Diffraction of Magnetoelastic Plane Waves through a Rigid Strip in an Orthotropic Medium: An Analytical Approach
Publication: Journal of Engineering Mechanics
Volume 150, Issue 12
Abstract
The present study provides the analytical solution for magnetoelastic plane-wave diffraction by a rigid strip in an infinite orthotropic medium. The mathematical formulation of the considered model involves a mixed boundary value problem, which is solved by using the integral equation method. The contour integration technique has been used to establish the closed-form expressions of vertical diffracted displacement and normal stress. The deduced expressions of the vertical diffracted displacement and normal stress are matched with preestablished result through the special cases and serves the validation of the present study. The pattern of the diffracted displacement component in the considered medium, and its varying behavior with various affecting parameters, i.e., magnetoelastic coupling parameter, wave number, phase velocity of the propagating magnetoelastic wave, and distance, are computed numerically and delineated by means of graphical representation for orthotropic and isotropic materials. Moreover, the impact of anisotropy of the infinite medium has been unrevealed through comparative study, which is one of the achievements of the present work.
Practical Applications
The diffraction of longitudinal magnetoelastic plane waves through a rigid strip in an orthotropic material holds significant applications across diverse engineering fields. In nondestructive testing (NDT), the understanding of wave diffraction patterns aids in the detection and characterization of defects or structural changes in orthotropic materials without causing damage. This knowledge is vital for structural health monitoring (SHM), allowing for the timely identification of damage, cracks, or alterations in material properties. Moreover, the insights gained from wave diffraction contribute to the design and optimization of magnetoelastic devices, including sensors, actuators, and transducers, enhancing their performance and sensitivity. In the realm of communication, the propagation of magnetoelastic waves through rigid strips in orthotropic materials is instrumental in designing efficient waveguides and communication devices. Additionally, the study of wave diffraction facilitates the development of magnetostrictive components for applications in robotics, medical devices, and automotive systems. Furthermore, the unique acoustic properties of orthotropic materials, influenced by magnetoelastic wave diffraction, contribute to the design and optimization of acoustic devices such as speakers and ultrasonic transducers.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The authors express their sincere gratitude to the reviewers for their valuable insights and constructive feedback, which significantly enhanced the quality of this paper. Dr. Moumita Mahanty conveys her sincere thanks to DST, Government of India, for providing Research Fellowship under Grant No. DST/INSPIRE Fellowship/2016/IF160054.
References
Acharya, D. P., I. Roy, and S. Sengupta. 2009. “Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media.” Acta Mech. 202 (1–4): 35–45. https://doi.org/10.1007/s00707-008-0027-5.
Bowen, A. W. 1973. “The effect of testing direction on the fatigue and tensile properties of a Ti-6Al-4V bar.” In Titanium science and technology, edited by R. I. Jaffee and H. M. Burte, 1271–1281. New York: Plenum Press.
Chattopadhyay, A., and S. Choudhury. 1990. “Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium.” Int. J. Eng. Sci. 28 (6): 485–495. https://doi.org/10.1016/0020-7225(90)90051-J.
Chattopadhyay, A., and G. A. Maugin. 1985. “Diffraction of magnetoelastic shear waves by a rigid strip.” J. Acoust. Soc. Am. 78 (1): 217–222. https://doi.org/10.1121/1.392561.
Chen, Q., L. Liu, C. Zhu, and K. Chen. 2018. “Mesomechanical modeling and numerical simulation of the diffraction elastic constants for Ti6Al4V polycrystalline alloy.” Metals 8 (10): 822. https://doi.org/10.3390/met8100822.
Cinar, A., and F. Erdogan. 1993. “The crack and wedging problem for an orthotropic strip.” Int. J. Fract. 23 (2): 83–102. https://doi.org/10.1007/BF00042809.
Datta, S. K. 1974. “Diffraction of SH-waves by an elliptic elastic cylinder.” Int. J. Solids Struct. 10 (1): 123–133. https://doi.org/10.1016/0020-7683(74)90105-X.
