Dynamic Response of Waves on a Non-Homogeneous Impedance Solid with Variable Amplitudes of Corrugated Surface under a Magnetic Field

Authors

https://doi.org/10.48314/apem.vi.50

Abstract

In this investigation, a solution model is proposed to characterize and analyze the stresses and displacements induced by surface waves in a corrugated, inhomogeneous, fibre-reinforced material under magneto-elastic influences, with some underlying mechanical inclinations. The governing equations of the model problem are presented using the material's constitutive relations. By the normal mode method, we derived the analytical solution of the model whilst utilizing non-dimensionalization of the equations of motion to reduce redundant parameters, and so on. Also, the model considers only a case in which the boundary corrugation or wavy-like phenomenon has various amplitudes and inhomogeneous impedance conditions, resulting in a complex geometry. Following this, suitable applications of the formulated boundary conditions – variable-amplitude corrugation and inhomogeneous impedance conditions, along with mechanical inclinations - are used to ensure that the complete solutions for the wave's stresses and displacements in the inhomogeneous medium are derived. In addition, the distributions of stresses and displacements in these fields are graphically presented using MATHEMATICA software to assess the variations and behaviors of the considered physical quantities, including the nonlocal parameter, variable-amplitude corrugation, inhomogeneous impedance parameters, and angles of inclination. We observe that these parameters significantly affect the distribution of the surface wave across the material, with the nonlocal, angle-of-inclination, and inhomogeneous parameters causing downward trends in the distribution profiles as they increase. Exceptional cases of constant amplitude can be obtained from our model if we neglect one of the quantities with variable amplitude in the corrugation and the magnetic impact on the medium. This study should prove helpful for examinations in geophysics and seismology, where the analysis of surface disturbances is required.

Keywords:

Variable amplitudes of corrugation, Magnetic influence, Inhomogeneous impedance boundaries, Inhomogeneous medium, Angles of inclination, Wavenumber

