Skip to main content
SpringerLink
Log in

Wave Propagation Characteristics in Thick Conventional and Auxetic Cellular Plates

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Based on Mindlin plate models and Kirchhoff plate models, this study was concerned with the wave propagation characteristics in thick conventional and auxetic cellular structures, with the objective to clarify the effects of negative Poisson’s ratio, shear factor and orthotropic mechanical properties on the dynamic behaviors of thick plates. Numerical results revealed that the predictions using variable shear factor in Mindlin plate models resulted in high wave frequencies, which were more significant for plates with negative values of Poisson’s ratio. The present study can be useful for the design of critical applications by varying the values of Poisson’s ratio.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Liu, Y. and Hu, H., A review on auxetic structures and polymeric materials. Scientific Research and Essays, 2010, 5(10): 1052–1063.

    Google Scholar 

  2. Lakes, R., Foam structures with a negative Poisson’s ratio. Science, 1987, 235(4792): 1038–1040.

    Article  Google Scholar 

  3. Scarpa, F. and Tomlinson, G., Theoretical characteristics of the vibration of sandwich plates with in-plane negative Poisson’s ratio values. Journal of Sound and Vibration, 2000, 230(1): 45–67.

    Article  Google Scholar 

  4. Ruzzene, M., Scarpa, F. and Soranna, F., Wave beaming effects in two-dimensional cellular structures. Smart Materials and Structures, 2003, 12(3): 363–372.

    Article  Google Scholar 

  5. Scarpa, F., Ciffo, L.G. and Yates, J.R., Dynamic properties of high structural integrity auxetic open cell foam. Smart Materials and Structures, 2004, 13(1): 49–56.

    Article  Google Scholar 

  6. Alderson, A., Alderson, K.L., Attard, D., Evans, K.E., Gatt, R., Grima, J.N., Miller, W., Ravirala, N., Smith, C.W. and Zied, K., Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Composites Science and Technology, 2010, 70(7): 1042–1048.

    Article  Google Scholar 

  7. Alderson, A., Alderson, K.L., Chirima, G., Ravirala, N. and Zied, K.M., The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs. Composites Science and Technology, 2010, 70(7): 1034–1041.

    Article  Google Scholar 

  8. Michelis, P. and Spitas, V., Numerical and experimental analysis of a triangular auxetic core made of CFR-PEEK using the Directionally Reinforced Integrated Single-yarn (DIRIS) architecture. Composites Science and Technology, 2010, 70(7): 1064–1071.

    Article  Google Scholar 

  9. Maruszewski, B.T., Drzewiecki, A. and Starosta, R., Thermoelastic damping in an auxetic rectangular plate with thermal relaxation—free vibrations. Smart Materials and Structures, 2013, 22(8): 084003.

    Article  Google Scholar 

  10. Teik-Cheng, L., Shear deformation in thick auxetic plates. Smart Materials and Structures, 2013, 22(8): 084001.

    Google Scholar 

  11. Lim, T.C., Elastic stability of thick auxetic plates. Smart Materials and Structures, 2014, 23(4): 045004.

    Google Scholar 

  12. Lim, T.C., Vibration of thick auxetic plates. Mechanics Research Communications, 2014, 61: 60–66.

    Article  Google Scholar 

  13. Gibson, L.J. and Ashby, M.F., Cellular Solids Structures and Properties. Cambridge, UK: Cambridge University Press, 2001.

    MATH  Google Scholar 

  14. Mindlin, R.D., Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics, 1951, 18: 31–38.

    MATH  Google Scholar 

  15. Xu, X.J., Deng, Z.C., Meng, J.M. and Zhang, K., Bending and vibration analysis of generalized gradient elastic plates. Acta Mechanica, 2014, 225(12): 3463–3482.

    Article  MathSciNet  Google Scholar 

  16. Zhu, H.X. and Chen, C.Y., Combined effects of relative density and material distribution on the mechanical properties of metallic honeycombs. Mechanics of Materials, 2011, 43(5): 276–286.

    Article  Google Scholar 

  17. Reddy, J.N., Mechanics of laminated composite plate and shells: Theory and analysis. New York: CRC, 2007.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory for Special Area Highway Engineering of Ministry of Education, School of Highway, Chang’an University, 710064, Xi’an, China

    Xiaojian Xu

  2. Department of Engineering Mechanics, Northwestern Polytechnical University, 710072, Xi’an, China

    Xiaojian Xu & Zichen Deng

Authors
  1. Xiaojian Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zichen Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zichen Deng.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11172239), the 111 project (No. B07050) and the Doctoral Program Foundation of Education Ministry of China (20126102110023).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, X., Deng, Z. Wave Propagation Characteristics in Thick Conventional and Auxetic Cellular Plates. Acta Mech. Solida Sin. 29, 159–166 (2016). https://doi.org/10.1016/S0894-9166(16)30104-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(16)30104-5

Key Words

Search

Navigation