International Journal of Applied Mathematics and Theoretical Physics

| Peer-Reviewed |

Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave

Received: 29 April 2019    Accepted: 21 May 2019    Published: 20 June 2019
Views:       Downloads:

Share This Article

Abstract

With the rapid development of nanotechnology, nano-components and nano-materials will be widely concerned and applied. At the nano-scale, due to the obvious increase the ratio of surface area to the volume effect and surface effect of nano-components and nano-materials are significant, making their mechanical properties significantly different from the material properties under the macroscopic conditions. And in the practical cases, the interface is not always perfect and smooth, they always have a certain form of defects. Therefore, the wave function expansion method is used in the analytical solutions of dynamic stress concentration factor (DSCF) around a coated fiber with an imperfect interface at nano-scale. The stress boundary conditions on the interface are obtained by using the generalized Young-Laplace equation and the imperfect displacement boundary conditions on the interface are modeled by a spring model. Considering the effects of surface and spring model, the influence of spring stiffness, the number of incident wave and the surface effects on the DSCF are analyzed. The results show that the frequency of incident wave, the spring stiffness and the surface energy have significant effects on the dynamic stress concentration distributions of the nano-sized coated fiber. The smaller the spring coefficient is, the stronger the interface imperfection is, and the stronger the stress concentration at the boundary is. When the spring coefficient reaches a certain value, it is almost close to the dynamic stress value under the ideal interface. The DSCF are obviously different under different incident wave frequencies.

DOI 10.11648/j.ijamtp.20190502.11
Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 5, Issue 2, June 2019)
Page(s) 38-44
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Scattering, Plane Compressional Wave, Imperfect Interface, Surface Effect, Dynamic Stress Concentration Factor

