DOI QR코드

DOI QR Code

Effect of quartic nonlinearity on elastic waves via successive approximation

  • Hamza Hameed (Abdus Salam School of Mathematical Sciences, Government College University) ;
  • F. D. Zaman (Abdus Salam School of Mathematical Sciences, Government College University)
  • 투고 : 2023.10.26
  • 심사 : 2024.02.07
  • 발행 : 2024.08.25

초록

The theory of nonlinear elastic wave propagation is important in multiple scientific and engineering fields. In this study, we present a comprehensive examination of nonlinear elastic wave profiles through a contemporary approach of successive approximation. This research is related to nonlinear elastic wave models along different types of nonlinearities. Murnaghan potential is used due to the assumption of the hyper-elastic materials. We explore the complication of the governing equations and go through the behaviors of nonlinear waves in one dimension. The comparative aspect of our study is a distinctive feature, as we evaluate and contrast the results obtained using successive approximation along different nonlinearities. Additionally, we present graphical representations of our findings, enhancing the visual comprehension of the wave profiles and their evolution. This study contributes to the nonlinear elastic wave analysis and comparison.

키워드

과제정보

The authors are grateful to (AS-SMS) Government College University, Lahore, Pakistan for supporting the research.

참고문헌

  1. Abderezak, R., Rabia, B., Daouadji, T.H., Abbes, B., Belkacem, A. and Abbes, F. (2018), "Elastic analysis of interfacial stresses in prestressed PFGM-RC hybrid beams", Adv. Mater. Res., 7(2), 83-103. https://doi.org/10.12989/amr.2018.7.2.83.
  2. Achenbach, J.D. (2012), Wave Propagation in Elastic Solids, Elsevier, New York, NY, USA.
  3. Apostol, B.F. (2003), "On a non-linear wave equation in elasticity", Phys. Lett. A, 318(6), 545-552. https://doi.org/10.1016/j.physleta.2003.09.064.
  4. Bai, H., Feng, X., Liu, Q., Hou, H. and An, Y. (2023), "Research progress and prospect of nonlinear elastic seismology", Progr. Geophys., 38(2), 513-531. https://doi.org/10.6038/pg2023GG0273.
  5. Belarbi, M.O., Salami, S.J., Garg, A., Hirane, H., Amine, D.A. and Houari, M.S.A. (2022), "Finite element bending and buckling analysis of functionally graded carbon nanotubes-reinforced composite beam under arbitrary boundary conditions", Steel Compos. Struct., 44(4), 451-471. https://doi.org/10.12989/scs.2022.44.4.451.
  6. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2018), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163.
  7. Bokhari, A.H., Kara, A.H. and Zaman, F.D. (2007), "Exact solutions of some general nonlinear wave equations in elasticity", Nonlinear Dyn., 48(1), 49-54. https://doi.org/10.1007/s11071-006-9050-z.
  8. Chen, B., Gao, Y., Ji, S. and Liu, Y. (2023), "Stability for time-domain elastic wave equations", arXiv preprint arXiv, 2023, 2301.07847. https://doi.org/10.48550/arXiv.2301.07847.
  9. Delory, A., Lemoult, F., Eddi, A. and Prada, C. (2023), "Guided elastic waves in a highly-stretched soft plate", Extreme Mech. Lett., 61(1), 102018. https://doi.org/10.1016/j.eml.2023.102018.
  10. Ewing, W.M., Jardetzky, W.S., Press, F. and Beiser, A. (1957), Elastic Waves in Layered Media, Taylor and Francis, Oxfordshire, UK.
  11. Fronk, M.D., Fang, L., Packo, P. and Leamy, M.J. (2023), "Elastic wave propagation in weakly nonlinear media and metamaterials: A review of recent developments", Nonlinear Dyn., 111(12), 10709-10741. https://doi.org/10.1007/s11071-023-08399-6.
  12. Garg, A., Belarbi, M.O., Li, L. and Tounsi, A. (2022), "Bending analysis of power-law sandwich FGM beams under thermal conditions", Adv. Aircr. Spacecr. Sci., 9(3), 243-261. https://doi.org/10.12989/aas.2022.9.3.243.
  13. Garg, A., Gupta, S., Chalak, H.D., Belarbi, M.O., Tounsi, A., Li, L. and Zenkour, A.M. (2023), "Free vibration analysis of power-law and sigmoidal sandwich FG plates using refined zigzag theory", Adv. Mater. Res., 12(1), 43-65. https://doi.org/10.12989/amr.2023.12.1.
  14. Garg, A., Shukla, N.K., Raja, M.R., Chalak, H.D., Belarbi, M.O., Tounsi, A. and Zenkour, A.M. (2023), "Finite element based free vibration analysis of sandwich FGM plates under hydrothermal conditions using zigzag theory", Steel Compos. Struct., 49(5), 547-570. https://doi.org/10.12989/scs.2023.49.5.547.
  15. Gartsev, S. (2023), On the Determination of Nonlinear Constants for Residual Stress Measurements Using Rayleigh Waves, Fraunhofer Verlag, Frankfurt, Germany.
  16. Houari, M.S.A., Bessaim, A., Merzouki, T., Daikh, A.A., Garg, A., Tounsi, A. and Belarbi, M. O. (2024), "Shear correction factors of a new exponential functionally graded porous beams", Struct. Eng. Mech., 89(1), 1-11. https://doi.org/10.12989/sem.2024.89.1.001.
