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Planar non-linear free vibrations of an elastic cable

Angelo Luongo, +2 more
- 01 Jan 1984 - 
- Vol. 19, Iss: 1, pp 39-52
TLDR
In this paper, a non-linear equation of the free motion of a heavy elastic cable about a deformed initial configuration is developed, which is obtained via a Galerkin procedure, an approximate solution is pursued through a perturbation method.
Abstract: 
Continuum non-linear equations of free motion of a heavy elastic cable about a deformed initial configuration are developed. Referring to an assumed mode technique one ordinary equation for the cable planar motion is obtained via a Galerkin procedure, an approximate solution of which is pursued through a perturbation method. Suitable nondimensional results are presented for the vibrations in the first symmetric mode with different values of the cable properties. Which procedure is the proper one to account consistently for the non-linear kinematical relations of the cable in one ordinary equation of motion is discussed.

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Planar non-linear free vibrations of an elastic cable
Angelo Luongo, Giuseppe Rega, Fabrizio Vestroni
To cite this version:
Angelo Luongo, Giuseppe Rega, Fabrizio Vestroni. Planar non-linear free vibrations of an elastic
cable. International Journal of Non-Linear Mechanics, Elsevier, 1984, 19 (1), pp.39-52. �hal-00787648�
Citations
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Journal ArticleDOI

Non-linear vibration of a traveling tensioned beam

J.A. Wickert
- 01 May 1992 - 
TL;DR: In this paper, a perturbation theory for the near-modal free vibration of a general gyroscopic system with weakly nonlinear stiffness and/or dissipation is derived through the asymptotic method of Krylov, Bogoliubov, and Mitropolsky.
Journal ArticleDOI

Nonlinear vibrations of suspended cables—Part I: Modeling and analysis

Giuseppe Rega
- 01 Nov 2004 - 
Journal ArticleDOI

Modal interactions in the non-linear response of elastic cables under parametric/external excitation

Noel C. Perkins
- 01 Mar 1992 - 
TL;DR: In this article, a two-degree-of-freedom approximation of the model is employed to examine a class of in-plane/out-ofplane motions that are coupled through the quadratic nonlinearities.
Journal ArticleDOI

Nonlinear dynamics and bifurcations of an axially moving beam

Francesco Pellicano, +1 more
- 01 Jan 2000 - 
TL;DR: In this article, the dynamic behavior of a simply supported beam subjected to an axial transport of mass is analyzed in the sub and supercritical speed ranges with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation.
Journal ArticleDOI

Nonlinear vibrations of suspended cables—Part II: Deterministic phenomena

Giuseppe Rega
- 01 Nov 2004 - 
References
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Journal ArticleDOI

Finite element formulations for large deformation dynamic analysis

Klaus-Jürgen Bathe, +2 more
- 01 Jan 1975 - 
TL;DR: In this paper, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived starting from continuum mechanics principles, and a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure.
Journal ArticleDOI

The linear theory of free vibrations of a suspended cable

H. M. Irvine, +1 more
- 10 Dec 1974 - 
TL;DR: In this paper, a linear theory for the free vibrations of a uniform suspended cable in which the ratio of sag to span is about 1:8, or less, was developed.
Journal ArticleDOI

On non-linear free vibrations of an elastic cable

Peter Hagedorn, +1 more
- 01 Jan 1980 - 
TL;DR: In this paper, the effect of non-linear terms in the equations of motion on the first normal modes of the oscillations of an elastic flexible cable under the action of gravity is studied.
Journal ArticleDOI

Parametric analysis of large amplitude free vibrations of a suspended cable

Giuseppe Rega, +2 more
- 01 Jan 1984 - 
TL;DR: Partial differential equations of motion suitable to study moderately large free oscillations of an clastic suspended cable arc are obtained in this paper, where an integral procedure is used to eliminate the spatial dependence and to reduce the problem to one ordinary differential equation which shows quadratic and cubic nonlincarities.
Journal ArticleDOI

Monofrequent oscillations of a non-linear model of a suspended cable.

Angelo Luongo, +2 more
- 22 May 1982 - 
TL;DR: In this paper, the effects of non-linearities on the free motion of a suspended cable were analyzed in a two-degree-of-freedom nonlinear elastic model and the possibility that effects arise due to nonlinear coupling was examined, and a numerical analysis was made for the first symmetric mode for different amplitude of motion by parametrically varying the geometric and mechanical properties of the cable.
Related Papers (5)

The linear theory of free vibrations of a suspended cable

H. M. Irvine, +1 more
- 10 Dec 1974 - 

Nonlinear vibrations of suspended cables—Part I: Modeling and analysis

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- 01 Nov 2004 - 

Modal interactions in the non-linear response of elastic cables under parametric/external excitation

Noel C. Perkins
- 01 Mar 1992 - 

Non-linear dynamics of an elastic cable under planar excitation

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- 01 Jan 1987 - 

Multiple resonances in suspended cables: direct versus reduced-order models

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- 01 Sep 1999 - 
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