References
[1] Yi, C. P., Zhang, P., Johansson, D. and Nyberg, U. (2014) Dynamic response of a circular lined tunnel with an imperfect interface subjected to cylindrical P-waves. Computers and Geotechnics, 55, 165-171.
[2] Yi, C. P., Lu, W. B., Zhang, P., Johansson, D. and Nyberg, U. (2016) Effect of imperfect interface on the dynamic response of a circular lined tunnel impacted by plane P-waves. Tunneling and Underground Space Technology, 51, 68-74.
[3] Fang, X. Q., Huang, H. C. and Liu, J. X. (2016) Predicting the crack opening displacements of a partially debonded pipeline in rock mass under P waves. Engineering Materials and Structures, 39, 886-895.
[4] Fang, X. Q., Jin, H. X., Liu, J. X. and Huang, M. J. (2016) Imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to shear waves. Tunnelling and Underground Space Technology, 56, 226-231.
[5] Fang, X. Q. and Jin, H. X. (2016) Visco-elastic imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to P and SV waves. Soil Dynamics and Earthquake Engineering, 88, 1-7.
[6] Fang, X. Q. and Jin, H. X. (2017) Dynamic response of a non-circular lined tunnel with visco-elastic imperfect interface in the saturated poroelastic medium. Computers and Geotechnics, 83, 98–105.
[7] Qin, B., Chen, J. J. and Cheng, J. C. (2005) Local resonant characteristics of a layered cylinder embedded in the elastic medium. Chinese Physics, 14, 2522-2528.
[8] Stamos, A. A. and Beskos, D. E. (1996) 3-D seismic response analysis of long lined tunnels in half-space. Soil Dynamics and Earthquake Engineering, 15, 111–118.
[9] Esmaeili M., Vahdani S. and Noorzad, A. (2006) Dynamic response of lined circular tunnel to plane harmonic waves. Tunneling and Underground Space Technology, 21, 511–519.
[10] Valier-Brasier, T., Dehoux, T. and Bertrand, A. (2012) Scaled behavior of interface waves at an imperfect solid-solid interface. Journal of Applied Physics, 112, 1-12.
[11] Wang, T. T., Hu, J. T., Chen, C. H. and Huang, T. H. (2014) Response of a tunnel in double layer rocks subjected to harmonic P and S waves. International Journal of Rock Mechanics and Mining Sciences, 70, 435–443.
[12] Huang, W., Wang, Y. J. and Rokhlin, S. I. (1996) Oblique scattering of an elastic wave from a multilayered cylinder in a solid. Journal of Acoustical Society of America, 99, 2742-2754.
[13] Hasheminejad, S. M. and Rajabi, M. (2007) Acoustic resonance scattering from a submerged functionally graded cylindrical shell. Journal of Sound and Vibration, 302, 208-228.
[14] Shindo, Y. and Niwa, N. (1996) Scattering of antiplane shear waves in a fiber-reinforced composite medium with interfacial layers. Acta Mechanica, 117, 181-190.
[15] Li, F. M., Hu, C. and Huang, W. H. (2002) Scattering of elastic waves in an elastic matrix containing an inclusion with interfaces. Acta Mechanica Solida Sinica, 15, 270-276.
[16] Gleiter, H. (2000) Nanostructured Materials: Basic Concepts and Microstructure. Acta Materialia, 4, 1-29.
[17] Gurtin, M. E. and Murdoch, A. I. (1975) A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 57, 291-323.
[18] Gurtin, M. E., Weissmüller, J. and Larché, F. (1998) A general theory of curved deformable interfaces in solids at equilibrium. Philosophical Magazine A, 78, 1093-1109.
[19] Wang, G. F. and Wang, T. J. (2006) Surface effects on the diffraction of plane compressional waves by a nano-sized circular hole. Applied Physics Letters, 89, 1-3.
[20] Wang, G. F. (2007) Diffraction of plane compressional wave by a nano-sized spherical cavity with surface effects. Applied Physics Letters, 90, 1-3.
[21] Wang, G. F. (2009) Multiple diffraction of plane compressional waves by two circular cylindrical holes with surface effects. Journal of Applied Physics, 105, 1-6.
[22] Ru, Y., Wang, G. F. and Wang, T. J. (2009) Diffraction of elastic waves and stress concentration near a cylindrical nano-Inclusion incorporating surface effect. Journal of Vibration and Acoustics, 131, 1-7.
[23] Ou, Z. Y. and Lee, D. W. (2012) Effects of interface energy on multiple scattering of plane compressional waves by two cylindrical fibers. International Journal of Applied Mechanics, 4, 1-19.
[24] Ru, Y., Wang, G. F., Su, L. C. and Wang, T. J. (2013) Scattering of vertical shear waves by a cluster of nano-sized cylindrical holes with surface effect. Acta Mechanica, 224, 935-944.
[25] Ou, Z. Y. and Lee, D. W. (2012) Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber. Journal of Sound and Vibration, 331, 5623-5643.
[26] Pao, Y. H. and Mow, C. C. (1973) Diffraction of elastic waves and dynamic stress concentrations. New York: Crane Russak & Company.
[27] Fan, Z. F., Zhang J. C., Xu H. (2019) Theoretical study of the dynamic response of a circular lined tunnel with an imperfect interface subjected to incident SV-waves. Computers and Geotechnics, 110, 308-318.
Author Information
  • School of Science, Lanzhou University of Technology, Lanzhou, China

  • School of Science, Lanzhou University of Technology, Lanzhou, China

  • School of Science, Lanzhou University of Technology, Lanzhou, China

Cite This Article
  • APA Style

    Dongxia Lei, Lizhen Wang, Zhiying Ou. (2019). Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave. International Journal of Applied Mathematics and Theoretical Physics, 5(2), 38-44. https://doi.org/10.11648/j.ijamtp.20190502.11

    Copy | Download

    ACS Style

    Dongxia Lei; Lizhen Wang; Zhiying Ou. Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave. Int. J. Appl. Math. Theor. Phys. 2019, 5(2), 38-44. doi: 10.11648/j.ijamtp.20190502.11

