English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The chief aim of the present work is to investigate the single-pulse chaotic dynamics for suspended cables with principal parametric and primary resonant excitation. Using higherdimensional Melnikov theory, explicit conditions for the existences of single-pulse Silnikov-type homoclinic orbits are obtained, which imply that chaotic motions in the sense of Smale horseshoes may occur for this system. Finally, numerical results are presented to verify these analytical predictions. Introduction The suspended cables are widely used in engineering, such as communications, transportation, cable-stayed bridge etc. In the past two decades, research works on it have received considerable attention [1–5]. Due to the development of the theories of nonlinear dynamics and chaos, prediction of the global bifurcations and the Shilnikov-type chaotic dynamics becomes possible for the suspended cable systems. In [6], four dimensional perturbed Hamiltonian systems were divided into three basic types, and Melnikov method was used to analyze the global bifurcations and chaotic dynamics of these three types systems. Based on the study given by Wiggins[6], a new global perturbation method which could be utilized to detected the existence of single-pulse homoclinic and heteroclinic orbits for some four dimensional systems was presented by Kovacic and Wiggins [7]. This global perturbation technique is a combination of higher-dimensional Melnikov theory, geometrical singular perturbation theory and the theory of invariant manifolds. It is considered that this technique is fairly effective when the Shilnikov-type single-pulse homoclinic and heteroclinic orbits are studied in four-dimensional nonlinear systems. Several researchers applied this technique to many engineering problems, see [3, 4, 8–18] for more details. In [4,5], using the method of multiple scales, a parametrically and externally excited suspended cables system was transformed to the averaged equations, and some local bifurcation behaviors were presented in [4]. In [5], Chen et.al had studied the multipulse homoclinic orbits in the case 2 1 f f  , y x c c k k k k    , , 6 3 5 2 of this suspended cables system, but we think it is necessary to consider further. Hence, based on their researches, in this paper, some cases of this system are considered by the method of normal form, and the studies of this paper focus on the single pulse homoclinic orbits and chaos for this system. This paper is organized as follows: Govern equations of the suspended cables, averaged equations and normal form of the averaged equations are presented in Section 2. In Section 3, some dynamical properties of the unperturbed system on heteroclinic bifurcations are obtained. Analysis about the perturbed system is presented in Section 4, and existence of the single-pulse Silinikov homoclinic orbits is given in Section 5. Some numerical simulations are given in Section 6 to verify our conclusions in Section 5. The work ends in Section 7 with a short summary.

Single-pulse Chaotic Dynamics in Suspended Cables with Parametric and External Excitations