Vibrations of slack cables with discrete masses

An efficient procedure for analyzing in-plane vibrations of flat-sag suspended cables carrying an array of moving oscillators with arbitrarily varying velocities is presented. The cable is modelled as a mono-dimensional elastic continuum, fully accounting for geometrical nonlinearities. By eliminating the horizontal displacement component through a standard condensation procedure, the nonlinear integro-differential equation governing vertical cable vibrations is derived. Due to the dynamic interaction at the contact points with the moving oscillators, such equation is coupled to the set of ordinary differential equations ruling the response of the travelling sub-systems. An improved series representation of vertical cable displacement is proposed, which allows to overcome the inability of the traditional Galerkin method to reproduce the kinks and abrupt changes of cable configuration at the interface with the moving sub-systems. Following the philosophy of the well-known ''mode-acceleration'' method, the convergence of the series expansion of cable response in terms of appropriate basis functions is improved through the introduction of the so-called ''quasi-static'' solution. Numerical results demonstrate that, despite the basis functions are continuous, the improved series enables to capture with very few terms the abrupt changes of cable profile at the contact points between the cable and the moving oscillators.

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“…doi:10. /j.ijsolstr.2007.03.004 Rosenthal, 1981), which may simulate sensors, buoyancy elements, instruments (e.g. hydrophones or cameras), etc.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of suspended cables carrying moving oscillators

Sofi

Muscolino

2007

International Journal of Solids and Structures

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“…They represent a taut cable by a succession of segment. Rosenthal [6] used an iterative method to find the modes of a cable with sag and masses. Cheng and Perkins [7] calculated the eigenmodes when the position of the mass is varying from one end of the cable to the other.…”

Section: Bibliographymentioning

confidence: 99%

Simulation of the Dynamic Behavior of a Bi-Cable Ropeway with Modal Bases

Hurel

Laborde

Jézéquel

2018

Topics in Modal Analysis &Amp; Testing, Volume 9

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This article presents the building of a dynamic model of a bi-cable ropeway. Thanks to the assumption of quasi-static advance of the vehicles, the calculation is performed step by step. At each step, a transient linearized dynamic solution is calculated around the quasi-static equilibrium using modal bases. The ropeway system is substructured considering the different elements: track rope, hauling rope and vehicles represented by pendulums. The results of time integration give the accelerations felt by the passengers according to the load case.

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“…9 The integrand is discontinuous at the locations of the individual attached masses, leading to a Stieltjes integral representation consisting of a regular integral representing the bare cable and a sum of discrete mass terms (Rosenthal, 1981). It is clear from the plotted mode shapes that in general the masses are in motion and do not lie at nodes of the vibration pattern.…”

Section: Related Investigationsmentioning

confidence: 99%

The Dynamics of Slack Marine Cables

Griffin

Rosenthal

1989

Journal of Offshore Mechanics and Arctic Engineering

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Examples of the uses of slack cables in marine and offshore applications include deepwater moorings and the guy lines of towers and platforms. A brief summary is given of some of the important aspects of the linear theory for the vibration of horizontal and inclined slack cables. Then the important differences between the two cases are pointed out through the use of analytical and computational examples. These examples use typical methods which have been developed in recent years for predicting the dynamics of slack cables with and without arrays of attached discrete masses.

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Vibrations of slack cables with discrete masses

Cited by 7 publications

References 3 publications

Dynamic analysis of suspended cables carrying moving oscillators

Dynamic analysis of suspended cables carrying moving oscillators

Simulation of the Dynamic Behavior of a Bi-Cable Ropeway with Modal Bases

The Dynamics of Slack Marine Cables

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