Der Wang, C., H. T. Chou, and D. H. Peng. 2017. “Love-wave propagation in an inhomogeneous orthotropic medium obeying the exponential and generalized power law models.” Int. J. Geomech. 17 (7): 04017003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000870.
Destrade, M., and R. W. Ogden. 2011. “On magneto-acoustic waves in finitely deformed elastic solids.” Math. Mech. Solids 16 (6): 594–604. https://doi.org/10.1177/1081286510387695.
Dunkin, J. W., and A. C. Eringen. 1963. “On the propagation of waves in an electromagnetic elastic solid.” Int. J. Eng. Sci. 1 (4): 461–495. https://doi.org/10.1016/0020-7225(63)90004-1.
Elmorabie, K. M., and R. R. Yahya. 2018. “Diffraction of elastic waves from object in layer with slightly corrugated surface.” Math. Mech. Solids 23 (9): 1249–1262. https://doi.org/10.1177/1081286517713341.
Eringen, A. C., and E. S. Suhubi. 1975. Elastodynamics, Vol. II, linear theory. San Francisco: Academic Press.
Faulkner, T. R. 1965. “Diffraction of an electromagnetic plane-wave by a metallic strip.” IMA J. Appl. Math. 1 (2): 149–163. https://doi.org/10.1093/imamat/1.2.149.
Gao, Y., X. Chen, N. Zhang, D. Dai, and X. Yu. 2018. “Scattering of plane SH waves induced by a semicylindrical canyon with a subsurface circular lined tunnel.” Int. J. Geomech. 18 (6): 06018012. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001137.
Ghosh, S., and S. C. Mandal. 2006. “Diffraction of P-wave by crack in an elastic strip at asymmetric position.” Eur. J. Mech. A Solids 25 (2): 299–307. https://doi.org/10.1016/j.euromechsol.2005.07.007.
Gubbins, D. 1990. Seismology and plate tectonics. Cambridge, MA: Cambridge University Press.
Hsu, M. H. 2010. “Vibration analysis of orthotropic rectangular plates on elastic foundations.” Compos. Struct. 92 (4): 844–852. https://doi.org/10.1016/j.compstruct.2009.09.015.
Itou, S. 2017. “Stresses around a moving Griffith crack at an interface between a nonhomogeneous bonding layer and two dissimilar orthotropic half-spaces.” Int. J. Mech. Sci. 124–125 (Sep): 122–131. https://doi.org/10.1016/j.ijmecsci.2017.03.004.
Jain, D. L., and R. P. Kanwal. 1972. “Diffraction of elastic waves by two coplanar and parallel rigid strips.” Int. J. Eng. Sci. 10 (11): 925–937. https://doi.org/10.1016/0020-7225(72)90002-X.
Jiang, S.-C., Y. Gou, B. Teng, and D.-Z. Ning. 2014. “Analytical solution of a wave diffraction problem on a submerged cylinder.” J. Eng. Mech. 140 (1): 225–232. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000637.
Knopoff, L. 1955. “The interaction between elastic wave motions and a magnetic field in electrical conductors.” J. Geophys. Res. 60 (4): 441–456. https://doi.org/10.1029/JZ060i004p00441.
Knopoff, L., and J. A. Hudson. 1964. “Scattering of elastic waves by small inhomogeneities.” J. Acoust. Soc. Am. 36 (2): 338–343. https://doi.org/10.1121/1.1918957.
Kumar, P., M. Mahanty, and A. Chattopadhyay. 2019. “An overview of stress-strain analysis for elasticity equations.” In Elasticity of materials basic principles and design of structures. London: IntechOpen.
Lee, V. W., H. Luo, and J. Liang. 2006. “Antiplane (SH) waves diffraction by a semicircular cylindrical hill revisited: An improved analytic wave series solution.” J. Eng. Mech. 132 (10): 1106–1114. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:10(1106).
Leyens, C., and M. Peters. 2003. Titanium and titanium alloys: Fundamentals and applications. Edited by C. Leyens and M. Peters. New York: Wiley-VCH.
Li, X. F. 2005. “Two perfectly-bonded dissimilar orthotropic strips with an interfacial crack normal to the boundaries.” Appl. Math. Comput. 163 (2): 961–975. https://doi.org/10.1016/j.amc.2004.05.003.
