[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(
)
周期性瞬时荷载作用下初始缺陷杆件稳定性研究
)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
- 周期性瞬时荷载作用下初始缺陷杆件稳定性研究
- Author(s):
- Cai Yong; Xie Jiawei
- School of Civil Engineering, Central South University, Changsha 410075, China
- 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.
- 为了研究初始缺陷在周期性瞬时荷载作用下对杆件动力稳定性的影响, 采用近似求解方法和傅里叶周期稳定解的方法, 考虑初始缺陷对杆件的影响, 对在周期性瞬时荷载作用下杆件的动力稳定性进行理论分析.同时通过对杆件不同挠度的研究, 采用Maple软件得到了杆件的动力不稳定性.理论分析结果表明:初始缺陷越大, 杆件的稳定解的振幅越大, 不稳定区域越宽, 发生参数共振导致失稳的可能性越大.在相同初始缺陷条件下, 杆件的阻尼是有效降低杆件发生动力失稳的重要因素.在马奇耶方程基础上, 推导了杆件初始缺陷与挠度的具体关系式, 得到了在不同初始缺陷下杆件的动力不稳定区域.分析表明, 实际工程中减少杆件的初始缺陷能够加强杆件的动力稳定性.
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.