Experimental Study of Resonant Vibrations of Suspended Steel Cables Using a 3D Motion Analysis System
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
Abstract
This 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 , , , and 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, vibration modal coordinates and their frequency spectra, single-point vibration trajectories, Poincaré sections, etc. Using the 3D motion analysis system, this experimental study offers a distinctive interpretation of the characteristics of nonlinear resonant vibration of cables in the spatial domain (based on mode-shape information of the entire cable), in addition to one in the time domain (based on real-time traces of one single point). Detailed experimental result analyses were made on the responses within certain excitation intervals (responses of intervals) and those of similar characteristics in the entire excitation frequency (responses of branches). This paper follows a previously published article by the same authors, in which the detailed description of the test as well as details on the modal identification process can be found.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alaggio, R., and Rega, G. (2000). “Characterizing bifurcations and classes of motion in the transition to chaos through 3D-tori of a continuous experimental system in solid mechanics.” Physica D (Amsterdam)PDNPDT, 137(1-2), 70–93.
Arafat, H. N., and Nayfeh, A. H. (2003). “Non-linear responses of suspended cables to primary resonance excitations.” J. Sound Vib.JSVIAG, 266(2), 325–354.
Benedettini, F., and Rega, G. (1997). “Experimental investigation of the nonlinear response of a hanging cable. Part II: Global analysis.” Nonlinear Dyn.NODYES, 14(2), 119–138.
Feeny, B. F., and Kappagantu, R. (1998). “On the physical interpretation of proper orthogonal modes in vibrations.” J. Sound Vib.JSVIAG, 211(4), 607–616.
Hu, J., and Pai, P. F. (2010). “Experimental study of the nonlinear dynamic characteristics of suspended taut steel cables using a 3-D motion analysis system.” J. Sound Vib.JSVIAG, 329(19), 3972–3998.
Ibrahim, R. (2004). “Nonlinear vibrations of suspended cables—Part III: Random excitation and interaction with fluid flow.” Appl. Mech. Rev.AMREAD, 57(6), 515–549.
Irvine, H. M., and Caughey, T. K. (1974). “The linear theory of free vibration of a suspended cable.” Proc. R. Soc. London, Ser. APRLAAZ, 341(1626), 299–315.
Kerschen, G., Golinval, J. -C., Vakakis, A. F., and Bergman, L. A. (2005). “The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: An overview.” Nonlinear Dyn.NODYES, 41(1-3), 147–169.
Lee, C., and Perkins, N. C. (1992). “Nonlinear oscillations of suspended cables containing a two-to-one internal resonance.” Nonlinear Dyn.NODYES, 3(6), 465–490.
Lee, C., and Perkins, N. C. (1995a). “Three-dimensional oscillations of suspended cables involving simultaneous internal resonances.” Nonlinear Dyn.NODYES, 8(1), 45–63.
Lee, C. L., and Perkins, N. C. (1995b). “Experimental investigation of isolated and simultaneous internal resonances in suspended cables.” J. Acoust. Soc. Am.JASMAN, 117(4), 385–391.
Lumley, J. L. (1970). Stochastic tools in turbulence, Academic, New York.
Macdonald, J. H. G., Taylor, C. A., Thomas, B. T., and Dagless, E. L. (1998). “Real-time remote monitoring of dynamic displacements by computer vision.” Proc., 8th Society for Earthquake and Civil Engineering Dynamics Conf., Oxford, 389–396.
Macdonald, J. H. G., Dietz, M. S., Neild, S. A., Gonzalez Buelga, A., Crewe, A. J., and Wagg, D. J. (2010). “Generalised modal stability of inclined cables subjected to support excitations.” J. Sound Vib.JSVIAG, 329(21), 4515–4533.
Nayfeh, A. H., Arafat, H. N., Chin, C.-M., and Lacarbonara, W. (2002). “Multimode interactions in suspended cables.” J. Vib. ControlJVCOFX, 8(3), 337–387.
Nayfeh, A. H., and Pai, P. F. (2004). Linear and nonlinear structural mechanics, Wiley, New York.
Pai, P. F., and Lee, S. Y. (2003). “Nonlinear structural dynamics characterization using a scanning laser vibrometer.” J. Sound Vib.JSVIAG, 264(3), 657–687.
Pai, P. F. (2007). Highly flexible structures: Modeling, computation and experimentation, AIAA, Reston, VA.
Perkins, N. C. (1992). “Modal interactions in the non-linear response of elastic cables under parametric/external excitation.” Int. J. Non-linear Mech.IJNMAG, 27(2), 233–250.
Rega, G., Alaggio, R., and Benedettini, F. (1997). “Experimental investigation of the nonlinear response of a hanging cable. Part I: Local analysis.” Nonlinear Dyn.NODYES, 14(2), 89–117.
Rega, G., and Alaggio, R. (2001). “Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system.” Int. J. Solids Struct.IJSOAD, 38(10-13), 2049–2068.
Rega, G. (2004a). “Nonlinear vibrations of suspended cables—Part I: Modeling and analysis.” Appl. Mech. Rev.AMREAD, 57(6), 443–478.
Rega, G. (2004b). “Nonlinear vibrations of suspended cables—Part II: Deterministic phenomena.” Appl. Mech. Rev.AMREAD, 57(6), 479–514.
Rega, G., Srinil, N., and Alaggio, R. (2008). “Experimental and numerical studies of inclined cables: Free and parametrically-forced vibrations.” J. Theoret. Appl. Mech., 46(3), 621–640.
Rega, G., and Alaggio, R. (2009). “Experimental unfolding of the nonlinear dynamics of a cable-mass suspended system around a divergence-Hopf bifurcation.” J. Sound Vib.JSVIAG, 322(3), 581–611.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 6 • June 2012
Pages: 640 - 661
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Oct 12, 2010
Accepted: Dec 8, 2011
Published online: Dec 12, 2011
Published in print: Jun 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.