    Copy | Download

    AMA Style

    Dongxia Lei, Lizhen Wang, Zhiying Ou. Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave. Int J Appl Math Theor Phys. 2019;5(2):38-44. doi: 10.11648/j.ijamtp.20190502.11

    Copy | Download

  • @article{10.11648/j.ijamtp.20190502.11,
      author = {Dongxia Lei and Lizhen Wang and Zhiying Ou},
      title = {Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {5},
      number = {2},
      pages = {38-44},
      doi = {10.11648/j.ijamtp.20190502.11},
      url = {https://doi.org/10.11648/j.ijamtp.20190502.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijamtp.20190502.11},
      abstract = {With the rapid development of nanotechnology, nano-components and nano-materials will be widely concerned and applied. At the nano-scale, due to the obvious increase the ratio of surface area to the volume effect and surface effect of nano-components and nano-materials are significant, making their mechanical properties significantly different from the material properties under the macroscopic conditions. And in the practical cases, the interface is not always perfect and smooth, they always have a certain form of defects. Therefore, the wave function expansion method is used in the analytical solutions of dynamic stress concentration factor (DSCF) around a coated fiber with an imperfect interface at nano-scale. The stress boundary conditions on the interface are obtained by using the generalized Young-Laplace equation and the imperfect displacement boundary conditions on the interface are modeled by a spring model. Considering the effects of surface and spring model, the influence of spring stiffness, the number of incident wave and the surface effects on the DSCF are analyzed. The results show that the frequency of incident wave, the spring stiffness and the surface energy have significant effects on the dynamic stress concentration distributions of the nano-sized coated fiber. The smaller the spring coefficient is, the stronger the interface imperfection is, and the stronger the stress concentration at the boundary is. When the spring coefficient reaches a certain value, it is almost close to the dynamic stress value under the ideal interface. The DSCF are obviously different under different incident wave frequencies.},
     year = {2019}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave
    AU  - Dongxia Lei
    AU  - Lizhen Wang
    AU  - Zhiying Ou
    Y1  - 2019/06/20
    PY  - 2019
    N1  - https://doi.org/10.11648/j.ijamtp.20190502.11
    DO  - 10.11648/j.ijamtp.20190502.11
    T2  - International Journal of Applied Mathematics and Theoretical Physics
    JF  - International Journal of Applied Mathematics and Theoretical Physics
    JO  - International Journal of Applied Mathematics and Theoretical Physics
    SP  - 38
    EP  - 44
    PB  - Science Publishing Group
    SN  - 2575-5927
    UR  - https://doi.org/10.11648/j.ijamtp.20190502.11
    AB  - With the rapid development of nanotechnology, nano-components and nano-materials will be widely concerned and applied. At the nano-scale, due to the obvious increase the ratio of surface area to the volume effect and surface effect of nano-components and nano-materials are significant, making their mechanical properties significantly different from the material properties under the macroscopic conditions. And in the practical cases, the interface is not always perfect and smooth, they always have a certain form of defects. Therefore, the wave function expansion method is used in the analytical solutions of dynamic stress concentration factor (DSCF) around a coated fiber with an imperfect interface at nano-scale. The stress boundary conditions on the interface are obtained by using the generalized Young-Laplace equation and the imperfect displacement boundary conditions on the interface are modeled by a spring model. Considering the effects of surface and spring model, the influence of spring stiffness, the number of incident wave and the surface effects on the DSCF are analyzed. The results show that the frequency of incident wave, the spring stiffness and the surface energy have significant effects on the dynamic stress concentration distributions of the nano-sized coated fiber. The smaller the spring coefficient is, the stronger the interface imperfection is, and the stronger the stress concentration at the boundary is. When the spring coefficient reaches a certain value, it is almost close to the dynamic stress value under the ideal interface. The DSCF are obviously different under different incident wave frequencies.
    VL  - 5
    IS  - 2
    ER  - 

    Copy | Download

  • Sections