We investigate nonlinear forced oscillations of sagged inclined cables under planar 1:1 internal resonance at avoidance. To account for frequency avoidance phenomena and associated hybrid modes, actually distinguishing inclined cables from horizontal cables, asymmetric inclined static configurations are considered. Emphasis is placed on highlighting nearly tuned 1:1 resonant interactions involving coupled hybrid modes. The inclined cable is subjected to a uniformly distributed vertical harmonic excitation at primary resonance of a high-frequency mode. Approximate nonlinear partial-differential equations of motion, capturing overall displacement coupling and dynamic extensibility effect, are analytically solved based on a multimode discretization and a second-order multiple scale approach. Bifurcation analyses of both equilibrium and dynamic solutions are carried out via a continuation technique, highlighting the influence of system parameters on internally resonant forced dynamics of avoidance cables. Direct numerical integrations of modulation equations are also performed to validate the continuation prediction and characterize nonlinear coupled dynamics in post-bifurcation states. Depending on the elasto-geometric (cable sag and inclination) and control parameters, and on assigned initial conditions, the hybrid modal interactions undergo several kinds of bifurcations and nonlinear phenomena, along with meaningful transition from periodic to quasiperiodic and chaotic responses. Moreover, corresponding spatio-temporal distributions of cable nonlinear dynamic displacement and tension are manifested.
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e-mail: giuseppe.rega@uniroma1.it
e-mail: narakorn.srinil@uniroma1.it
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October 2007
Research Papers
Nonlinear Hybrid-Mode Resonant Forced Oscillations of Sagged Inclined Cables at Avoidances
Giuseppe Rega,
Giuseppe Rega
Department of Structural and Geotechnical Engineering,
e-mail: giuseppe.rega@uniroma1.it
SAPIENZA University of Rome
, via A. Gramsci 53, Rome 00197, Italy
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Narakorn Srinil
Narakorn Srinil
Department of Structural and Geotechnical Engineering,
e-mail: narakorn.srinil@uniroma1.it
SAPIENZA University of Rome
, via A. Gramsci 53, Rome 00197, Italy
Search for other works by this author on:
Giuseppe Rega
Department of Structural and Geotechnical Engineering,
SAPIENZA University of Rome
, via A. Gramsci 53, Rome 00197, Italye-mail: giuseppe.rega@uniroma1.it
Narakorn Srinil
Department of Structural and Geotechnical Engineering,
SAPIENZA University of Rome
, via A. Gramsci 53, Rome 00197, Italye-mail: narakorn.srinil@uniroma1.it
J. Comput. Nonlinear Dynam. Oct 2007, 2(4): 324-336 (13 pages)
Published Online: March 28, 2007
Article history
Received:
September 15, 2006
Revised:
March 28, 2007
Citation
Rega, G., and Srinil, N. (March 28, 2007). "Nonlinear Hybrid-Mode Resonant Forced Oscillations of Sagged Inclined Cables at Avoidances." ASME. J. Comput. Nonlinear Dynam. October 2007; 2(4): 324–336. https://doi.org/10.1115/1.2756064
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