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Dispersion curves of 2D rods with complex cross-sections: double orthogonal polynomial approach

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Abstract

Orthogonal polynomial series approach has been used to analyze the guided wave propagation in structures for about 20 years. These structures have always one infinite dimension in the waveguiding direction and, sometimes a regular finite cross-section (axially infinite solid or hollow cylinder for instance) and mostly often an infinite cross-section (infinite flat plate or half-space for instance). This paper presents a double orthogonal polynomial approach to investigate guided wave propagation in structures with only one infinite dimension in the waveguiding direction and a finite but complicated cross-sectional geometries as, rectangular type, L-type, 工-type and 回-type cross-sections. Through a numerical comparison with results available in literature, the validity of the extended polynomial approach is illustrated for a specific geometry. The dispersion properties of guided waves in rods with complex cross-sections as mentioned above are discussed.

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Acknowledgments

The work was supported by the National Natural Science Foundation of China (No. 11272115), the Outstanding Youth Science Foundations of Henan Province (No. 144100510016). Jiangong Yu gratefully acknowledges the support by the Alexander von Humboldt-Foundation (AvH) to conduct his research work at the Chair of Structural Mechanics, University of Siegen, Germany.

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, 454003, People’s Republic of China

    J. G. Yu

  2. Department of Civil Engineering, University of Siegen, 57068, Siegen, Germany

    J. G. Yu & Ch. Zhang

  3. Université Lille Nord de France, 59000, Lille, France

    J. E. Lefebvre

  4. IEMN-DOAE, UVHC, 59313, Valenciennes Cedex 9, France

    J. E. Lefebvre

  5. CNRS, UMR 8520, 59650, Villeneuve d’Ascq, France

    J. E. Lefebvre

  6. LAPAUF, Université de Fianarantsoa, Fianarantsoa, Madagascar

    F. E. Ratolojanahary

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  1. J. G. Yu
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  2. J. E. Lefebvre
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  3. Ch. Zhang
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  4. F. E. Ratolojanahary
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Correspondence to J. G. Yu.

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Yu, J.G., Lefebvre, J.E., Zhang, C. et al. Dispersion curves of 2D rods with complex cross-sections: double orthogonal polynomial approach. Meccanica 50, 109–117 (2015). https://doi.org/10.1007/s11012-014-0058-z

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  • DOI: https://doi.org/10.1007/s11012-014-0058-z

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