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Effect of Interface Damage on Band Structures in a Periodic Multilayer Plate

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Mechanics of Composite Materials Aims and scope

The interface/interphase is modeled by distributed springs, and the degree of interface damage is characterized by the flexibility coefficient of the springs. Considering different degrees of damage at different interfaces, a general dispersion equation by the transfer matrix method was obtained. For the purpose of application, the transmission coefficient of finite-period phononic crystals is also derived. Additionally, the band structures and the transmission coefficients are calculated for different degrees of damage to confirm the interface effect on band gaps. A numerical simulation of the transmission coefficient is performed using the commercial FEM software Comsol Multiphysics. The numerical results obtained agree well with the analytical solution. Finally, based on a monotonic decreasing relationship between the degree of interface damage and the central frequency of band gaps and a monotonic relationship between the degree of interface damage and the amplitude of transmission coefficients, a new method how to evaluate the degree of interface damage theoretically is proposed.

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References

  1. R. Rikards, A. Chate, A. K. Bledzki, et al., “Numerical modelling of damping properties of laminated composites,” Mech. Compos. Mater., 30, 256-266 (1994).

    Article  Google Scholar 

  2. N. D. Cristescu, E. M. Craciun, and E. Soos, Mechanics of Elastic Composites, Chapman & Hall / CRC Press, Boca Raton, Florida (2004).

    Google Scholar 

  3. U. Kaatze, F. Eggers, and K. Lautscham, “Ultrasonic velocity measurements in liquids with high resolution—techniques, selected applications and perspectives,” Measurement Science and Technology, 19, No. 6, 062001 (2008).

    Article  Google Scholar 

  4. M. Asif, M. A. Khan, S. Z. Khan, R. S. Choudhry, and K. A. Khan, “Identification of an effective nondestructive technique for bond defect determination in laminate composites — A technical review, ” Journal of Composite Materials, 0021998318766595 (2018).

  5. X. Liu, L. Bo, Y. Liu, Y. Zhao, J. Zhang, M. Deng, and N. Hu, “Location identification of closed crack based on Duffing oscillator transient transition,” Mech. Syst. Signal Pr., 100, 384-397 (2018).

    Article  Google Scholar 

  6. W. Xisen, W. Jihong, and Y. Dianlong, Phononic Crystals [in Chinese], National Defence Industry Press, Beijing (2009).

    Google Scholar 

  7. L. Donglong, et al., “Elastic fields caused by eigenstrains in two joined half-spaces with an interface of coupled imperfections: Dislocation-like and force-like conditions,” International Journal of Engineering Science, 126, 22-52 (2018).

    Article  Google Scholar 

  8. W. Yuesheng, Y. Guilan, Z. Zimao, et al, “Review on elastic wave propagation under complex interface (interface layer) conditions,” Advances in Mechanics, 30, No. 3, 378-390 (2000).

    Google Scholar 

  9. L. Nazarenko, H. Stolarski, and H. Altenbach, “A model of cylindrical inhomogeneity with spring layer interphase and its application to analysis of short-fiber composites,” Composite Structures, 160, 635-652 (2017).

    Article  Google Scholar 

  10. X. Liu and P. Wei, “Estimation of interface damage of fiber-reinforced composites,” Mech. of Compos. Mater., 44, No.1, 37-44 (2008).

    Article  Google Scholar 

  11. Y. Shi, Y. Wan, and Z. Zhong, “Dynamic effective property of fibrous piezoelectric composites with spring-or membranetype imperfect interfaces,” Mechanics Research Communications, 84, 116-124 (2017).

    Article  Google Scholar 

  12. Z. An, X. Wang, M. Deng, et al, “A nonlinear spring model for an interface between two solids,” Wave Motion, 50, No. 2, 295-309 (2013).

  13. S. I. Rokhlin, A. Baltazar, B. Xie, J. Chen, and R. Reuven. “Method for monitoring environmental degradation of adhesive bonds,” Materials Evaluation, 60, No. 6, 795-801 (2002).

  14. J. Chen, D. Zhang, Y. Mao, and J. Cheng, “Contact acoustic nonlinearity in a bonded solid–solid interface,” Ultrasonics, 44, e1355-e1358 (2006).

    Article  Google Scholar 

  15. N. Peride, A. Carabineanu, and E. M. Craciun, “Mathematical modelling of the interface crack propagation in a prestressed fiber reinforced elastic composite,” Comp. Mater. Sci., 45, No. 3, 684-692 (2009).