  17. Hussain, A., Usman, M., Al-Sinan, B.R., Osman, W.M. and Ibrahim, T.F. (2023), "Symmetry analysis and closed-form invariant solutions of the nonlinear wave equations in elasticity using optimal system of lie subalgebra", Chin. J. Phys., 83(1), 1-13. https://doi.org/10.1016/j.cjph.2023.02.011.
  18. Kaur, I., Lata, P. and Singh, K. (2020), "Reflection of plane harmonic wave in rotating media with fractional order heat transfer", Adv. Mater. Res., 9(4), 289-309. https://doi.org/10.12989/amr.2020.9.4.289.
  19. Ladmek, M., Belkacem, A., Daikh, A.A., Bessaim, A., Garg, A., Houari, M.S.A. and Ouldyerou, A. (2023), "Free vibration of functionally graded carbon nanotubes reinforced composite nanobeams", Adv. Mater. Res., 12(2), 161-177. https://doi.org/10.12989/amr.2023.12.2.161.
  20. Landau, L.D. and Lifshitz, E.M. (2013), Theory of Elasticity, Elsevier, New York, NY, USA.
  21. Lata, P. and Kaur, I. (2019), "Effect of hall current in transversely isotropic magneto thermoelastic rotating medium with fractional order heat transfer due to normal force", Adv. Mater. Res., 7(3), 203-220. https://doi.org/10.12989/amr.2018.7.3.203.
  22. Lata, P. and Kaur, I. (2019), "Effect of inclined load on transversely isotropic magneto thermoelastic rotating solid with time harmonic source", Adv. Mater. Res., 8(2), 83-102. https://doi.org/10.12989/amr.2019.8.2.083.
  23. Miao, Z.H. and Wang, Y.Z. (2023), "In-plane non-symmetric propagation of nonlinear elastic waves through a corrugated interface", Int. J. Non Linear Mech., 148(1), 104266. https://doi.org/10.1016/j.ijnonlinmec.2022.104266.
  24. Mohammadimehr, M. (2022), "Buckling and bending analyses of a sandwich beam based on nonlocal stress-strain elasticity theory with porous core and functionally graded facesheets", Adv. Mater. Res., 11(4), 279. https://doi.org/10.12989/amr.2022.11.4.279.
  25. Mustafa, M.T. and Masood, K. (2009), "Symmetry solutions of a nonlinear elastic wave equation with third-order anharmonic corrections", Appl. Math. Mech., 30(1), 1017-1026. https://doi.org/10.1007/s10483-009-0808-z.
  26. Namayandeh, M.J., Mohammadimehr, M., Mehrabi, M. and Sadeghzadeh-Attar, A. (2020), "Temperature and thermal stress distributions in a hollow circular cylinder composed of anisotropic and isotropic materials", Adv. Mater. Res., 9(1), 15. https://doi.org/10.12989/amr.2020.9.1.015.
  27. Othman, M.I., Said, S.M. and Abd-Elaziz, E.M. (2023), "Effect of magnetic field and gravity on thermoelastic fiber-reinforced with memory-dependent derivative", Adv. Mater. Res., 12(2), 101-118. https://doi.org/10.12989/amr.2023.12.2.101.
  28. Rushchitsky, J.J. (2014), Nonlinear Elastic Waves in Materials, Springer International Publishing, Cham, Switzerland.
  29. Sabherwal, P., Belarbi, M.O., Raman, R., Garg, A., Li, L., Devidas Chalak, H. and Avcar, M. (2024), "Free vibration analysis of laminated sandwich plates using wavelet finite element method", AIAA J., 62(2), 1-9. https://doi.org/10.2514/1.J063364.
  30. Sang, S., Xu, C., Wang, Z., Side, C., Fowler, B., Fan, J. and Miao, D. (2023), "Accurate prediction of topology of composite plates via machine learning and propagation of elastic waves", Compos. Commun., 37(1), 101465. https://doi.org/10.1016/j.coco.2022.101465.
  31. Shi, C.Z., Zheng, H., Wen, P.H. and Hon, Y.C. (2023), "The local radial basis function collocation method for elastic wave propagation analysis in 2D composite plate", Eng. Anal. Bound. Elem., 150(1), 571-582. https://doi.org/10.1016/j.enganabound.2014.11.006.
  32. Shojaei, A., Hermann, A., Seleson, P., Silling, S.A., Rabczuk, T. and Cyron, C.J. (2023), "Peri-dynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet type absorbing boundary conditions", Comput. Method. Appl. Mech. Eng., 407(1), 115948. https://doi.org/10.1016/j.cma.2023.115948.
  33. Usman, M. and Zaman, F.D. (2023), "Lie symmetry analysis and conservation laws of non-linear (2+1) elastic wave equation", Arab. J. Math., 12(1), 265-276. https://doi.org/10.1007/s40065-022-00392-y.
  34. Yang, H., Fu, L.Y., Li, H., Du, Q. and Zheng, H. (2023), "3D acoustoelastic FD modeling of elastic wave propagation in prestressed solid media", J. Geophys. Eng., 20(2), 297-311. https://doi.org/10.1093/jge/gxad010.
  35. Yu, G., Xia, J., Lai, L., Peng, T., Zhu, H., Jiang, C. and Li, Y. (2023), "Klein-tunneling increases the signal modulation rate of elastic wave systems", Int. J. Mech. Sci., 253(1), 108412. https://doi.org/10.1016/j.ijmecsci.2023.108412.
  36. Zhang, W.Y., Chen, H., Lai, H.S., Xie, J.L., He, C. and Chen, Y.F. (2023), "Multimode topological interface states in a one-dimensional elastic-wave phononic crystal", Phys. Lett. A, 479(1), 128929. https://doi.org/10.1016/j.physleta.2023.128929.
  37. Zhang, Z., Wang, E., Zhang, H., Bai, Z., Zhang, Y. and Chen, X. (2023), "Research on nonlinear variation of elastic wave velocity dispersion characteristic in limestone dynamic fracture process", Fract., 31(1), 2350008. https://doi.org/10.1142/S0218348X23500081.