Structural Engineering and Mechanics

Techno-Press (테크노프레스)
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Locating a weakened interface in a laminated elastic plate

  • Zhu, J. (Department of Civil Engineering, Zhejiang University, Zijingang Campus) ;
  • Yang, J.S. (Department of Engineering Mechanics, University of Nebraska) ;
  • Chen, W.Q. (State Key Lab of CAD & CG, Zhejiang University, Zijingang Campus)
  • Received : 2011.03.08
  • Accepted : 2012.02.21
  • Published : 2012.03.25
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Abstract

We study thickness-shear (TSh) free vibrations of an unbounded, laminated elastic plate with three layers of different materials. One of the two interfaces is slightly weakened as described by the shear-lag model that allows the displacement to be discontinuous across the interface. A frequency equation is obtained from the linear theory of elasticity. A perturbation solution of the frequency equation is obtained from which the frequency shifts of TSh modes due to the weakened interface can be calculated. It is shown that the frequency shifts of TSh modes of different orders are different, and they satisfy different conditions when different interfaces are weakened. These conditions are obtained which can potentially be used as criteria for determining specifically which interface is weakened.

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References

  1. Accuratus Corporation, "Fused Silica, $SiO_2$ Material Properties", http://accuratus.com/fused.html, 2012-02-02.
  2. Chen, W.Q., Cai, J.B. and Ye, G.R. (2003), "Exact solutions of cross-ply laminates with bonding imperfections", AIAA J., 41(11), 2244-2250. https://doi.org/10.2514/2.6817
  3. Chen, W.Q., Cai, J.B. and Ye, G.R. (2005), "Responses of cross-ply laminates with viscous interfaces in cylindrical bending," Comput. Meth. Appl. M., 194(6-8), 823-835. https://doi.org/10.1016/j.cma.2004.06.016
  4. Chen, W.Q., Wang, Y.F., Cai, J.B. and Ye, G.R. (2004), "Three-dimensional analysis of cross-ply laminated cylindrical panels with weak interfaces", Int. J. Solids Struct., 41(9-10), 2429-2446. https://doi.org/10.1016/j.ijsolstr.2003.12.018
  5. Chen, Y.J., Shib, Y.W. and Zhang, X.P. (1998), "Detection of weak bonding in friction welds by ultrasound", Ultrasonics, 36(1-5), 141-146. https://doi.org/10.1016/S0041-624X(97)00143-1
  6. Cheng, Z.Q., Kennedy, D. and Williams, F.W. (1996), "Effect of interfacial imperfection on buckling and bending behavior of composite laminates", AIAA J., 34(12), 2590-2595. https://doi.org/10.2514/3.13443
  7. Di Sciuva, M. (1997), "Geometrically nonlinear theory of multilayered plates with interlayer slips", AIAA J., 35(11), 1753-1759. https://doi.org/10.2514/2.23
  8. Fan, H., Yang, J.S. and Xu, L.M. (2006), "Piezoelectric waves near an imperfectly bonded interface between two half-spaces", Appl. Phys. Lett., 88(20), 203509. https://doi.org/10.1063/1.2206702
  9. Friswell, M.I. (2007), "Damage identification using inverse methods", Phil. Trans. R. Soc. A., 365(1851), 393-410. https://doi.org/10.1098/rsta.2006.1930
  10. Friswell, M.I. and Mottershead, J.E. (2001), "Inverse methods in structural health monitoring", Key Eng. Mat., 204-205, 201-210. https://doi.org/10.4028/www.scientific.net/KEM.204-205.201
  11. Icardi, U., Di Sciuva, M. and Librescu, L. (2000), "Dynamic response of adaptive cross-ply cantilevers featuring interlaminar bonding imperfections", AIAA J., 38(3), 499-506. https://doi.org/10.2514/2.988
