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- Title
Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II: Internal resonance activation, reduced-order models and nonlinear normal modes.
- Authors
Narakorn Srinil; Giuseppe Rega
- Abstract
Abstract??Resonant multi-modal dynamics due to planar 2:1 internal resonances in the non-linear, finite-amplitude, free vibrations of horizontal/inclined cables are parametrically investigated based on the second-order multiple scales solution in Part I [1] (in press). The already validated kinematically non-condensed cable model accounts for the effects of both non-linear dynamic extensibility and system asymmetry due to inclined sagged configurations.Actual activationof 2:1 resonances is discussed, enlightening on a remarkable qualitative difference of horizontal/inclined cables as regards non-linear orthogonality properties of normal modes. Based on the analysis of modal contribution and solution convergence of various resonant cables, hints are obtained on properreduced-order modelselections from the asymptotic solution accounting for higher-order effects of quadratic nonlinearities. The dependence of resonant dynamics on coupled vibration amplitudes, and the significant effects of cable sag, inclination and extensibility on system non-linear behavior are highlighted, along with meaningful contributions of longitudinal dynamics. The spatio-temporal variation of non-linear dynamic configurations and dynamic tensions associated with 2:1resonant non-linear normal modesis illustrated. Overall, the analytical predictions are validated by finite difference-based numerical investigations of the original partial-differential equations of motion.
- Subjects
BASES (Linear topological spaces); CABLE vibration; MECHANICS (Physics); ANALYTICAL mechanics
- Publication
Nonlinear Dynamics, 2007, Vol 48, Issue 3, p253
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-006-9087-z