Abstract
The near resonant response of suspended, elastic cables driven by planar excitation is investigated using a three degree-of-freedom model. The model captures the interaction of a symmetric in-plane mode with two out-of-plane modes. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. For particular magnitudes of equilibrium curvature, the natural frequency of the in-plane mode is simultaneously commensurable with the natural frequencies of the two out-of-plane modes in 1:1 and 2:1 ratios. A second nonlinear order perturbation analysis is used to determine the existence and stability of four classes of periodic solutions. The perturbation solutions are compared with results obtained by numerically integrating the equations of motion. Furthermore, numerical simulations demonstrate the existence of quasi-periodic responses.
A portion of this work was presented at the 1992 ASME Winter Annual Meeting, Anaheim, CA.
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© 1995 Springer Science+Business Media Dordrecht
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Lee, C., Perkins, N.C. (1995). Three-Dimensional Oscillations of Suspended Cables Involving Simultaneous Internal Resonances. In: Bajaj, A.K., Shaw, S.W. (eds) Advances in Nonlinear Dynamics: Methods and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0367-1_3
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DOI: https://doi.org/10.1007/978-94-011-0367-1_3
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