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Qualitative Properties of Frequencies and Modes of Beams Modeled by Discrete Systems

Published online by Cambridge University Press:  05 May 2011

D. J. Wang ,
C. S. Chou  and
Q. S. Wang
D. J. Wang*
Affiliation:
Department of Mechanical Engineering Science, Peking University, Beijing 100871, China
C. S. Chou*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Q. S. Wang*
Affiliation:
Department of Physics, Anqing Teachers College, Anhui Province 246011, China
*
*Professor
*Professor
*Professor
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Abstract

In this paper, a discrete system model and its equation of motion for beams with arbitrary supports at two ends are established. These supports include elastic, rigid and free supports in translation and rotation directions. Based on theory of oscillatory matrices, a series of qualitative properties of frequencies and modes of this system are derived. The basic properties include: non-zero frequencies are distinct; the ith displacement mode has i - 1 nodes; nodes of ith mode and (i + 1)th mode interlace.

Some additional important qualitative properties owned by rotation modes and strain modes are given as well.

Keywords

FrequencyModeBeamQualitative property.
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 1 , March 2003 , pp. 169 - 175
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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References

REFERENCES

1Gantmakher, F. P. and Krein, M. G., Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, Moscow-Leningrad State Publishing House of Technical-Theoretical Literature (1950), Translation, WashingTon D. C., U. S., Atome Energy Commission (1961).Google Scholar
2Gladwell, G. M. L., Inverse Problems in Vibration, Martinus Nijhoff Publishers (1986).CrossRefGoogle Scholar
3Gladwell, G. M. L., “Qualitative Properties of Vibrating System,” Proc. R. Soc. Lond. A., 401, pp. 299–315 (1985).Google Scholar
4Gladwell, G. M. L., Willms, N. B., He, Beichang and Wang, DaJun, “How Can We Recognize an Acceptable Mode Shape for a Vibrating Beam.” Q. J. Mech. Appl. Math., 42(2), pp. 303–310 (1989).CrossRefGoogle Scholar
5Wang, Qishen, He, Beichang and Wang, Dajun, “Some Qualitative Properties of Frequencies and Modes of Euler Beams,” J. Vibration Engin., 3(4), in Chinese, pp. 58–66 (1990).Google Scholar
6Wang, Dajun, He, Beichang and Wang, Qishen, “On the Construction of the Euler-Bernoulli Beam via Two Sets of Modes and the Corresponding Frequencies,” Acta Mechanica Sinica, 22(4), pp. 479–483 (1990).Google Scholar