Acta Mechanica Sinica

, Volume 34, Issue 3, pp 493–506 | Cite as

Macroscopic damping model for structural dynamics with random polycrystalline configurations

  • Yantao Yang
  • Junzhi CuiEmail author
  • Yifan Yu
  • Meizhen Xiang
Research Paper


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.


Polycrystalline cluster Dynamical equation Damping coefficient Two-scale homogenization method Atomic–Continuum Coupled Model 



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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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Yantao Yang
    • 1
  • Junzhi Cui
    • 1
    Email author
  • Yifan Yu
    • 1
  • Meizhen Xiang
    • 2
  1. 1.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Laboratory of Computational PhysicsInstitute of Applied Physics and Computational MathematicsBeijingChina

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