Journal ArticleDOI
On the symmetric modal interaction of the suspended cable: Three-to-one internal resonance
Yueyu Zhao,Lianhua Wang +1 more
TLDR
In this article, the authors applied multiple scales to attack the nonlinear partial differential equation and the boundary conditions, which leads to the modulation equations for the primary resonance of either the first or third symmetric mode.About:
This article is published in Journal of Sound and Vibration.The article was published on 2006-07-01. It has received 56 citations till now. The article focuses on the topics: Nonlinear resonance & Nonlinear system.read more
Citations
More filters
Journal ArticleDOI
Dynamic modeling and in-plane 1:1:1 internal resonance analysis of cable-stayed bridge
TL;DR: In this paper, a nonlinear dynamic double-cable-stayed shallow-arch model is established and the in-plane 1:1:1 internal resonance between three first modes of shallow arch and two cables under both external primary and subharmonic resonance is investigated, respectively.
Journal ArticleDOI
Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances
Lianhua Wang,Yueyu Zhao +1 more
TL;DR: In this paper, the Galerkin method is used to discretize the governing nonlinear integral-partial-differential equation and the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance.
Journal ArticleDOI
Nonlinear analysis of an elastic cable under harmonic excitation
M. M. Kamel,Yasser Salah Hamed +1 more
TL;DR: In this article, the nonlinear behavior of an elastic cable subjected to harmonic excitation is studied and solved, and the stability of the proposed analytic nonlinear solution near the simultaneous principle primary-internal resonance is investigated.
Journal ArticleDOI
Multiple internal resonances and non-planar dynamics of shallow suspended cables to the harmonic excitations
Lianhua Wang,Yueyu Zhao +1 more
TL;DR: In this paper, the nonlinear response of a shallow suspended cable with multiple internal resonances to the primary resonance excitation is investigated, and the effects of the excitation amplitude on the frequency-response curves of the cable are also analyzed.
Book ChapterDOI
Theoretical and Experimental Nonlinear Vibrations of Sagged Elastic Cables
TL;DR: In this paper, a comprehensive overview of recent advancements in the theoretical and experimental research on modelling, analysis, response, and nonlinear/nonregular phenomena in the finite amplitude, resonant, forced dynamics of sagged, horizontal or inclined, elastic cables is presented.
References
More filters
Book
Practical bifurcation and stability analysis : from equilibrium to chaos
TL;DR: In this article, the Branching Behaviour of Nonlinear Equations of Boundary-value Problems Stability of Periodic Solutions Qualitative Instruments Chaos Chaos and Continuation of Continuation.
Journal ArticleDOI
The linear theory of free vibrations of a suspended cable
H. M. Irvine,T. K. Caughey +1 more
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
Modal interactions in the non-linear response of elastic cables under parametric/external excitation
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
Planar non-linear free vibrations of an elastic cable
TL;DR: 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.