A. C. Eringen. Theory of nonlocal thermoelasticity. International Journal of Engineering Science, 12, (1974), pp. 1063–1077. DOI: https://doi.org/10.1016/0020-7225(74)90033-0
F. Balta and E. S. Şuhubi. Theory of nonlocal generalised thermoelasticity. International Journal of Engineering Science, 15, (1977), pp. 579–588. DOI: https://doi.org/10.1016/0020-7225(77)90054-4
B. Singh. Rayleigh-type surface waves in a nonlocal thermoelastic solid half space with voids. Waves in Random and Complex Media, 31, (2020), pp. 2103–2114. DOI: https://doi.org/10.1080/17455030.2020.1721612
A. S. Pramanik and S. Biswas. Surface waves in nonlocal thermoelastic medium with state space approach. Journal of Thermal Stresses, 43, (2020), pp. 667–686. DOI: https://doi.org/10.1080/01495739.2020.1734129
S. Biswas. Rayleigh waves in a nonlocal thermoelastic layer lying over a nonlocal thermoelastic half-space. Acta Mechanica, 231, (2020), pp. 4129–4144. DOI: https://doi.org/10.1007/s00707-020-02751-2
P. Lata and S. Singh. Rayleigh wave propagation in a nonlocal isotropic magnetothermoelastic solid with multi-dual-phase lag heat transfer. GEM - International Journal on Geomathematics, 13, (2022). DOI: https://doi.org/10.1007/s13137-022-00195-5
A. M. Abd-Alla, S. M. Abo-Dahab, S. M. Ahmed, and M. M. Rashid. Effect of magnetic field and voids on Rayleigh waves in a nonlocal thermoelastic halfspace. The Journal of Strain Analysis for Engineering Design, 57, (2021), pp. 61–72. DOI: https://doi.org/10.1177/03093247211001243
M. Kumar, P. Kaswan, N. Sarkar, X. Liu, and M. Kumari. Rayleigh waves in nonlocal generalized thermoelastic media. International Journal of Numerical Methods for Heat & Fluid Flow, 33, (2023), pp. 2049–2072. DOI: https://doi.org/10.1108/HFF-08-2022-0468
S. Biswas. Rayleigh waves in porous nonlocal orthotropic thermoelastic layer lying over porous nonlocal orthotropic thermoelastic half space. Waves in Random and Complex Media, 33, (2021), pp. 136–162. DOI: https://doi.org/10.1080/17455030.2021.1876279
K. Jangid, M. Gupta, and S. Mukhopadhyay. On propagation of harmonic plane waves under the Moore–Gibson–Thompson thermoelasticity theory. Waves in Random and Complex Media, 34, (2021), pp. 1976–1999. DOI: https://doi.org/10.1080/17455030.2021.1949071
G. Romano, R. Barretta, M. Diaco, and F. Marotti de Sciarra. Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams. International Journal of Mechanical Sciences, 121, (2017), pp. 151–156. DOI: https://doi.org/10.1016/j.ijmecsci.2016.10.036
J. Kaplunov, D. A. Prikazchikov, and L. Prikazchikova. On non-locally elastic Rayleigh wave. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380, (2022). DOI: https://doi.org/10.1098/rsta.2021.0387
J. Kaplunov, D. A. Prikazchikov, and L. Prikazchikova. On integral and differential formulations in nonlocal elasticity. European Journal of Mechanics - A/Solids, 100, (2023). DOI: https://doi.org/10.1016/j.euromechsol.2021.104497
V. T. N. Anh and P. C. Vinh. Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces. Mathematics and Mechanics of Solids, 28, (2023), pp. 2420–2435. DOI: https://doi.org/10.1177/10812865231164332
V. T. N. Anh, P. C. Vinh, T. T. Tuan, and L. T. Hue. Weakly nonlocal Rayleigh waves with impedance boundary conditions. Continuum Mechanics and Thermodynamics, 35, (5), (2023), pp. 2081–2094. DOI: https://doi.org/10.1007/s00161-023-01235-7
M. Lazar and E. Agiasofitou. Nonlocal elasticity of Klein–Gordon type: Fundamentals and wave propagation. Wave Motion, 114, (2022). DOI: https://doi.org/10.1016/j.wavemoti.2022.103038
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