Inverse Frequency Problem of Discrete System of Symmerty Beam with Two Fixed Ends

Abstract:

This paper discussed some properties of the discrete system of the Eulers beam in vibration, which geometrical, physical parameters and supporting forms at both ends are symmetry about the midpoint of the span. On this foundation the inverse frequency problem based on the beam with both fixed-ends is raised and solved, i.e. given a set of frequency spectrum of the beam with both fixed-ends and other n positive number satisfying the interlace relation as following: the discrete system of the above symmetry beam fixed at both ends could be constructed, and would be the natural frequency of the fixed-free half-beam which is cut off from the midpoint of the beam fixed at both ends.

• Periodical: Applied Mechanics and Materials (Volume 328)
• Pages: 564-569
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.328.564
• Online since: June 2013
• Authors: Min He, Quan Jin Liu, Qi Shen Wang
• Keywords: Beam with both Fixed-Ends, Frequency, Inverse Problem, Symmetrical Structure

References

[1] Gantmakher F. P., Krein M. G., Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems (Trans Atomic Energy Commission Washington D. C, U. S. 1961).

[2] Krein, M G, Some new problems in the theory of Sturm systems, Prikladnaya Mathematika Imekhanika, 16, (1952), pp.555-563. (In Russian).

[3] Gladwell G M L. Inverse Problems in Vibration [M]. Dordrecht: Martinus Nijhoff Publishers, 1st ed, 1986. 2nd ed, (2004).

[4] Gladwell G M L, England A H, Dajun Wang, Examples of Reconstruction of an Euler-Bernouli Beam from Spectral Data, Journal of Sound & Vibration, Vol.19, No.1, (1987), pp.81-94.

DOI: 10.1016/0022-460x(87)90190-8

[5] Beichang He, Qishen Wang, Dajun Wang. Inverse Problem for the Finite Difference Model of Euler Beam in Vibration, Journal of Vibration Engineering, Vol.2, No.2, (1989), pp.1-9(in Chinese)

[6] Dajun Wang, Beichang He, Qishen Wang. On the Construction of the Euler-Bernouli Beam via Two Sets of Modes and the Corresponding Frequencies, Acta Mechanica Sinica, Vol.22, No.4, (1990), pp.479-483(in Chinese)

[7] Qishen Wang, Dajun Wang, Beichang He. Construction of the Difference Discrete System for the Simple-support Beam from the Spectra Data, Engineering Mechanics, Vol.8, No.4, (1991), pp.10-19(in Chinese)

[8] Qishen Wang, Dajun Wang. Difference Discrete System of the Euler-Beam With Arbitrary Supports and Sign-Oscillatory Property of Stiffness Matrices, Applied Mathematics and Mechanics, Vol.27, No.3, (2006), pp.351-356(in Chinese)

DOI: 10.1007/s10483-006-0316-y

[9] Qishen Wang, The Half a Structure of Rod or Beam with Symmetric Distributed Parameters about Structure Midpoint, Journal of Anqing Teachers College (Natural Science Edition), Vol.18, No.4, (2012),pp.58-62 (in Chinese).