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Macroscopic damping model for structural dynamics with random polycrystalline configurations

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Abstract

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro–nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom (SDOF) along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro–nano scales is set up.

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Fig. 1

(Source: “Microstructure of VT22 (Ti5Al5Mo5V1,5Cr) after quenching” by Edward Pleshakov, used under the CC BY-SA 3.0 license)

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Acknowledgements

This work was partially supported by the National Basic Research Program of China (973 Program Grant 2012CB025904), the National Natural Science Foundation of China (Grant 11102221), and the State Key Laboratory of Science and Engineering Computing (LSEC).

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yantao Yang, Junzhi Cui & Yifan Yu

  2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Meizhen Xiang

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  1. Yantao Yang
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  2. Junzhi Cui
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  3. Yifan Yu
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  4. Meizhen Xiang
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Correspondence to Junzhi Cui.

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Yang, Y., Cui, J., Yu, Y. et al. Macroscopic damping model for structural dynamics with random polycrystalline configurations. Acta Mech. Sin. 34, 493–506 (2018). https://doi.org/10.1007/s10409-017-0733-0

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  • DOI: https://doi.org/10.1007/s10409-017-0733-0

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