Love, A. 1892. A treatise on the mathematical theory of elasticity. New York: Cambridge University Press.
Lowengrub, M., and K. N. Srivastava. 1968. “On two coplanar griffith cracks in an infinite elastic medium.” Int. J. Eng. Sci. 6 (6): 359–362. https://doi.org/10.1016/0020-7225(68)90056-6.
Lu, A., N. Zhang, X. Zhang, D. Lu, and W. Li. 2015. “Analytic method of stress analysis for an orthotropic rock mass with an arbitrary-shaped tunnel.” Int. J. Geomech. 15 (4): 04014068. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000408.
Mandal, S. C., and M. L. Ghosh. 1994. “Interaction of elastic waves with a periodic array of coplanar griffith cracks in an orthotropic elastic medium.” Int. J. Eng. Sci. 32 (1): 167–178. https://doi.org/10.1016/0020-7225(94)90158-9.
Manolis, G. D., and P. S. Dineva. 2015. “Elastic waves in continuous and discontinuous geological media by boundary integral equation methods: A review.” Soil Dyn. Earthquake Eng. 70 (Jan): 11–29. https://doi.org/10.1016/j.soildyn.2014.11.013.
Maugin, G. A. 1981. “Wave motion in magnetizable deformable solids.” Int. J. Eng. Sci. 19 (3): 321–388. https://doi.org/10.1016/0020-7225(81)90059-8.
Monfared, M. M., and M. Ayatollahi. 2013. “Dynamic stress intensity factors of multiple cracks in an orthotropic strip with FGM coating.” Eng. Fract. Mech. 109 (Jun): 45–57. https://doi.org/10.1016/j.engfracmech.2013.07.002.
Mukherjee, S., and S. Das. 2007. “Interaction of three interfacial Griffith cracks between bonded dissimilar orthotropic half planes.” Int. J. Solids Struct. 44 (17): 5437–5446. https://doi.org/10.1016/j.ijsolstr.2006.10.024.
Prosser, W. H., and R. E. Green. 1990. “Characterization of the nonlinear elastic properties of graphite/epoxy composites using ultrasound.” J. Reinf. Plast. Compos. 9 (2): 162–173. https://doi.org/10.1177/073168449000900206.
Sarkar, J., M. L. Ghosh, and S. C. Mandal. 1995. “Diffraction of elastic waves by two parallel rigid strips embedded in an infinite orthotropic medium.” Int. J. Eng. Sci. 33 (13): 1943–1958. https://doi.org/10.1016/0020-7225(95)00036-W.
Sih, G. C., and J. F. Loeber. 1969. “A class of wave diffraction problems involving geometrically-induced singularities.” J. Math. Mech. 19 (4): 327–349. https://doi.org/10.2307/24901754.
Singh, A. K., A. Lakshman, and A. Chattopadhyay. 2016. “Effect of irregularity and anisotropy on the dynamic response due to a shear load moving on an irregular orthotropic half-space under influence of gravity.” Multidiscip. Model. Mater. Struct. 12 (1): 194–214. https://doi.org/10.1108/MMMS-04-2015-0020.
Singh, A. K., M. K. Pal, A. Negi, and K. C. Mistri. 2019. “Analytical study on dynamic response due to a moving load on distinctly characterized orthotropic half-spaces under different physical conditions with comparative approach.” Arab. J. Sci. Eng. 44 (5): 4863–4883. https://doi.org/10.1007/s13369-018-3577-4.
Singh, B. M., J. Rokne, and R. S. Dhaliwal. 1983. “Diffraction of torsional wave by a circular rigid disc at the interface of two bonded dissimilar elastic solids.” Acta Mech. 49 (1–2): 139–146. https://doi.org/10.1007/BF01181760.
Tricomi, F. G. 1951. “On the finite Hilbert transformation.” Q. J. Math. 2 (1): 199–211. https://doi.org/10.1093/qmath/2.1.199.
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 12 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 2, 2023
Accepted: Jun 21, 2024
Published online: Sep 24, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 24, 2025
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