    Article  CAS  Google Scholar 

  16. W. Liu, J. Chen, Y. Liu, and X. Su, “Effect of interface/surface stress on the elastic wave band structure of two-dimensional phononic crystals,” Phys. Lett. A., 376, 605-609 (2012).

    Article  CAS  Google Scholar 

  17. S. P. Hepplestone and G. P. Srivastava, “Hypersonic modes in nanophononic semiconductors,” Phys. Rev. Lett., 101, 105502 (2008).

    Article  CAS  Google Scholar 

  18. N. Zhen, Y. Wang, and C. Zhang, “Bandgap calculation of in-plane waves in nanoscale phononic crystals taking account of surface/interface effects,” Physica E: Low-dimensional Systems and Nanostructures, 54, 125-132 (2013).

    Article  CAS  Google Scholar 

  19. M. Zheng and P. Wei, “Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces,” Int. J. Miner. Metall. Mater., 16, 608-614 (2009).

    Article  CAS  Google Scholar 

  20. R. Leiderman, J. C. Figueroa, A. M. B. Braga and F. A. Rochinha, “Scattering of ultrasonic guided waves by heterogeneous interfaces in elastic multilayered structures,” Wave Motion, 63, 68-82 (2016).

    Article  Google Scholar 

  21. I. V. Andrianov, V. V. Danishevskyy, H. Topol, and G. A. Rogerson, “Propagation of Floquet–Bloch shear waves in viscoelastic composites: analysis and comparison of interface/interphase models for imperfect bonding," Acta Mechanica, 228, 1177-1196 (2017).

    Article  Google Scholar 

  22. S. I. Rokhlin and Y. J. Wang, “Analysis of boundary conditions for elastic wave interaction with an interface between two solids,” J. Acoust. Soc. Am., 89, 503-515 (1991).

    Article  Google Scholar 

  23. J. L. Rose. Ultrasonic Waves in Solid Media [in Chinese], Science Press, Beijing China (2004) (C. He, B. Wu, and Y. Wang, Transl.)

  24. N. A. Haskell, “The dispersion of surface waves on multilayered media,” B. Seismol. Soc. Am., 43, No. 1, 17-34 (1953).

    Google Scholar 

  25. M. J. S. Lowe, “Matrix techniques for modeling ultrasonic waves in multilayered media,” IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 42, No. 4, 525-542 (1995).

  26. S. I. Rokhlin and D. Marom, “Study of adhesive bonds using low-frequency obliquely incident ultrasonic waves,” J. Acoust. Soc. Am., 80, No. 2, 585-590 (1986).

    Article  Google Scholar 

  27. A. Pilarski and J. L. Rose, “Ultrasonic oblique incidence for improved sensitivity in interface weakness determination,” J. Appl. Phys., 62, No. 2, 300-307 (1988).

    Article  Google Scholar 

  28. S. I. Tamura, D. C. Hurley, and J. P. Wolfe, “Acoustic-phonon propagation in superlattices,” Physical Review B, 38, No.2, 1427-1449 (1988).

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Acknowledgement

This work was supported by the National Key R&D Program of China (Grant No. 2017YFA0303700), the National Natural Science Foundation of China (Grant Nos. 11374157, 11634006, and 81127901), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and Advanced Research Foundation of Army Engineering University of PLA.

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Authors and Affiliations

  1. Collaborative Innovation Center of Advanced Microstructures and Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing, 210093, P.R. China

    X. Liu, Z. Gong, X. Wang, J. Yang, B. Liang & J. Cheng

  2. Department of General Education, Army Engineering University of PLA, Nanjing, 211101, P.R. China

    X. Liu

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  1. X. Liu
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  2. Z. Gong
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  3. X. Wang
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  4. J. Yang
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  5. B. Liang
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  6. J. Cheng
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Corresponding author

Correspondence to J. Cheng.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 55, No. 6, pp. 1139-1154, November-December, 2019.

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Liu, X., Gong, Z., Wang, X. et al. Effect of Interface Damage on Band Structures in a Periodic Multilayer Plate. Mech Compos Mater 55, 785–796 (2020). https://doi.org/10.1007/s11029-020-09850-0

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  • DOI: https://doi.org/10.1007/s11029-020-09850-0

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