Analysis of SH-Wave Propagation in Magnetoelastic Fiber-Reinforced Layer Resting over Inhomogeneous Viscoelastic Half-Space with Corrugation
Publication: International Journal of Geomechanics
Volume 21, Issue 11
Abstract
The analysis of the wave propagation phenomenon on magnetoelastic fiber-reinforced (MEFR) composites has not yet been much explored. The present paper investigates the dispersive behavior of SH waves in a MEFR crustal layer lying over an inhomogeneous viscoelastic half-space under the action of corrugated boundary surfaces. The MEFR material is polarized in the x1-axis direction. The exponential variation of the space variable, which is pointing positively downward, causes inhomogeneity in the inhomogeneous viscoelastic half-space. The frequency relation of SH-wave propagation on the considered composite structure is obtained by employing a variable-separable technique, Whittaker’s equation, and nontraditional boundary conditions. The profound effect of material parameters, corrugation, undulatory, inhomogeneity, and viscoelasticity on the phase velocity of SH waves is discussed with the help of numerical calculations and shown by graphical illustrations. The obtained result is well-matched with the classical case of a Love wave for validation, and is discussed as one of the problem’s special cases. The findings of this research may be useful in interpreting geomechanical, geological, and geodynamical applications within the Earth’s crust, which contains natural resources.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is supported by UGC, Government of India under NET-JRF Scheme to Dharmendra Kumar and DST-SERB/EMR/2017/001505 to Santimoy Kundu.
Notation
The following symbols are used in this paper:
- magnetic induction vector;
- induced electric field;
- total magnetic field vector;
- primary magnetic field vector;
- H1
- average thickness of the layer;
- electric current vector;
- Lorentz force;
- reinforcement of the fiber-reinforced medium in the preferred direction;
- bi (i = 1, 2)
- amplitudes of upper and intermediary corrugated surfaces;
- c
- common wave velocity;
- eij
- layer’s strain components;
- hi = (h1, h2, h3)
- change in the magnetic field;
- k
- wave number;
- linearised Maxwell’s stress tensor;
- stress components of the layer and half-space;
- (ui, vi, wi) (i = 1, 2)
- displacement components of the layer and half-space;
- α1
- wave number of corrugation;
- α, β
- specific stress components of the layer;
- γH
- dimensionless magnetoelastic coupling parameter;
- δij
- Kronecker delta function;
- ε
- inhomogeneity parameter;
- θ
- angle at which the wave intersects the magnetic field;
- λ
- Lame’s constant;
- μL
- longitudinal elastic shear modulus of the layer;
- μT
- transverse elastic shear modulus of the layer;
- μe
- induced permeability;
- μ2
- rigidity of the half-space;
- half-space viscosity;
- ρi(i = 1, 2)
- densities of the layer and half-space; and
- σ
- conduction coefficient.
References
Abd-Alla, A. M., S. M. Abo-Dahab, and A. Al-Mullise. 2013. “Effects of rotation and gravity field on surface waves in fibre-reinforced thermoelastic media under four theories.” J. Appl. Math. 2013 (3): 1–20. https://doi.org/10.1155/2013/562369.
Abualnour, M., A. Chikh, H. Hebali, A. Kaci, A. Tounsi, A. A. Bousahla, and A. Tounsi. 2019. “Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory.” Comput. Concr. 24 (6): 489–498.
Achenbach, J. D., and G. Herrmann. 1968. “Dispersion of free harmonic waves in fiber-reinforced composites.” AIAA J. 6 (10): 1832–1836. https://doi.org/10.2514/3.4888.
Al-Furjan, M., M. Habibi, D. won Jung, S. Sadeghi, H. Safarpour, A. Tounsi, and G. Chen. 2020. “A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel.” Eng. Comput. 1–18. https://doi.org/10.1007/s00366-020-01130-8.
Alam, P., S. Kundu, and S. Gupta. 2017. “Dispersion and attenuation of torsional wave in a viscoelastic layer bonded between a layer and a half-space of dry sandy media.” Appl. Math. Mech. 38 (9): 1313–1328. https://doi.org/10.1007/s10483-017-2239-8.
Asano, S. 1966. “Reflection and refraction of elastic waves at a corrugated interface.” Bull. Seismol. Soc. Am. 56 (1): 201–221. https://doi.org/10.1785/BSSA0560010201.
Belbachir, N., M. Bourada, K. Draiche, A. Tounsi, F. Bourada, A. A. Bousahla, and S. Mahmoud. 2020. “Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory.” Smart Struct. Syst. 25 (4): 409–422.
Belbachir, N., K. Draich, A. A. Bousahla, M. Bourada, A. Tounsi, and M. Mohammadimehr. 2019. “Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings.” Steel Compos. Struct. 33 (1): 81–92.
Belfield, A., T. Rogers, and A. Spencer. 1983. “Stress in elastic plates reinforced by fibres lying in concentric circles.” J. Mech. Phys. Solids 31 (1): 25–54. https://doi.org/10.1016/0022-5096(83)90018-2.
Bellal, M., H. Hebali, H. Heireche, A. A. Bousahla, A. Tounsi, F. Bourada, S. Mahmoud, E. Bedia, and A. Tounsi. 2020. “Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model.” Steel Compos. Struct. 34 (5): 643–655.
Bhattacharya, J. 1969. “The possibility of the propagation of love type waves in an intermediate heterogeneous layer lying between two semi-infinite isotropic homogeneous elastic layers.” Pure Appl. Geophys. 72 (1): 61–71. https://doi.org/10.1007/BF00875693.
