In this chapter, the vibration behaviour of cables is considered. The starting point is to consider horizontal cables, which are initially assumed to be inextensible. Of particular importance is cable sag, the static displacement of a cable due to gravity. Sag results in cables having complex dynamic behaviour. This is seen when the nonlinear equations of motion for an inclined cable are developed. Inclined cables are important for applications such as cable-stayed bridges. Galerkin–s method is used to convert the nonlinear partial differential equations into a set of modal equations in which the linear terms are decoupled. However, modal coupling remains in the nonlinear terms. These nonlinear coupled terms lead to internal resonance, such as autoparametric resonance. This type of resonance can be observed for cable-stay bridges when certain combinations of external excitation frequency, deck frequency and cable mode frequency occur.
In the final part of the chapter, a case study of cable vibration is considered. In the case study the techniques of averaging, multiple scales and normal forms are compared when applied to the analysis of a single mode of vibration of an inclined cable.
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References
Benedettini, F., Rega, G., and Alaggio, R. (1995). Non-linear oscillations of a nonlinear model of a suspended cable. Journal of Sound and Vibration,182, 775–798.
Casciati, F. and Ubertini, F. (2008). Nonlinear vibration of shallow cables with semiactive tuned mass damper. Nonlinear Dynamics, 53(1–2), 89–106.
El-Attar, M., Ghobarah, A., and Aziz, T. S. (2000). Non-linear cable response to multiple support periodic excitation. Engineering Structures, 22, 1301–1312.
Gatulli, V., Lepidi, M., Macdonald, J., and Taylor, C. (2005). One to two global local interaction in a cable-stayed beam observed through analytical, finite element and experimental models. International Journal of Non-linear Mechanics, 40, 571–588.
Gonzalez-Buelga, A., Neild, S., Wagg, D., and Macdonald, J. (2008). Modal stability of inclined cables subjected to vertical support excitation. Journal of Sound and Vibration, 318, 565–579.
Irvine, H. M. and Caughey, T. K. (1974). The linear theory of free vibrations of a suspended cable. Proc. Roy. Soc. A, 341(1626), 299–315.
Irvine, H. M. (1992). Cable Structures. Dover.
Krenk, S. (2001). Mechanics and analysis of beams, columns and cables: A modern introduction to the classic theories. Springer.
Massow, C., Gonzalez-Buelga, A., Macdonald, J., Neild, S., Wagg, D., and Champneys, A. (2007). Theoretical and experimental identification of parametric excitation of inclined cables. In 7th International Symposium on Cable Dynamics, number 40 in 1, pages 97–104, Vienna, Austria.
Perkins, N. (1992). Modal interactions in the non-linear response of elastic cables under parametric/external excitation. Internacional Journal Non-linear Mechanics, 27(2), 233–250.
Rayleigh, J. W. S. (1894a).Theory of sound: Volume 1. Macmillan and Co: London.
Rayleigh, J. W. S. (1894b). Theory of sound: Volume 2. Macmillan and Co: London.
Srinil, N. and Rega, G. (2007). Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. part ii: Internal resonance activation, reduced-order models and nonlinear normal modes. Nonlinear Dynamics, 48(3), 253–274.
Srinil, N., Rega, G., and Chucheepsakul, S. (2004). Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables. Journal of Sound and Vibration, 269(3–5), 823–852.
Srinil, N., Rega, G., and Chucheepsakul, S. (2007). Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. part i: Theoretical formulation and model validation. Nonlinear Dynamics, 48(3), 231–252.
Virgin, L. N. (2007). Vibration of Axially-Loaded Structures. Cambridge.
von Kármán, T. and Biot, M. A. (1940). Mathematical Methods in Engineering. McGraw-Hill.
Warnitchai, Y., Fujino, T., and Susumpov, A. (1995). A nonlinear dynamic model for cables and its application to a cable structure-system. Journal of Sound and Vibration, 187(3), 695–712.
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(2010). Cables. In: Wagg, D., Neild, S. (eds) Nonlinear Vibration with Control. Solid Mechanics and Its Applications, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2837-2_7
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