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Difference discrete system of Euler-beam with arbitrary supports and sign-oscillatory property of stiffness matrices

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Abstract

The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory of oscillatory matrix, the signoscillatory property of stiffness matrices of this system was proved, and the necessary and sufficient condition for the system to be positive was obtained completely.

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References

  1. Gantmakher F P, Krein M G. Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems[M]. State Publishing House for Technical and Theoretical Literature, Moscow, 1950 (in Russian). (transl) AEC, Washington D C, US, 1961 (English Version).

    Google Scholar 

  2. Gladwell G M L. Inverse Problems in Vibration[M]. Martinus Nijhoff Publishers, Boston, 1986, 23–26, 219–225.

    Google Scholar 

  3. Gladwell G M L. Qualitative properties of vibration systems[J]. Proc Roy Soc London, Series A, 1985, 401: 299–315.

    MATH  MathSciNet  Google Scholar 

  4. He Beichang, Wang Dajun, Wang Qishen. Inverse problem for the finite difference model of euler beam in vibration[J]. J Vibration Engineering, 1989, 2(2): 1–9 (in Chinese).

    Google Scholar 

  5. Wang Qishen, He Beichang, Wang Dajun. Some qualitative properties of frequencies and modes of euler beams[J], J Vibration Engineering, 1990, 3(4): 58–66 (in Chinese).

    MathSciNet  Google Scholar 

  6. Wang Dajun, Chon C S, Wang Qishen. Qualitative properties of frequencies and modes of beams modeled by discrete systems[J]. The Chinese J of Mechanics, Series A, 2003, 19(1): 169–175.

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Anqing Teachers College, Anqing, 246011, Anhui Province, P. R. China

    Wang Qi-shen  (王其中) (Professor)

  2. State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing, 100871, P. R. China

    Wang Da-jun  (王大钧)

  3. Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, P. R. China

    Wang Da-jun  (王大钧)

Authors
  1. Wang Qi-shen  (王其中)
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  2. Wang Da-jun  (王大钧)
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Corresponding author

Correspondence to Wang Qi-shen  (王其中).

Additional information

Communicated by YE Qing-kai

Project supported by the National Natural Science Foundation of China (No. 60034010)

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Wang, Qs., Wang, Dj. Difference discrete system of Euler-beam with arbitrary supports and sign-oscillatory property of stiffness matrices. Appl Math Mech 27, 393–398 (2006). https://doi.org/10.1007/s10483-006-0316-y

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  • DOI: https://doi.org/10.1007/s10483-006-0316-y

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2000 Mathematics Subject Classification

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