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DYNAMIC STRESS CONCENTRATION IN A PIEZOELECTRIC MATERIAL WITH A NON-CIRCULAR HOLE SUBJECTED TO AN SH-WAVE

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

In this paper, the influence of the dynamic stress concentration in a piezoelectric material with a non-circular hole subjected to a shear wave polarized so that its particle motion and direction of propagation are aligned in a horizontal plane (SH-wave) is investigated. The boundary conditions of the non-circular hole can be mapped into a unit circle by applying complex variables and conformal mapping. The analytical solution of the dynamic stress concentration factor is determined by the unknown mode coefficients obtained by using the boundary conditions. Numerical examples are presented to analyze the influence of the incident wave number, piezoelectric constant of the material, and eccentricity ratio of the hole on the distribution of the dynamic stress concentration factor. The analysis reveals that the distribution of the dynamic stress concentration factor on the incident direction of the SH-wave is significantly different from that on the other side.

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REFERENCES

  1. X. D. Wang and S. A. Meguid, “Modelling and Analysis of the Dynamic Behaviour of Piezoelectric Materials Containing Interacting Cracks," Mech. Materials 32 12, 723–737 (2000); DOI: 10.1016/s0167-6636(00)00043-0.

  2. L. Ma, L. Z. Wu, Z. G. Zhou, et al., “Scattering of Harmonic Anti-Plane Shear Waves by Two Collinear Cracks in Functionally Graded Piezoelectric Materials," Europ. J. Mech., A: Solids23 (4), 633–643 (2004); DOI: 10.1016/j.euromechsol.2004.03.002.

  3. C. H. Chue and W. H. Hsu, “Antiplane Internal Crack Normal to the Edge of a Functionally Graded Piezoelectric/Piezomagnetic Half Plane," Meccanica 43 (3), 307–325 (2008); DOI: 10.1007/s11012-007-9096-0.

  4. A. Hassan and T. S. Song, “Dynamic Anti-Plane Analysis for Two Symmetrically Interfacial Cracks near Circular Cavity in Piezoelectric Bi-Materials," Appl. Math. Mech. 35 (10), 1261–1270 (2014); DOI: 10.1007/s10483-014-1891-9.

  5. T. S. Song and A. Hassan, “Dynamic Anti-Plane Analysis for Symmetrically Radial Cracks near a Non-Circular Cavity in Piezoelectric Bi-Materials," Acta Mech. 226 (7), 2089–2101 (2015); DOI: 10.1007/s00707-015-1303-9.

  6. X. Q. Fang, C. Hu, and W. H. Huang, “Dynamic Stress of a Circular Cavity Buried in a Semi-Infinite Functionally Graded Piezoelectric Material Subjected to Shear Waves," Europ. J. Mech., A: Solids26 (6), 1016–1028 (2007); DOI: 10.1016/j.euromechsol.2007.05.003.

  7. X. Q. Fang, “Multiple Scattering of Electro-Elastic Waves from a Buried Cavity in a Functionally Graded Piezoelectric Material Layer," Int. J. Solids Struct. 45 (22/23), 5716–5729 (2008); DOI: 10.1016/j.ijsolstr.2008.06.014.

  8. X. Q. Fang, J. X. Liu, D. B. Wang, et al., “Dynamic Stress from a Subsurface Cavity in a Semi-Infinite Functionally Graded Piezoelectric/Piezomagnetic Material," Appl. Math. Model.34 (10), 2789–2805 (2010); DOI: 10.1016/j.apm.2009.12.013.

  9. Y. H. Yang, L. Z. Wu, and X. Q. Fang, “Non-Destructive Detection of a Circular Cavity in a Finite Functionally Graded Material Layer Using Anti-Plane Shear Waves," J. Nondestruct. Evaluat. 29(4), 233–240 (2010); DOI: 10.1007/s10921-010-0081-5.

  10. X. H. Wang, X. Q. Fang, J. X. Liu, et al., “Dynamic Stress from a Circular Hole in a Functionally Graded Piezoelectric/Piezomagnetic Material Subjected to Shear Waves," Philos. Mag. 89(33), 3059–3074 (2009); DOI:10.1080/14786430903179570.

  11. P. Dineva, D. Gross, R. Mueller, et al., “Dynamic Stress and Electric Field Concentration in a Functionally Graded Piezoelectric Solid with a Circular Hole," Z. Angew. Math. Mech.91 (2), 110–124 (2011); DOI: 10.1002/zamm.201000140.

  12. X. Y. Miao and G. Q. Li, “Analysis of Piezoelectric Plates with a Hole using Nature Boundary Integral Equation and Domain Decomposition," Eng. Anal. Bound. Elem. 40, 71–77 (2014); DOI: 10.1016/j.enganabound.2013.11.012.

  13. D. K. Liu and C. Hu, “Scattering of Flexural Waves and Dynamic Stress Concentrations in Mindlin Thick Plates with a Cutout," Acta Mech. Sinica 12 (2), 169–185 (1996); DOI: 10.1007/BF02486795.

  14. Y. H. Pao and C. C. Mow, Diffraction of Elastic Waves and Dynamic Stress Concentrations (Crane Russak, New York, 1973).

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Authors and Affiliations

  1. College of Civil Engineering and Transportation, Beihua University, 132013, Jilin, China

    X. L. Wang, X. J. Yang & R. Zhang

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  1. X. L. Wang
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  2. X. J. Yang
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  3. R. Zhang
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Correspondence to X. L. Wang.

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Wang, X.L., Yang, X.J. & Zhang, R. DYNAMIC STRESS CONCENTRATION IN A PIEZOELECTRIC MATERIAL WITH A NON-CIRCULAR HOLE SUBJECTED TO AN SH-WAVE. J Appl Mech Tech Phy 61, 661–668 (2020). https://doi.org/10.1134/S0021894420040203

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  • DOI: https://doi.org/10.1134/S0021894420040203

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