Chattopadhyay, A., and A. K. Singh. 2012. “Propagation of a crack due to magnetoelastic shear waves in a self-reinforced medium.” J. Vib. Control 20 (3): 406–420. https://doi.org/10.1177/1077546312458134.
Cooper, H. F. 1967. “Reflection and transmission of oblique plane waves at a plane interface between viscoelastic media.” J. Acoust. Soc. Am. 42 (5): 1064–1069. https://doi.org/10.1121/1.1910691.
Draiche, K., A. A. Bousahla, A. Tounsi, A. S. Alwabli, A. Tounsi, and S. Mahmoud. 2019. “Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory.” Comput. Concr. 24 (4): 369–378.
Gogna, M., and S. Chander. 1985. “Reflection and transmission of SH-waves at an interface between anisotropic inhomogeneous elastic and viscoelastic half-spaces.” Acta Geophys. 33 (4): 357–375.
Gubbins, D. 1990. Seismology and plate tectonics. Cambridge, UK: Cambridge University Press.
Gupta, S., M. Ahmed, and J. C. Misra. 2019. “Effects of periodic corrugated boundary surfaces on plane SH-waves in fiber-reinforced medium over a semi-infinite micropolar solid under the action of magnetic field.” Mech. Res. Commun. 95 (1): 35–44. https://doi.org/10.1016/j.mechrescom.2018.11.007.
Kumar, D., S. Kundu, R. Kumhar, and S. Gupta. 2020. “Vibrational analysis of love waves in a viscoelastic composite multilayered structure.” Acta Mech. 231 (10): 4199–4215. https://doi.org/10.1007/s00707-020-02767-8.
Kumari, C., S. Kundu, A. Kumari, and S. Gupta. 2020. “Analysis of dispersion and damping characteristics of love wave propagation in orthotropic visco-elastic FGM layer with corrugated boundaries.” Int. J. Geomech. 20 (2): 04019172. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001569.
Kumari, P., and V. K. Sharma. 2013. “Propagation of torsional waves in a viscoelastic layer over an inhomogeneous half space.” Acta Mech. 225 (6): 1673–1684. https://doi.org/10.1007/s00707-013-1021-0.
Love, A. 1927. A treatise on the mathematical theory of elasticity. Cambridge, UK: Cambridge University Press.
Maity, M., S. Kundu, D. K. Pandit, and S. Gupta. 2018. “Characteristics of torsional wave profiles in a viscous fiber-reinforced layer resting over a sandy half-space under gravity.” Int. J. Geomech. 18 (7): 06018015. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001207.
Rouabhia, A., A. Chikh, A. A. Bousahla, F. Bourada, H. Heireche, A. Tounsi, K. H. Benrahou, A. Tounsi, and M. M. Al-Zahrani. 2020. “Physical stability response of a slgs resting on viscoelastic medium using nonlocal integral first-order theory.” Steel Compos. Struct. 37 (6): 695.
Sahla, M., H. Saidi, K. Draiche, A. A. Bousahla, F. Bourada, and A. Tounsi. 2019. “Free vibration analysis of angle-ply laminated composite and soft core sandwich plates.” Steel Compos. Struct. 33 (5): 663–679.
Schoenberg, M. 1971. “Transmission and reflection of plane waves at an elastic-viscoelastic interface.” Geophys. J. Int. 25 (1–3): 35–47. https://doi.org/10.1111/j.1365-246X.1971.tb02329.x.
Sengupta, P. R., and S. Nath. 2001. “Surface waves in fibre-reinforced anisotropic elastic media.” Sadhana 26 (4): 363–370. https://doi.org/10.1007/BF02703405.
Seshadri, S. 1978. “Love wave interaction in a thin film with a periodic surface corrugation.” IEEE Trans. Sonics Ultrason. 25 (6): 378–383. https://doi.org/10.1109/T-SU.1978.31046.
Tomar, S. K., and J. Kaur. 2007. “Shear waves at a corrugated interface between anisotropic elastic and visco-elastic solid half-spaces.” J. Seismolog. 11 (3): 235–258. https://doi.org/10.1007/s10950-007-9050-6.
Tomar, S. K., and S. S. Singh. 2006. “Plane SH-waves at a corrugated interface between two dissimilar perfectly conducting self-reinforced elastic half-spaces.” Int. J. Numer. Anal. Methods Geomech. 30 (6): 455–487. https://doi.org/10.1002/(ISSN)1096-9853.
Zenzen, R., S. Khatir, I. Belaidi, C. L. Thanh, and M. A. Wahab. 2020. “A modified transmissibility indicator and artificial neural network for damage identification and quantification in laminated composite structures.” Compos. Struct. 248 (3): 112497. https://doi.org/10.1016/j.compstruct.2020.112497.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 11 • November 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 24, 2020
Accepted: Jul 7, 2021
Published online: Sep 6, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 6, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Arpita Maji, Sudarshan Dhua, Propagation of Magnetoelastic Shear Wave in an Initially Stressed Inhomogeneous Composite-Layered Structure with an Imperfect Interface, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-8860, 23, 12, (2023).
- Yue Ma, Jun Feng, Shangqi Ge, Kai Wang, Xiaohui Chen, Aizhong Ding, Constitutive Modeling of Hydromechanical Coupling in Double Porosity Media Based on Mixture Coupling Theory, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-7731, 23, 6, (2023).
- Dharmendra Kumar, Raju Kumhar, Santimoy Kundu, Shishir Gupta, Analysis the dispersive nature of Love wave in fibre‐reinforced composite materials plate: A Green's function approach, Mathematical Methods in the Applied Sciences, 10.1002/mma.8702, 46, 4, (3445-3462), (2022).