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Dynamic analysis of modal shifting and mode jumping in thermally buckled plates

Publication ,  Journal Article
Chen, H; Virgin, LN
Published in: Journal of Sound and Vibration
November 22, 2004

Both analytical and finite element investigations are performed for the various static and dynamic aspects of the mode jumping phenomenon of a simply-supported rectangular plate heated deeply into the post-buckling regime. For the analytical method, the von Kármán plate equation is reduced to a system of non-linear ODEs by expressing the transverse deflection as a series of linear buckling modes. The ODEs, combined with the non-linear algebraic constraint equations obtained from in-plane boundary conditions, are then solved numerically under the parametric variation of the temperature. The results are checked by the finite element method, where a hybrid static-dynamic scheme is implemented. The contribution of each assumed (buckling) mode component is studied systematically. Characterized by the strong geometrical non-linearity, the secondary bifurcation point of the thermally loaded plate with fixed in-plane boundary conditions occurs far beyond the primary buckling point, and the jump behavior cannot be predicted correctly without sufficient assumed modes. Stationary bifurcation analysis indicates that while the post-buckling deflection before mode jumping is composed of pure symmetric modes, additional pure antisymmetric modes will appear after the occurrence of the snapping and they play the role of destabilizing the equilibrium. Furthermore, by monitoring natural frequencies and modal shapes, we find that a mode shifting phenomenon (the exchanging of vibration modes) exists in the primary post-buckling regime. Breaking of the symmetry of the dynamic modes is also found. By introducing a linear temperature sweeping scheme, transient analysis is performed to capture the snapping phenomenon dynamically, which occurs with moderate heating ratio. Comparison between the analytic and finite element results shows good agreement. © 2003 Elsevier Ltd. All rights reserved.

Duke Scholars

Published In

Journal of Sound and Vibration

DOI

ISSN

0022-460X

Publication Date

November 22, 2004

Volume

278

Issue

1-2

Start / End Page

233 / 256

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
 

Citation

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Chen, H., & Virgin, L. N. (2004). Dynamic analysis of modal shifting and mode jumping in thermally buckled plates. Journal of Sound and Vibration, 278(1–2), 233–256. https://doi.org/10.1016/j.jsv.2003.10.054
Chen, H., and L. N. Virgin. “Dynamic analysis of modal shifting and mode jumping in thermally buckled plates.” Journal of Sound and Vibration 278, no. 1–2 (November 22, 2004): 233–56. https://doi.org/10.1016/j.jsv.2003.10.054.
Chen H, Virgin LN. Dynamic analysis of modal shifting and mode jumping in thermally buckled plates. Journal of Sound and Vibration. 2004 Nov 22;278(1–2):233–56.
Chen, H., and L. N. Virgin. “Dynamic analysis of modal shifting and mode jumping in thermally buckled plates.” Journal of Sound and Vibration, vol. 278, no. 1–2, Nov. 2004, pp. 233–56. Scopus, doi:10.1016/j.jsv.2003.10.054.
Chen H, Virgin LN. Dynamic analysis of modal shifting and mode jumping in thermally buckled plates. Journal of Sound and Vibration. 2004 Nov 22;278(1–2):233–256.
Journal cover image

Published In

Journal of Sound and Vibration

DOI

ISSN

0022-460X

Publication Date

November 22, 2004

Volume

278

Issue

1-2

Start / End Page

233 / 256

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences