volume | PIER Journals

Abstract

The present paper investigates the propagation and dispersion of elastic surface waves in an asymmetric inhomogeneous isotropic three-layered plate in the presence of magnetic field and rotational effects. The skin layers are exposed to an external magnetic field force while the core layer is assumed to be in a rotational frame of reference, which are perfectly bounded together with free-ends conditions. The resultant displacements and shear stresses in the respective layers are derived analytically together with the general dispersion relation. Further, the general dispersion relation is analyzed for some physical cases of interest. Finally, the effects of the magnetic field, rotation and electric field on the propagation and dispersion of the present model are presented graphically.

1. Achenbach, J. D., Wave Propagation in Elastic Solids, Eight Impression, Elsevier, 1999.

2. Kaplunov, J. D., L. Y. Kossovich, and E. V. Nolde, Dynamics of Thin Walled Elastic Bodies, Academic Press, 1998.

3. Andrianov, I. V., J. Awrejcewicz, V. V. Danishevs’kyy, and O. A. Ivankov, Asymtotic Methods in the Theory of Plates with Mixed Boundary Conditions, John Wiley & Sons, Ltd., 2014.

4. Knopoff, L., "The interaction between elastic wave motion and a magnetic field in electrical conductors," J. Geophys. Research, Vol. 60, 441-456, 1955.

5. Chadwick, P., "Elastic wave propagation in a magnetic field," Proceedings of the 9th International Congress of Applied Mechanics, Vol. 7, 143-153, 1957.

6. Kaliski, S. and J. Petykiewicz, "Equation of motion coupled with the field of temperature in a magnetic field involving mechanical and electrical relaxation for anisotropic bodies," Proceedings of Vibration Problems, Vol. 4, No. 1, 1959.

7. Kumar, R. and V. Chawla, "Effect of rotation and stiffness on surface wave propagation in a elastic layer lying over a generalized thermodiffusive elastic half-space with imperfect boundary," J. Solid Mechanics, Vol. 2, No. 1, 28-42, 2010.

8. Lotfy, K., "Wave propagation of generalized magneto-thermo elastic interactions in an elastic medium under influence of initial stress," Iranian J. Sci. Techn.: Trans. Mech. Eng., 2019.

9. Wang, Y. Z., F. M. Li, and K. Kishimoto, "Thermal effects on vibration properties of double-layered nanoplates at small scales," Composites Part B: Eng., Vol. 42, No. 5, 1311-1317, 2011.

10. El-Naggar, A. M., A. M. Abd-Allaa, and S. M. Ahmad, "Rayleigh waves in A magneto-elastic initially stressed conducting medium with the gravity field," Bull Calcutta, Math. Soc., Vol. 86, 51-56, 1994.

11. Abo-Dahab, S. M., R. A. Mohamed, and B. Singh, "Rotation and magnetic field effects on P wave reflection from stressfree surface elastic half-space with voids under one thermal relaxation time," Journal of Vibration and Control, Vol. 17, No. 12, 1827-1839, 2011.

12. Abd-Alla, A. M., S. M. Abo-Dahab, and F. S. Bayones, "Effect of the rotation on an infinite generalized magneto-thermoelastic diffusion body with a spherical cavity," Int. Review Phy., Vol. 5, No. 4, 171-181, 2011.

13. Selim, M. M., "Effect of thermal stress and magnetic field on propagation of transverse wave in an anisotropic incompressible dissipative initially stressed plate," Appl. Math. Inf. Sci., Vol. 11, No. 1, 195-200, 2017.

14. Qian, Z., F. Jin, K. Kishimoto, and Z. Wang, "Effect of initial stress on the Propagation behavior of SH-waves in multilayered piezoelectric composite structures," Sensors and Actuators A: Phys., Vol. 112, No. 2–3, 368-375, 2004.

15. Abo-Dahab, S. M., "Propagation of P waves from stress-free surface elastic half-space with voids under thermal relaxation and magnetic field," Appl. Math. Model., Vol. 34, No. 7, 1798-1806, 2010.

16. Leissa, A. W., Vibrations of Continous Systems, McGraw Hill Companies, Inc., 2011.

17. Aouadi, M., "A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion," Int. J. Solids Struct., Vol. 44, No. 17, 5711-5722, 2007.

