[1] Cai Yong, Xie Jiawei,. Stability of columns with original defectsunder periodic transient loadings [J]. Journal of Southeast University (English Edition), 2017, 33 (1): 64-69. [doi:10.3969/j.issn.1003-7985.2017.01.011]

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Stability of columns with original defectsunder periodic transient loadings()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

33

Issue:

2017 1

Page:

64-69

Research Field:

Civil Engineering

Publishing date:

2017-03-30

Info

Title:

Stability of columns with original defectsunder periodic transient loadings

Author(s):

Cai Yong;  Xie Jiawei

School of Civil Engineering, Central South University, Changsha 410075, China

Keywords:

periodic transient loading;  parametric resonance;  original defect;  dynamic stability

PACS:

TU311.3

DOI:

10.3969/j.issn.1003-7985.2017.01.011

Abstract:

To study the influence of original defects on the dynamic stability of the columns under periodic transient loadings, the approximate solution method and the Fourier method of the stable periodic solution are adopted while considering the influence of original defects on columns.The dynamic stability of the columns under periodic transient loadings is analyzed theoretically.Through the study of different deflections, the dynamic instability of the columns is obtained by Maple software. The results of theoretical analysis show that the larger the original defects, the greater the unstable area, the stable solution amplitude of columns and the risk of instability caused by parametric resonance will be. The damping of columns is a vital factor in reducing dynamic instability at the same original defects. On the basis of the Mathieu-Hill equation, the relationship between the original defects and deflection is deduced, and the dynamic instability region of the columns under different original defects is obtained. Therefore, reducing the original defects of columns can further enhance the dynamic stability of the compressed columns in practical engineering.

References:

[1] Movchan A A. The direct method of Liapunov in stability problems of elastic systems[J]. Journal of Applied Mathematics and Mechanics, 1959, 23(3): 686-700. DOI:10.1016/0021-8928(59)90161-3.
[2] Tong Y H, Zhang L X, Shi P, et al. A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems[J]. International Journal of Systems Science, 2013, 44(11): 1994-2003. DOI:10.1080/00207721.2012.683830.
[3] Bolotin V V. The dynamic stability of elastic systems[M].San Francisco, CA, USA: Pergamon Press, 1964:12-132.
[4] Wu B, Diebold G J. Mathieu function solutions for the photoacoustic effect in two- and three-dimensional structures and optical traps[J]. International Journal of Thermophysics, 2012, 33(10): 2185-2193. DOI:10.1007/s10765-012-1266-1.
[5] Raftoyiannis I G. Parametric resonance of steel bridges pylons due to periodic traffic loads[J]. Archive of Applied Mechanics, 2012, 82(10): 1601-1611. DOI:10.1007/s00419-012-0666-9.
[6] Wang J F, An W G, Song X H. Method for improving dynamic unstable boundary of Mathieu equation[J].Journal of Vibration and Shock, 2015, 34(12):182-188.(in Chinese)
[7] Wang L H, Yi Z P, Zhang H. Dynamic stability of arch with the geometrical imperfection subject to the periodic load[J]. Journal of Hunan University, 2007, 34(11):16-20.(in Chinese)
[8] Wang X J, Wang L, Qiu Z P. Failure analysis of dynamic buckling of initial geometric imperfections[J].Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(12):1484-1489.(in Chinese)
[9] Holzer S M. Stability of columns with transient loads[J].Journal of the Engineering Mechanics Division, 1970, 96(6):913-930.
[10] Xie W-C. Dynamic stability of structures[M].New York: Cambridge University Press, 2006:45-63.
[11] Holzer S M. Response bounds for columns with transient loads[J].Journal of Applied Mathematics, 1971, 38(1):157-161. DOI:10.1115/1.3408736.
[12] Chopra A K. Dynamics of structures[M].New Jersey, USA: Prentice Hall, 2011:114-119.
[13] Anderson T L, Moody M L. Parametric vibrations of columns[J].Journal of Engineering Mechanics, 1969, 95(3):665-677.
[14] Liu Y Z, Chen L Q. Nonlinear vibrations[M]. Beijing: Higher Education Press, 2001:152-168.(in Chinese)
[15] Wu X G, Zheng B L, He P F, et al. Deflection governing equation of constrained buckling on column[J].Journal of Tongji University, 2011, 39(6):798-801.(in Chinese)
[16] Dong G W, Li Z Y, Zhao J Y. Determination of the maximum deflection of long slender compression rod[J].Mechanical Research and Application, 2014, 27(1):15-18.(in Chinese)

Memo

Memo:

Biography: Cai Yong(1968—), male, doctor, associate professor, caiyong@csu.edu.cn.
Foundation item: The National Natural Science Foundation of China(No.51078354).
Citation: Cai Yong, Xie Jiawei. Stability of columns with original defects under periodic transient loadings[J].Journal of Southeast University(English Edition), 2017, 33(1):64-69.DOI:10.3969/j.issn.1003-7985.2017.01.011.

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