Close Eigenvalues of Periodic Structures With Finite Unit Cells

WU Feng; GAO Qiang; ZHONG Wan-xie

doi:10.3879/j.issn.1000-0887.2013.11.001

Volume 34 Issue 11

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WU Feng, GAO Qiang, ZHONG Wan-xie. Close Eigenvalues of Periodic Structures With Finite Unit Cells[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1119-1129. doi: 10.3879/j.issn.1000-0887.2013.11.001

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Close Eigenvalues of Periodic Structures With Finite Unit Cells

doi: 10.3879/j.issn.1000-0887.2013.11.001

State Key Laboratory of Structural Analysis of Industrial Equipment; Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2009CB918501）

Received Date: 2013-07-31
Rev Recd Date: 2013-09-01
Publish Date: 2013-11-15

Abstract

Abstract

For a periodic structure with finite unit cells, the range where eigenvalues existed was estimated based on the eigenproblem of the unit cell. A more precise estimate of the eigenvalue distriution range for a one dimensional periodic structure with finite unit cells was presented based on the energy band theory in solid physics. In terms of the estimated range of eigenvalues, the close eigenvalue phenomenon was made clear. The analysis results show that, for a periodic structure with finite unit cells, the larger the number of the unit cells is, the closer the eigenvalues are. Numerical tests demonstrate the correctness of the proposed conclusions.
- periodic structure,
- close eigenvalue,
- energy band,
- symplectic

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References(17)

References

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