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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 72
A Method for the Dynamic Analysis of Suspended Cables Carrying Moving Masses G. Muscolino1 and A. Sofi2
1Department of Civil Engineering, University of Messina, Italy
Full Bibliographic Reference for this paper
G. Muscolino, A. Sofi, "A Method for the Dynamic Analysis of Suspended Cables Carrying Moving Masses", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 72, 2006. doi:10.4203/ccp.83.72
Keywords: suspended cable, moving masses, convective acceleration, series expansion, mode-acceleration method, quasi-static solution, slope discontinuity.
Summary
Cables are used in many engineering applications, such as electrical and optical
signal transmission lines, tethers and umbilicals, aerial cableways, cable supported
bridges etc. It is well-known, however, that due to their inherent flexibility, light
weight and low structural damping, cables are prone to large amplitude oscillations,
which may impair their performances. For this reason since the 18th century many
investigations have focused on the dynamics of suspended cables [1].
The addition of attached masses, simulating sensors, buoyancy elements, instruments (e.g. hydrophones or cameras), greatly complicates the description of cable motion [2] which cannot be accomplished by directly applying the procedures developed for bare cables, i.e. those without masses. An attached mass, in fact, produces a singularity which makes a cable deformed profile which can no longer be described by a smooth continuous curve. In many engineering applications, such as aerial cableways or tramways, the analysis of cable vibrations is even more difficult. In fact, the dynamics of a nonlinear distributed system (the cable) coupled to moving masses or oscillators (cabins or payloads) has to be investigated. The dynamics of stretched strings has attracted significant attention in the past [3], while, to the authors' knowledge, comparatively fewer studies have focused on the response of sagged cables to moving loads [4,5,6].
This paper deals with nonlinear in-plane vibrations of suspended cables with
small sag-to-span ratios carrying an arbitrary number of moving masses. The cable
is modelled as a mono-dimensional elastic continuum, fully accounting for
geometrical nonlinearities. The interaction between the moving masses, regarded as
rigid bodies, and the supporting structure is appropriately described by retaining the
convective acceleration terms. The equations governing nonlinear in-plane
vibrations of the cable-mass system are derived by applying the extended
Hamilton's principle. Neglecting the longitudinal inertia forces of both the cable and
the masses, and applying a standard condensation procedure, the equations of motion
are reduced to a unique integro-differential equation in the vertical displacement
component. The spatial dependence is eliminated by the Galerkin method
representing the solution as a series expansion in terms of appropriate basis
functions. The discretization yields a set of coupled nonlinear ordinary differential
equations with time-dependent coefficients in the generalized coordinates which can
be integrated by standard step-by-step algorithms, such as Newmark- References
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