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Large oscillations of beams and columns including self-weight

Publication ,  Journal Article
Santillan, ST; Plaut, RH; Witelski, TP; Virgin, LN
Published in: International Journal of Non-Linear Mechanics
October 1, 2008

Large-amplitude, in-plane beam vibration is investigated using numerical simulations and a perturbation analysis applied to the dynamic elastica model. The governing non-linear boundary value problem is described in terms of the arclength, and the beam is treated as inextensible. The self-weight of the beam is included in the equations. First, a finite difference numerical method is introduced. The system is discretized along the arclength, and second-order-accurate finite difference formulas are used to generate time series of large-amplitude motion of an upright cantilever. Secondly, a perturbation method (the method of multiple scales) is applied to obtain approximate solutions. An analytical backbone curve is generated, and the results are compared with those in the literature for various boundary conditions where the self-weight of the beam is neglected. The method is also used to characterize large-amplitude first-mode vibration of a cantilever with non-zero self-weight. The perturbation and finite difference results are compared for these cases and are seen to agree for a large range of vibration amplitudes. Finally, large-amplitude motion of a postbuckled, clamped-clamped beam is simulated for varying degrees of buckling and self-weight using the finite difference method, and backbone curves are obtained. © 2008 Elsevier Ltd.

Duke Scholars

Published In

International Journal of Non-Linear Mechanics

DOI

ISSN

0020-7462

Publication Date

October 1, 2008

Volume

43

Issue

8

Start / End Page

761 / 771

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics
 

Citation

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Santillan, S. T., Plaut, R. H., Witelski, T. P., & Virgin, L. N. (2008). Large oscillations of beams and columns including self-weight. International Journal of Non-Linear Mechanics, 43(8), 761–771. https://doi.org/10.1016/j.ijnonlinmec.2008.04.007
Santillan, S. T., R. H. Plaut, T. P. Witelski, and L. N. Virgin. “Large oscillations of beams and columns including self-weight.” International Journal of Non-Linear Mechanics 43, no. 8 (October 1, 2008): 761–71. https://doi.org/10.1016/j.ijnonlinmec.2008.04.007.
Santillan ST, Plaut RH, Witelski TP, Virgin LN. Large oscillations of beams and columns including self-weight. International Journal of Non-Linear Mechanics. 2008 Oct 1;43(8):761–71.
Santillan, S. T., et al. “Large oscillations of beams and columns including self-weight.” International Journal of Non-Linear Mechanics, vol. 43, no. 8, Oct. 2008, pp. 761–71. Scopus, doi:10.1016/j.ijnonlinmec.2008.04.007.
Santillan ST, Plaut RH, Witelski TP, Virgin LN. Large oscillations of beams and columns including self-weight. International Journal of Non-Linear Mechanics. 2008 Oct 1;43(8):761–771.
Journal cover image

Published In

International Journal of Non-Linear Mechanics

DOI

ISSN

0020-7462

Publication Date

October 1, 2008

Volume

43

Issue

8

Start / End Page

761 / 771

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics