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Scattering of anti-plane shear waves by arbitrarily distributed circular cylinders in a functionally graded multiferroic fibrous composite

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Abstract

In this work, a theoretical framework is developed for the multiple scattering of an anti-plane shear wave by a functionally graded multiferroic fibrous composite. The composite consists of arbitrarily distributed circular cylinders and may have different sizes and material constituents. The cylinders are exponentially graded along the radial direction. We exploit the multipole expansions, transition matrix, and Graf’s addition/binomial expansion theorems to obtain a complete solution of the multiple scattering problem in the scenario of functionally graded multiferroic composites. These solved magneto-electro-elastic fields are then used to obtain the directivity patterns of the scattered wave, dynamic stress (electric displacement/magnetic flux) concentration factors, and scattering cross sections. Numerical results reveal the profound influence of the functionally graded parameter, the material properties of constituent phases, the number of inclusions, as well as the frequency of a propagating SH wave on the scattered field induced by the functionally graded fibers. It is expected that the formulation and numerical results serve as useful references for the design and manufacture of functionally graded piezoelectric–piezomagnetic fibrous composites under dynamic loadings.

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References

  1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)

    MATH  Google Scholar 

  2. Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists. Academic Press, San Diego (2001)

    MATH  Google Scholar 

  3. Bhangale, R.K., Ganesan, N.: Static analysis of simply supported functionally graded and layered magneto–electro-elastic plates. Int. J. Solids Struct. 43, 3230–3253 (2006)

    Article  MATH  Google Scholar 

  4. Bostock, M.G., Kennet, B.L.N.: Multiple scattering of surface waves from discrete obstacles. Geophys. J. Int. 108, 52–70 (1992)

    Article  Google Scholar 

  5. Cai, L.-W.: Scattering of antiplane shear waves by layered circular elastic cylinder. J. Acoust. Soc. Am. 115, 515–522 (2004)

    Article  Google Scholar 

  6. Chen, T., Kuo, H.-Y.: Transport properties of composites consisting of periodic arrays of exponentially graded cylinders with cylindrically orthotropic materials. J. Appl. Phys. 98, 033716 (2005)

    Article  Google Scholar 

  7. Chen, P., Shen, Y.: Propagation of axial shear magneto–electro-elastic waves in piezoelectric–piezomagnetic composites with randomly distributed cylindrical inhomogeneities. Int. J. Solids Struct. 44, 1511–1532 (2007)

    Article  MATH  Google Scholar 

  8. Chen, J., Pan, E., Chen, H.: Wave propagation in magneto–electro-elastic multilayered plates. Int. J. Solids Struct. 44, 1073–1085 (2007)

    Article  MATH  Google Scholar 

  9. Du, J.K., Shen, Y.P., Ye, D.Y., Yue, F.R.: Scattering of anti-plane shear waves at a partially debonded magneto–electro-elastic circular cylindrical inhomogeneity. Int. J. Eng. Sci. 42, 887–913 (2004)

    Article  Google Scholar 

  10. Eerenstein, W., Mathur, N.D., Scott, J.F.: Multiferroic and magnetoelectric materials. Nature 442, 759–765 (2006)

    Article  Google Scholar 

  11. Kagemoto, H., Yue, D.K.P.: Interactions among multiple three-dimensional bodies in water wave: an exact algebraic method. J. Fluid Mech. 166, 189–209 (1986)

    Article  MATH  Google Scholar 

  12. Kanaun, S.K., Levin, V.M.: Propagation of shear elastic waves in composites with a random set of spherical inclusions (effective field approach). Int. J. Solids Struct. 42, 3971–3997 (2005)

    Article  MATH  Google Scholar 

  13. Kuo, H.-Y.: Multicoated elliptical fibrous composites of piezoelectric and piezomagnetic phases. Int. J. Eng. Sci. 49, 561–575 (2011)

    Article  MATH  Google Scholar 

  14. Kuo, H.-Y., Chen, Y.: Effective transport properties of arrays of multicoated or graded sphers with spherically transversely isotropic constituents. J. Appl. Phys. 99, 093702 (2006)

    Article  Google Scholar 

  15. Kuo, H.-Y., Yu, S.-H.: Effect of the imperfect interface on the scattering of SH wave in a piezoelectric cylinder in a piezomagnetic matrix. Int. J. Eng. Sci. 85, 186–202 (2014)

    Article  Google Scholar 

  16. Lanczos, C.: Linear Differential Operators. Van Nostrand, New York (1961)

    MATH  Google Scholar 

  17. Levin, V.M., Michelitsch, T.M., Gao, H.: Propagation of electroacoustic waves in the transversely isotropic piezoelectric medium reinforced by randomly distributed cylindrical inhomogeneities. Int. J. Solids Struct. 39, 5013–5051 (2002)

