Experimental Study of Resonant Vibrations of Suspended Steel Cables Using a 3D Motion Analysis System

AbstractThis paper presents the results of an experimental study of regular resonant vibrations of steel cables using a camera-based three-dimensional (3D) motion analysis system. The cable had one fixed end, and the other end was subjected to harmonic vertical excitation. Retroreflective markers were fixed to the cable and evenly distributed along it. The 3D motion analysis system was used to obtain 3D time traces of all marker vibrations; these traces were then entered into other programs for further signal processing. Time-varying modal coordinates were extracted from the trajectories of the markers using a modal decomposition technique. The resonant vibrations observed include isolated and simultaneous 1∶1, 2∶2∶1, 1∶1∶2∶2, and 4∶2∶4∶2 internal resonances. Subharmonic and superharmonic resonances, period-doubling bifurcations, hardening nonlinearity effect, and complex traveling vibrations were observed and studied. The resonant vibrations were characterized by examining time-varying vibration profiles...

[1]  Giuseppe Rega,et al.  Characterizing bifurcations and classes of motion in the transition to chaos through 3D-tori of a continuous experimental system in solid mechanics , 2000 .

[2]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[3]  A. Nayfeh,et al.  Linear and Nonlinear Structural Mechanics , 2002 .

[4]  R. Alaggio,et al.  Experimental and numerical studies of inclined cables: free and parametrically-forced vibrations , 2008 .

[5]  Noel C. Perkins,et al.  Modal interactions in the non-linear response of elastic cables under parametric/external excitation , 1992 .

[6]  Noel C. Perkins,et al.  Three-dimensional oscillations of suspended cables involving simultaneous internal resonances , 1995, Nonlinear Dynamics.

[7]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[8]  Raouf A. Ibrahim,et al.  Nonlinear vibrations of suspended cables—Part III: Random excitation and interaction with fluid flow , 2004 .

[9]  David J. Wagg,et al.  Generalised modal stability of inclined cables subjected to support excitations , 2010 .

[10]  Giuseppe Rega,et al.  Experimental unfolding of the nonlinear dynamics of a cable-mass suspended system around a divergence-Hopf bifurcation , 2009 .

[11]  Noel C. Perkins,et al.  Experimental Investigation of Isolated and Simultaneous Internal Resonances in Suspended Cables , 1995 .

[12]  Noel C. Perkins,et al.  Nonlinear oscillations of suspended cables containing a two-to-one internal resonance , 1992, Nonlinear Dynamics.

[13]  P. Frank Pai,et al.  Experimental study of the nonlinear dynamic characteristics of suspended taut steel cables using a 3-D motion analysis system , 2010 .

[14]  Hisashi Kobayashi,et al.  Modeling and analysis , 1978 .

[15]  P. F. Pai,et al.  Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer , 2003 .

[16]  Ali H. Nayfeh,et al.  Multimode Interactions in Suspended Cables , 2001 .

[17]  Giuseppe Rega,et al.  Experimental Investigation of the Nonlinear Response of a Hanging Cable. Part I: Local Analysis , 1997 .

[18]  G. Rega,et al.  Nonlinear vibrations of suspended cables—Part II: Deterministic phenomena , 2004 .

[19]  Ali H. Nayfeh,et al.  Non-linear responses of suspended cables to primary resonance excitations , 2003 .

[20]  P. Frank Pai,et al.  Highly Flexible Structures : Modeling, Computation, and Experimentation , 2007 .

[21]  Giuseppe Rega,et al.  Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system , 2001 .

[22]  Giuseppe Rega,et al.  Nonlinear vibrations of suspended cables—Part I: Modeling and analysis , 2004 .

[23]  J. Lumley.  Stochastic tools in turbulence , 1970 .