18. Craster, R. V. and J. Kaplunov, Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism, Springer Wien Heidelberg, 2013.

19. Ewing, W. M., W. S. Jardetzky, and F. Press, Elastic Layers in Layered Media, McGraw-Hill, 1957.

20. Altenbach, H., V. A. Eremeyev, and K. Naumenko, "On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer," ZAMM, Vol. 95, No. 10, 1004-1011, 2015.

21. Lee, P. and N. Chang, "Harmonic waves in elastic sandwich plates," J. Elasticity, Vol. 9, No. 1, 51-69, 1979.

22. Kaplunov, J., D. Prikazchikov, and L. Prikazchikova, "Dispersion of elastic waves in a strongly inhomogeneous three-layered plate," Int. J. Solids Struct., Vol. 113, 169-179, 2017.

23. Naumenko, K. and V. A. Eremeyev, "A layer-wise theory for laminated glass and photovoltaic panels," Compos. Struct., Vol. 112, 283-291, 2014.

24. Sayyad, A. S. and Y. M. Ghugal, "Bending, buckling and free vibration of laminated composite and sandwich beams: a critical review of literature," Compos. Struct., Vol. 171, 486-504, 2017.

25. Sahin, O., B. Erbas, J. Kaplunov, and T. Savsek, "The lowest vibration modes of an elastic beam composed of alternating stiff and soft components," Arch. Appl. Mech., 2019, doi.org/10.1007/s00419-019-01612-2.

26. Belarbi, M. O., A. Tati, H. Ounis, and A. Khechai, "On the free vibration analysis of laminated composite and sandwich plates: A layerwise finite element formulation," Latin American J. Solids Struc., 2017.

27. Shishehsaz, M., H. Raissi, and S. Moradi, "Stress distribution in a five-layer circular sandwich composite plate based on the third and hyperbolic shear deformation theories," Mechanics Adv. Materials Struct., 2019.

28. Jiangong, Y., M. Qiujuan, and S. Shan, "Wave propagation in non-homogeneous magneto-electro-elastic hollow cylinders," Ultrasonic, Vol. 48, No. 8, 664-677, 2008.

29. Bin, W., Y. Jiangong, and C. Cunfu, "Wave propagation in non-homogeneous magneto-electro-elastic plates," J. Sound Vib., Vol. 317, No. 1–2, 250-264, 2008.

30. Mandi, A., S. Kundu, P. Chandra, and P. Pati, "An analytic study on the dispersion of Love wave propagation in double layers lying over inhomogeneous half-space," J. Solid Mechanics, Vol. 11, No. 2, 570-580, 2019.

31. Soliman, S. A. M., K. F. A. Hussein, and A. A. Ammar, "Electromagnetic resonances of natural grasslands and their effects on radar vegetation index," Progress In Electromagnetics Research B, Vol. 86, 9-38, 2020.

32. Demirkus, D., "Antisymmetric bright solitary SH waves in a nonlinear heterogeneous plate," Z. Angew. Math. Phys., Vol. 69, 2018.

33. Satti, J. U., M. Afzal, and R. Nawaz, "Scattering analysis of a partitioned wave-bearing cavity containing different material properties," Phisica Scripta, Vol. 94, No. 11, 2019.

34. Abo-Dahab, S. M., K. Lotfy, and K. Gohaly, "A. Rotation and magnetic field effect on surface waves propagation in an elastic layer lying over a generalized thermoelastic diffusive half-space with imperfect boundary," Math. Probl. Eng., 671783, 2015.

35. Anya, A. I., M. W. Akhtar, S. M. Abo-Dahab, H. Kaneez, A. Khan, and A. Jahangir, "Effects of a magnetic field and initial stress on reflection of SV-waves at a free surface with voids under gravity," J. Mech. Behavior Mat., 20180002, 2018.

36. Farhan, A. M. and A. M. Abd-Alla, "Effect of rotation on the surface wave propagation in magneto-thermoelastic materials with voids," J. Ocean Engr. Sci., Vol. 3, 334-342, 2018.

Dr. Rahmatullah Ibrahim Nuruddeen

Dr. Rab Nawaz

Dr. Qazi Muhammad Zia