References

  1. [1] Spencer, A. J. M. (1972). Deformations of fibre-reinforced materials. Oxford university press. https://cir.nii.ac.jp/crid/1970586434862824359
  2. [2] Barak, M. S., & Dhankhar, P. (2023). Thermo-mechanical interactions in a rotating nonlocal functionally graded transversely isotropic elastic half-space. ZAMM-journal of applied mathematics and mechanics zeitschrift für angewandte mathematik und mechanik, 103(2), e202200319. https://doi.org/10.1002/zamm.202200319
  3. [3] Barak, M. S., Poonia, R., Devi, S., & Dhankhar, P. (2024). Nonlocal and dual-phase-lag effects in a transversely isotropic exponentially graded thermoelastic medium with voids. ZAMM-journal of applied mathematics and mechanics/zeitschrift für angewandte mathematik und mechanik, 104(5), e202300579. https://doi.org/10.1002/zamm.202300579
  4. [4] Singh, B. (2017). Reflection of elastic waves from plane surface of a half-space with impedance boundary conditions. Geosciences research, 2(4), 242–253. https://dx.doi.org/10.22606/gr.2017.24004
  5. [5] Asano, S. (1966). Reflection and refraction of elastic waves at a corrugated interface. Bulletin of the seismological society of america, 56(1), 201–221. https://doi.org/10.1785/BSSA0560010201
  6. [6] Singh, S. S., & Tomar, S. K. (2008). qP-wave at a corrugated interface between two dissimilar pre-stressed elastic half-spaces. Journal of sound and vibration, 317(3–5), 687–708. https://doi.org/10.1016/j.jsv.2008.03.036
  7. [7] Singh, A. K., Das, A., Kumar, S., & Chattopadhyay, A. (2015). Influence of corrugated boundary surfaces, reinforcement, hydrostatic stress, heterogeneity and anisotropy on Love-type wave propagation. Meccanica, 50(12), 2977–2994. https://doi.org/10.1007/s11012-015-0172-6%0A%0A
  8. [8] Singh, A. K., Mistri, K. C., & Pal, M. K. (2018). Effect of loose bonding and corrugated boundary surface on propagation of Rayleigh-type wave. Latin american journal of solids and structures, 15(1), e01. https://doi.org/10.1590/1679-78253577
  9. [9] Das, S. C., Acharya, D. P., & Sengupta, P. R. (1992). Surface waves in an inhomogeneous elastic medium under the influence of gravity. Applied mechanics series, 37(5), 539–551. https://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=4902394
  10. [10] Abd-Alla, A. M., Abo-Dahab, S. M., & Alotaibi, H. A. (2016). Effect of the rotation on a non-homogeneous infinite elastic cylinder of orthotropic material with magnetic field. Journal of computational and theoretical nanoscience, 13(7), 4476–4492. https://doi.org/10.1166/jctn.2016.5308
  11. [11] Chattopadhyay, A. (1975). On the dispersion equation for love waves due to irregularity in the thickness of the non-homogeneous crustal layer. Acta geologica polonica, 23, 307_317. http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=PASCALGEODEBRGM7730291681
  12. [12] Roy, I., Acharya, D. P., & Acharya, S. (2017). Propagation and reflection of plane waves in a rotating magneto-elastic fibre-reinforced semi space with surface stress. Mechanics and mechanical engineering, 21(4), 1043–1061. https://doi.org/10.2478/mme-2018-0074
  13. [13] Singh, B., & Sindhu, R. (2011). Propagation of waves at an Interface between a liquid half-space and an orthotropic micropolar solid half-space. Advances in acoustics and vibration, 2011(1), 159437. https://doi.org/10.1155/2011/159437
  14. [14] Gupta, R. R., & Gupta, R. R. (2014). Surface wave characteristics in a micropolar transversely isotropic halfspace underlying an inviscid liquid layer. International journal of applied mechanics and engineering, 19(1), 49–60. 10.2478/ijame-2014-0005%0D
  15. [15] Anya, A. I., Akhtar, M. W., Abo-Dahab, S. M., Kaneez, H., Khan, A., & Jahangir, A. (2018). Effects of a magnetic field and initial stress on reflection of SV-waves at a free surface with voids under gravity. Journal of the mechanical behavior of materials, 27(5–6), 20180002. doi/10.1515/jmbm-2018-0002/html
  16. [16] Anya, A. I., & Khan, A. (2019). Reflection and propagation of plane waves at free surfaces of a rotating micropolar fibre-reinforced medium with voids. Geomechanics & engineering, 18(6), 605–614. https://doi.org/10.12989/gae.2019.18.6.605%0A
  17. [17] Anya, A. I., & Khan, A. (2020). Reflection and propagation of magneto-thermoelastic plane waves at free surfaces of a rotating micropolar fibre-reinforced medium under GL theory. International journal of acoustics and vibration, 25(2), 190–199. https://doi.org/10.20855/ijav.2020.25.21575
  18. [18] Anya, A. I., & Khan, A. (2022). Plane waves in a micropolar fibre-reinforced solid and liquid interface for non-insulated boundary under magneto-thermo-elasticity. Journal of computational applied mechanics, 53(2), 204–218. https://doi.org/10.22059/jcamech.2022.341656.712
  19. [19] Maleki, J., & Jafarzadeh, F. (In Press). Model tests on determining the effect of various geometrical aspects on horizontal impedance function of surface footings. Scientia iranica. https://doi.org/10.24200/sci.2023.59744.6403
