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CLC number: U448.25

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Received: 2006-04-23

Revision Accepted: 2006-10-21

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.2 P.245~256

http://doi.org/10.1631/jzus.2007.A0245


Finite element analysis of dynamic stability of skeletal structures under periodic loading


Author(s):  THANA Hemantha Kumar, AMEEN Mohammed

Affiliation(s):  Department of Civil Engineering, National Institute of Technology, Calicut, Kerala 673601, India

Corresponding email(s):   hemanth0252000@yahoo.co.in, ameen@nitc.ac.in

Key Words:  Finite element analysis, Dynamic stability, Mathieu-Hill equation


THANA Hemantha Kumar, AMEEN Mohammed. Finite element analysis of dynamic stability of skeletal structures under periodic loading[J]. Journal of Zhejiang University Science A, 2007, 8(2): 245~256.

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author="THANA Hemantha Kumar, AMEEN Mohammed",
journal="Journal of Zhejiang University Science A",
volume="8",
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pages="245~256",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0245"
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%A AMEEN Mohammed
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%@ 1673-565X
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A0245

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T1 - Finite element analysis of dynamic stability of skeletal structures under periodic loading
A1 - THANA Hemantha Kumar
A1 - AMEEN Mohammed
J0 - Journal of Zhejiang University Science A
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SP - 245
EP - 256
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0245


Abstract: 
This paper addresses the dynamic stability problem of columns and frames subjected to axially applied periodic loads. Such a structure can become unstable under certain combinations of amplitudes and frequencies of the imposed load acting on its columns/beams. These are usually shown in the form of plots which describe regions of instability. The finite element method (FEM) is used in this work to analyse dynamic stability problems of columns. Two-noded beam elements are used for this purpose. The periodic loading is decomposed into various harmonics using Fourier series expansion. Computer codes in C++ using object oriented concepts are developed to determine the stability regions of columns subjected to periodic loading. A number of numerical examples are presented to illustrate the working of the program. The direct integration of the equations of motions of the discretised system is carried out using Newmark’s method to verify the results.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[6] Cook, R.D., Malkus, D.S., Plesha, M.E., Witt, R.J., 2003. Concepts and Applications of Finite Element Analysis. John Wiley & Sons, New York.

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[8] McLachlan, N.W., 1957. Theory and Applications of Mathieu Functions. Oxford University Press, New York.

[9] Meirovitch, L., 1970. Methods of Analytical Dynamics. McGraw Hill, New York.

[10] Park, H.I., Jung, D.H., 2002. A finite element method for dynamic analysis of long slender marine structures under combined parametric and forcing excitations. Ocean Engineering, 29(11):1313-1325.

[11] Sugiyama, Y., Katayama, K., Kiriyama, K., 2000. Experimental verification of dynamic stability of vertical cantilevered columns subjected to a sub-tangential force. Journal of Sound & Vibration, 236(2):193-207.

[12] Sygulski, R., 1996. Dynamic stability of pneumatic structures in wind: theory and experiment. Journal of Fluids & Structures, 10(8):945-963.

[13] Zounes, R.S., Rand, R.H., 1998. Transition curves for the quasi-periodic Mathieu Equation. SIAM J. Appl. Math., 58(4):1094-1115.

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