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Article
Nonlinear Oscillations of Suspended Cables Containing a Two-to-One Internal Resonance
1990-1999
  • Christopher L Lee, Franklin W. Olin College of Engineering
  • Noel C Perkins
Document Type
Article
Publication Date
1-1-1992
Abstract

The near-resonant response of suspended, elastic cables driven by planar excitation is investigated using a two degree-of-fredom model. The model captures the interaction of a symmetric in-plane mode and an out-of-plane mode with near commensurable natural frequencies in a 2:1 ratio. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. The existence and stability of periodic solutions are investigated using a second order perturbation analysis. The first order analysis shows that suspended cables may exhibit saturation and jump phenomena. The second order analysis, however, reveals that the cubic nonlinearities and higher order corrections disrupt saturation. The stable, steady state solutions for the second order analysis compare favorably with results obtained by numerically integrating the equations of motion.

Comments

© 1992 Springer-Verlag. This article was published in Nonlinear Dynamics, vol. 3, no. 6, p. 465-490 and may be found here.

Citation Information
Christopher L Lee and Noel C Perkins. "Nonlinear Oscillations of Suspended Cables Containing a Two-to-One Internal Resonance" (1992)
Available at: http://works.bepress.com/christopher_lee/34/