  20. [20] Chowdhury, S., Kundu, S., Alam, P., & Gupta, S. (2021). Dispersion of stoneley waves through the irregular common interface of two hydrostatic stressed MTI media. Scientia iranica, 28(2), 837–846. https://doi.org/10.24200/sci.2020.52653.2820
  21. [21] Singh, B., & Kaur, B. (2022). Rayleigh surface wave at an impedance boundary of an incompressible micropolar solid half-space. Mechanics of advanced materials and structures, 29(25), 3942–3949. https://doi.org/10.1080/15376494.2021.1914795
  22. [22] Singh, B., & Kaur, B. (2020). Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions. Journal of vibration and control, 26(21–22), 1980–1987. https://doi.org/10.1177/1077546320909972
  23. [23] Sahu, S. A., Mondal, S., & Nirwal, S. (2023). Mathematical analysis of rayleigh waves at the nonplanner boundary between orthotropic and micropolar media. International journal of geomechanics, 23(3), 4022313. https://doi.org/10.1061/IJGNAI.GMENG-7246
  24. [24] Giovannini, L. (2022). Theory of dipole-exchange spin-wave propagation in periodically corrugated films. Physical review b, 105(21), 214426. https://doi.org/10.1103/PhysRevB.105.214426%0A%0A
  25. [25] Rakshit, S., Mistri, K. C., Das, A., & Lakshman, A. (2022). Effect of interfacial imperfections on SH-wave propagation in a porous piezoelectric composite. Mechanics of advanced materials and structures, 29(25), 4008–4018. https://doi.org/10.1080/15376494.2021.1916138
  26. [26] Rakshit, S., Mistri, K. C., Das, A., & Lakshman, A. (2022). Stress analysis on the irregular surface of visco-porous piezoelectric half-space subjected to a moving load. Journal of intelligent material systems and structures, 33(10), 1244–1270. https://doi.org/10.1177/1045389X211048226
  27. [27] Eringen, A. C. (1972). Linear theory of nonlocal elasticity and dispersion of plane waves. International journal of engineering science, 10(5), 425–435. https://doi.org/10.1016/0020-7225(72)90050-X
  28. [28] Eringen, A. C., & Wegner, J. L. (2003). Nonlocal continuum field theories. American society of mechanical engineers digital collection. https://doi.org/10.1115/1.1553434
  29. [29] Roy, I., Acharya, D. P., & Acharya, S. (2015). Rayleigh wave in a rotating nonlocal magnetoelastic half-plane. Journal of theoretical and applied mechanics, 45(4), 61. https://doi.org/10.1515/jtam-2015-0024
  30. [30] Said, S. M., Abd-Elaziz, E. M., & Othman, M. I. A. (2022). The effect of initial stress and rotation on a nonlocal fiber-reinforced thermoelastic medium with a fractional derivative heat transfer. ZAMM - Journal of applied mathematics and mechanics, 102(1), e202100110. https://doi.org/10.1002/zamm.202100110
  31. [31] Anya, A. I., Nwachioma, C., & Ali, H. (2023). Magnetic effects on surface waves in a rotating non-homogeneous half-space with grooved and impedance boundary characteristics. International journal of applied mechanics and engineering, 28(4), 26–42. https://doi.org/10.59441/ijame/172634%0D
  32. [32] Anya, A. I., & Khan, A. (2019). Propagation and reflection of magneto-elastic plane waves at the free surface of a rotating micropolar Fibre-reinforced medium with voids. Journal of theoretical and applied mechanics, 57(4), 869–881. https://doi.org/10.15632/jtam-pl/112066%0D
  33. [33] Khan, A., Anya, A. I., & Kaneez, H. (2015). Gravitational effects on surface waves in non-homogeneous rotating fibre-reinforced anisotropic elastic media with voids. International journal of applied science and engineering research, 4(5), 620–632. https://www.researchgate.net/publication/343628158
  34. [34] Sethi, M., Sharma, A., & Sharma, A. (2016). Propagation of SH waves in a double non-homogeneous crustal layers of finite depth lying over an homogeneous half-space. Latin american journal of solids and structures, 13(14), 2628–2642. https://doi.org/10.1590/1679-78253005
  35. [35] Azhar, E., Ali, H., Jahangir, A., & Anya, A. I. (2023). Effect of hall current on reflection phenomenon of magneto-thermoelastic waves in a non-local semiconducting solid. Waves in random and complex media, 1–18. https://doi.org/10.1080/17455030.2023.2182146
  36. [36] Ailawalia, P., Sachdeva, S. K., & Pathania, D. (2015). A two dimensional fibre reinforced micropolar thermoelastic problem for a half-space subjected to mechanical force. Theoretical and applied mechanics, 42(1), 11–25. https://doi.org/10.2298/TAM1501011A
  37. [37] Othman, M. I. A., Said, S. M., & Gamal, E. M. (2024). A new model of rotating nonlocal fiber-reinforced visco-thermoelastic solid using a modified Green-Lindsay theory. Acta mechanica, 235(5), 3167–3180. https://doi.org/10.1007/s00707-024-03874-6%0A%0A

Downloads

Published

2025-12-17

Issue

Vol. 2 No. 4 (2025): Annals of Process Engineering and Management

Section

Articles

How to Cite

Anya, A. I. (2025). Dynamic Response of Waves on a Non-Homogeneous Impedance Solid with Variable Amplitudes of Corrugated Surface under a Magnetic Field. Annals of Process Engineering and Management, 2(4), 269-285. https://doi.org/10.48314/apem.vi.50

Similar Articles

1-10 of 18

You may also start an advanced similarity search for this article.