  12. Jin, F., Kishimoto, K., Inoue, H. and Tateno, T. (2005), "Experimental investigation on the interface properties evaluation in piezoelectric layered structures by loves waves propagation", Key Eng. Mat., 297-300, 807-812. https://doi.org/10.4028/www.scientific.net/KEM.297-300.807
  13. Kumar, R. and Singh, M. (2009), "Effect of rotation and imperfection on reflection and transmission of plane waves in anisotropic generalized thermoelastic media", J. Sound Vib., 324(3-5), 773-797. https://doi.org/10.1016/j.jsv.2009.02.024
  14. Li, F.M., Wang, Y.Z., Fang, B. and Wang, Y.S. (2007), "Propagation and localization of two- dimensional inplane elastic waves in randomly disordered layered piezoelectric phononic crystals", Int. J. Solids Struct., 44(22-23), 7444-7456. https://doi.org/10.1016/j.ijsolstr.2007.04.021
  15. Librescu, L. and Schmidt, R. (2001), "A general linear theory of laminated composite shells featuring interlaminar bonding imperfections", Int. J. Solids Struct., 38(19), 3355-3375. https://doi.org/10.1016/S0020-7683(00)00263-8
  16. Lu, X. and Liu, D. (1992), "Interlaminar shear slip theory for cross-ply laminates with non-rigid interfaces", AIAA J., 30(4), 1063-1073. https://doi.org/10.2514/3.11028
  17. Piskunov, V.G. and Rasskazov, A.O. (2002), "Evolution of the theory of laminated plates and shells", Int. Appl. Mech., 38(2), 135-166. https://doi.org/10.1023/A:1015756726070
  18. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton.
  19. Rinker, B.A., Jamieson, E.E., Samayoa, J.A., Abeln, T.G., Lerch, T.P. and Neal, S.P. (2003), "Detection of weak interface signals for same material bond/weld inspection", AIP Conf. Proc., 657(1), 1080-1087.
  20. Shu, X.P. (2001), "Vibration and bending of antisymmetrically angle-ply laminated plates with perfectly and weakly bonded layers", Compos. Struct., 53(2), 245-255. https://doi.org/10.1016/S0263-8223(01)00008-3
  21. Tomar, S.K. and Gogna, M.L. (1995), "Reflection and refraction of longitudinal wave at an interface between two micropolar elastic solids in welded contact", J. Acoust. Soc. Am., 97(2), 822-830. https://doi.org/10.1121/1.413086
  22. Tsubouchi, K., Sugai, K. and Mikoshiba, N. (1981), "AlN material constants evaluation and SAW properties on $AlN/Al_2O_3$ and AlN/Si", IEEE Ultrasonics Symp., 375-380.
  23. Wang, Y.Z., Li, F.M., Huang, W.H. and Wang, Y.S. (2008), "The propagation and localization of Rayleigh waves in disordered piezoelectric phononic crystals", J. Mech. Phys. Solids, 56(4), 1578-1590. https://doi.org/10.1016/j.jmps.2007.07.014
  24. Wang, Y.Z., Li, F.M., Kishimoto, K., Wang, Y.S. and Huang, W.H. (2010), "Wave localization in randomly disordered layered three-component phononic crystals with thermal effects", Arch. Appl. Mech., 80(6), 629-640. https://doi.org/10.1007/s00419-009-0329-7
  25. Yang, J.S., Hu, Y.T., Zeng, Y. and Fan, H. (2006), "Thickness-shear vibration of rotated Y-cut quartz plates with imperfectly bonded surface mass layers", IEEE Trans. Ultrason. Ferroelect. Freq. Contr., 53(1), 241-245. https://doi.org/10.1109/TUFFC.2006.1588410
  26. Yang, S., Gu, L. and Gibson R.F. (2001), "Nondestructive detection of weak joints in adhesively bonded composite structures", Compos. Struct., 51(1), 63-71. https://doi.org/10.1016/S0263-8223(00)00125-2

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