Open Access
Research Article
Response of memory to the imperfect fluid–double porous non–local thermoelastic solid interface
*Rajesh KumarCorresponding authorrajesh.kumar@miet.ac.inDepartment of Mathematics Indira Gandhi UniversityDepartment of Computer Science and Engineering (AIML) Meerut institute of Engineering and TechnologyMeerut, Uttar Pradesh, 250005, India0000-0003-2065-1372View full profile → , Vipin Guptavipin@gurugramuniversity.ac.inDepartment of Mathematics Gurugram UniversityGurugram, Haryana, 122003, India0000-0002-5238-1963View full profile → , Vijayata Pathaniavpmsmrc@gmail.comDepartment of Mathematics Himachal Pradesh University Regional Center DharamshalaDharamshala, Himachal Pradesh, 176057, India0000-0003-3842-0759View full profile → , M. S. Barakms_barak@igu.ac.inDepartment of Mathematics Indira Gandhi UniversityMeerpur, Haryana, 122502, India0000-0001-9947-000XView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Jun 2023
- Published Online:
- 01 Jul 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1608
- Pages:
- 1479–1503
Abstract
This manuscript delves into the study of plane wave behavior in a half-space denoted as M1, representing a double porous nonlocal thermoelastic solid. This solid encompasses dual-phase-lag (DPL) effects with memory, interacting with an inviscid fluid half-space referred to as M2. The model is solved using the eigenmode method after converting the dimensionless governing equations into a two-dimensional format. Through this investigation, it has been discerned that the medium M1 exhibits five distinct types of waves: four longitudinal waves, one transverse wave, and one mechanical wave in M2. By imposing boundary conditions at the interface, the corresponding secular equations are derived. The components of various physical fields are then obtained in closed form. Numerical simulations are employed to visualize the impact of nonlocal, memory, and stiffness on the fundamental properties of waves. Graphical representations effectively convey the outcomes of these simulations, providing insights into how these parameters influence wave characteristics.
Keywords
Subject Classifications
74H4574J0574F0576S05
References
[1] D. G. B. Edelen and N. Laws, ‘On the thermodynamics of systems with nonlocality’, Arch. Ration. Mech. Anal., vol. 43, no. 1, pp. 24–35 (1971), doi: 10.1007/BF00251543.[2] A. C. Eringen and D. G. B. Edelen, ‘On nonlocal elasticity’, Int. J. Eng. Sci., vol. 10, no. 3, pp. 233–248, Mar. (1972), doi: 10.1016/0020-7225(72)90039-0.[3] C. Polizzotto, ‘Nonlocal elasticity and related variational principles’, Int. J. Solids Struct., vol. 38, no. 42–43, pp. 7359–7380 (2001), doi: 10.1016/S0020-7683(01)00039-7.[4] A. Chakraborty, ‘Wave propagation in anisotropic media with non-local elasticity’, Int. J. Solids Struct., vol. 44, no. 17, pp. 5723–5741 (2007), doi: 10.1016/j.ijsolstr.2007.01.024.[5] R. Kumar, A. K. Vashishth, and S. Ghangas, ‘Nonlocal heat conduction approach in a bi-layer tissue during magnetic fluid hyperthermia with dual phase lag model’, Biomed. Mater. Eng., vol. 30, no. 4, pp. 387–402 (2019), doi: 10.3233/BME-191061.[6] J.-L. Wang and H.-F. Li, ‘Surpassing the fractional derivative: Concept of the memory-dependent derivative’, Comput. Math. with Appl., vol. 62, no. 3, pp. 1562–1567, Aug. (2011), doi: 10.1016/j.camwa.2011.04.028.[7] M. Caputo and F. Mainardi, ‘A new dissipation model based on memory mechanism’, Pure Appl. Geophys., vol. 91, no. 1, pp. 134–147 (1971).