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Flexural wave propagation in narrow Mindlin’s plate

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Abstract

Appling Mindlin’s theory of thick plates and Hamilton system to propagation of elastic waves under free boundary condition, a solution of the problem was given. Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method. It was compared with the dispersion relation that was gained through solution of thick plate theory proposed by Mindlin. Based on the two kinds of theories, the dispersion curves show great difference in the region of short waves, and the cutoff frequencies are higher in Hamiltonian systems. However, the dispersion curves are almost the same in the region of long waves.

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References

  1. Reissner E. The effect of transverse shear deformation on the bending of elastic plates[J]. Journal of Applied Mechanics, 1945, 12(2):69–77.

    MathSciNet  Google Scholar 

  2. Reissner E. On the theory of transverse bending of elastic plates[J]. Internal Journal of Solids and Structures, 1976, 12(8):545–554.

    Article  MATH  MathSciNet  Google Scholar 

  3. Mindlin R D. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates[J]. Journal of Applied Mechanics, 1951, 18(2):31–38.

    MATH  Google Scholar 

  4. Pao Y H. Diffractions of flexural waves by a cavity in an elastic plate[J]. AIAA, 1964, 2(1):2000–2010.

    MathSciNet  Google Scholar 

  5. Liu D K, Hu C. Scattering of flexural wave and dynamic stress concentrations in Mindlin’s thick plates[J]. Acta Mechanica Sinica, 1996, 12(2):69–185.

    Google Scholar 

  6. Narris Andrew N. Flexural waves on narrow plates[J]. J Acoust Soc Amer, 2003, 113(5):2647–2658.

    Article  Google Scholar 

  7. Xu P C, Datta S K. Guided waves in a bonded plate: a parametric study[J]. Journal of Applied Physics, 1990, 67(11):6779–6786.

    Article  Google Scholar 

  8. Timoshenko S P, Goodier J N. Theory of Elasticity[M]. McGraw-Hill, London, 1951, 15–66.

    Google Scholar 

  9. Zhong Wanxie. A New Systematic Methodology of Theory of Elasticity[M]. Dalian University of Technology Press, Dalian, 1995, 20–97 (in Chinese).

    Google Scholar 

  10. Zhong Wanxie, Yao Wei’an. New solution systems for plate bending and its application[J]. Acta Mechanica Sinica, 1999, 31(2):173–184 (in Chinese).

    Google Scholar 

  11. Hu Haichang. Variational Principle in Elasticity and Its Applications[M]. Science Press, Beijing, 1981, 50–83 (in Chinese).

    Google Scholar 

  12. Huang Zhixun. Waveguide Theory with Cutoff Frequenc[M]. Measurement Press of China, Beijing, 1991, 42–97 (in Chinese).

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Aerospace Engineering, Harbin Institute of Technology, Harbin, 150001, P. R. China

    Hu Chao  (胡超) (Professor), Han Gang  (韩刚), Fang Xue-qian  (房学谦) & Huang Wen-hu  (黄文虎)

  2. School of Aerospace Engineering and Mechanics, Tongji University, Shanghai, 200092, P. R. China

    Hu Chao  (胡超) (Professor)

Authors
  1. Hu Chao  (胡超)
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  2. Han Gang  (韩刚)
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  3. Fang Xue-qian  (房学谦)
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  4. Huang Wen-hu  (黄文虎)
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Corresponding author

Correspondence to Hu Chao  (胡超).

Additional information

Communicated by ZHONG Wan-xie

Project supported by the National Natural Science Foundation of China (No.10572045)

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Hu, C., Han, G., Fang, Xq. et al. Flexural wave propagation in narrow Mindlin’s plate. Appl Math Mech 27, 793–801 (2006). https://doi.org/10.1007/s10483-006-0610-y

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  • DOI: https://doi.org/10.1007/s10483-006-0610-y

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2000 Mathematics Subject Classification

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