    Article  MATH  Google Scholar 

  18. Li, J.Y., Dunn, M.L.: Anisotropic cooupled-field inclusion and inhomogeneity problems. Philos. Mag. A 77, 1341–1350 (1998)

    Article  Google Scholar 

  19. Liu, Y., Wu, R.-S., Ying, C.F.: Scattering of elastic waves by an elastic or viscoelastic cylinder. Geophys. J. Int. 142, 439–460 (2000)

    Article  Google Scholar 

  20. Liu, Q., Zhao, M., Zhang, C.: Antiplane scattering of SH waves by a circular cavity in an exponentially graded half space. Int. J. Eng. Sci. 78, 61–72 (2014)

    Article  MathSciNet  Google Scholar 

  21. Martin, P.A.: On functionally graded balls and cones. J. Eng. Math. 42, 133–142 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Martin, P.A.: Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  23. Martin, P.A.: Scattering by a cavity in an exponentially graded half-space. Trans. ASME J. Appl. Mech. 76, 031009 (2009)

    Article  Google Scholar 

  24. Mow, C.C., Pao, Y.H.: The Diffraction of Elastic Waves and Dynamic Stress Concentrations. Rand Corporation, Santa Monica (1971)

    Google Scholar 

  25. Nan, C.-W., Bichurin, M.I., Dong, S., Viehland, D., Srinivasan, G.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101 (2008)

    Article  Google Scholar 

  26. Pan, E.: Exact solution for simply supported and multilayered magneto–electro-elastic plates. J. Appl. Mech. 68, 608–618 (2001)

    Article  MATH  Google Scholar 

  27. Piliposyan, D.G., Ghazaryan, K.B., Piliposian, G.T.: Internal resonances in a periodic magneto–electro-elastic strucure. J. Appl. Phys. 116, 044107 (2014)

    Article  Google Scholar 

  28. Sherer, S.E.: Scattering of sound from axisymmetric sources by multiple circular cylinders. J. Acoust. Soc. Am. 115, 488–496 (2004)

    Article  Google Scholar 

  29. Soh, A.K., Liu, J.X.: Interfacial shear horizontal waves in a piezoelectric–piezomagnetic bi-material. Philos. Mag. Lett. 86, 31–35 (2006)

    Article  Google Scholar 

  30. Sun, W.-H., Ju, G.-L., Pan, J.-W., Li, Y.-D.: Effects of the imperfect interface and piezoelectric/piezomagnetic stiffening on the SH wave in a multiferroic composite. Ultrasonics 51, 831–838 (2011)

    Article  Google Scholar 

  31. Suresh, S.: Graded materials for resistance to contact deformation and damage. Science 292, 2447–2451 (2001)

    Article  Google Scholar 

  32. Terrón, J.M., Salazar, A., Sánchez-Lavega, A.: General solution for the thermal wave scattering in fiber composites. J. Appl. Phys. 91, 1087–1098 (2002)

    Article  Google Scholar 

  33. Wang, Y.W., Chew, W.C.: A recursive T-matrix approach for the solution of electromagnetic scattering by many spheres. IEEE Trans. Antennas Propag. 41, 1633–1639 (1993)

    Article  Google Scholar 

  34. Wang, B.L., Mai, Y.-W., Niraula, O.P.: A horizontal shear surface wave in magneto–electro-elastic materials. Philos. Mag. Lett. 87, 53–58 (2007)

    Article  Google Scholar 

  35. Wang, X., Pan, E., Roy, A.K.: Scattering of antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface. Acta Mech. 193, 177–195 (2007)

    Article  MATH  Google Scholar 

  36. Wang, X., Sudak, L.J.: Scattering of elastic waves by multiple circular cylinders with imperfect interface. Waves Random Complex Media 17, 159–187 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, National Chiao Tung University, Hsinchu, 30010, Taiwan

    Hsin-Yi Kuo, Yu-An Huang & Chi-Hsiang Sun

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  1. Hsin-Yi Kuo
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  2. Yu-An Huang
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  3. Chi-Hsiang Sun
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Correspondence to Hsin-Yi Kuo.

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Kuo, HY., Huang, YA. & Sun, CH. Scattering of anti-plane shear waves by arbitrarily distributed circular cylinders in a functionally graded multiferroic fibrous composite. Acta Mech 229, 1483–1501 (2018). https://doi.org/10.1007/s00707-017-2079-x

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  • DOI: https://doi.org/10.1007/s00707-017-2079-x

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