[8] J. W. Nunziato and S. C. Cowin, ‘A nonlinear theory of elastic materials with voids’, Arch. Ration. Mech. Anal., vol. 72, no. 2, pp. 175–201 (1979), doi: 10.1007/BF00249363.[9] D. Ieşan, ‘A theory of thermoelastic materials with voids’, Acta Mech., vol. 60, no. 1, pp. 67–89 (1986).[10] D. Ieşan and R. Quintanilla, ‘On a theory of thermoelastic materials with a double porosity structure’, J. Therm. Stress., vol. 37, no. 9, pp. 1017–1036 (2014), doi: 10.1080/01495739.2014.914776.[11] V. Gupta, R. Kumar, M. Kumar, V. Pathania, and M. S. Barak, ‘Reflection/transmission of plane waves at the interface of an ideal fluid and nonlocal piezothermoelastic medium’, Int. J. Numer. Methods Heat Fluid Flow, vol. 33, no. 2, pp. 912–937, Jan. (2023), doi: 10.1108/HFF-04-2022-0259.[12] M. S. Barak, R. Kumar, R. Kumar, and V. Gupta, ‘The effect of memory and stiffness on energy ratios at the interface of distinct media’, Multidiscip. Model. Mater. Struct., vol. 19, no. 3, pp. 464–492 (2023), doi: 10.1108/MMMS-10-2022-0209.[13] V. Gupta, R. Kumar, R. Kumar, and M. S. Barak, ‘Energy analysis at the interface of piezo/thermoelastic half spaces’, Int. J. Numer. Methods Heat Fluid Flow, vol. 33, no. 6, pp. 2250–2277, May (2023), doi: 10.1108/HFF-11-2022-0654.[14] M. S. Barak, R. Kumar, R. Kumar, and V. Gupta, ‘The effect of memory and stiffness on energy ratios at the interface of distinct media’, Multidiscip. Model. Mater. Struct., vol. 19, no. 3, pp. 464–492, Apr. (2023), doi: 10.1108/MMMS-10-2022-0209.[15] V. Gupta and M. S. Barak, ‘Quasi-P wave through orthotropic piezo-thermoelastic materials subject to higher order fractional and memory-dependent derivatives’, Mech. Adv. Mater. Struct., vol. 0, no. 0, pp. 1–15, Jun. (2023), doi: 10.1080/15376494.2023.2217420.[16] V. Pathania, R. Kumar, V. Gupta, and M. S. Barak, ‘Generalized Plane Waves in a Rotating Thermoelastic Double Porous Solid’, Int. J. Appl. Mech. Eng., vol. 27, no. 4, pp. 138–154, Dec. (2022), doi: 10.2478/ijame-2022-0055.[17] M. S. Barak and V. Gupta, ‘Memory-dependent and fractional order analysis of the initially stressed piezo-thermoelastic medium’, Mech. Adv. Mater. Struct., vol. 0, no. 0, pp. 1–15, May (2023), doi: 10.1080/15376494.2023.2211065.[18] M. S. Barak, M. Kumari, and M. Kumar, ‘Effect of local fluid flow on the propagation of plane waves at an interface of water/double-porosity solid with underlying uniform elastic solid’, Ocean Eng., vol. 147, no. May 2017, pp. 195–205 (2018), doi: 10.1016/j.oceaneng.2017.10.030.[19] A. C. Eringen, ‘Linear theory of nonlocal elasticity and dispersion of plane waves’, Int. J. Eng. Sci., vol. 10, no. 5, pp. 425–435, May (1972), doi: 10.1016/0020-7225(72)90050-X.[20] M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, ‘On dual-phase-lag thermoelasticity theory withmemory-dependent derivative’, Mech. Adv. Mater. Struct., vol. 24, no. 11, pp. 908–916 (2017), doi: 10.1080/15376494.2016.1196793.[21] J. D. Achenbach, Wave Propagation in Elastic Solids. Elsevier (1975).[22] V. Pathania and P. Joshi, ‘Waves in thermoelastic solid half-space containing voids with liquid loadings’, ZAMM Zeitschrift fur Angew. Math. und Mech., vol. 101, no. 12, pp. 1–19 (2021), doi: 10.1002/zamm.202100093.[23] D. Singh, D. Kumar, and S. K. Tomar, ‘Plane harmonic waves in a thermoelastic solid with double porosity’, Math. Mech. Solids, vol. 25, no. 4, pp. 869–886 (2020), doi: 10.1177/1081286519890053.
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