Analysis of High Codimensional Bifurcation and Chaos for the Quad Bundle Conductor's Galloping

Liu, Fuhao; Zhang, Qichang; Tan, Ying

doi:10.1088/0256-307x/27/4/044702

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…A number of investigations on internal resonances of galloping have been published [34–37]; however, these methods have been restricted to single span with fixed ends. In addition, Zhou et al .…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of transmission lines based on the dynamic stiffness method

Liu

Cai

2019

R. Soc. open sci.

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An improved mathematical model used to study the coupling characteristic of the multi-span transmission lines is developed. Based on the solution method for single-span cable, an expression for the dynamic stiffness of two-span transmission lines with an arbitrary inclination angle is formulated. The continuity of displacements and forces at a suspension point is used to derive the dynamic stiffness. Interactions between insulator strings and adjacent spans are accommodated. Considering the infinite dynamic stiffness corresponds to the natural frequencies of the transmission lines, the finite-element method (FEM) is employed to assess the validity of the dynamic stiffness. In the numerical investigation, attention is focused on the effect of the inclination angles, Irvine parameter, insulator string length and damping parameter. In addition, the modal function corresponding to the natural frequencies is derived. Then, the results of comprehensive parametric studies are presented and discussed. Special attention is paid to the effect of the Irvine parameter and damping parameter on the in-plane modal shapes. Finally, according to the theoretical model of two-span transmission lines, the generalized dynamic stiffness of transmission lines with an arbitrary number of spans and inclination angles is derived. The method can be used as the basis of the vibration analysis on a wide variety of multi-span transmission lines.

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Section: Introductionmentioning

confidence: 99%

Free vibration analysis of transmission lines based on the dynamic stiffness method

Liu

Cai

2019

R. Soc. open sci.

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Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

Yang

Tian

2013

Chinese Phys. B

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A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.

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Calculation Method for Dynamic Stiffness of Multispan Overhead Transmission Lines

Zhang²,

Liu

et al. 2022

IEEE Access

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The dynamic motion of a span is coupled to the other spans in transmission lines. From the continuity conditions, force equilibrium conditions, and dynamical equations of every span conductor and insulator string, a close-form expression for the dynamic stiffness of a coupled two spans in harmonic motion is presented. Unlike some existing theories of single span conductor, the effect between the conductors and insulator strings is considered here. By means of example calculations, the validity of the dynamic stiffness of two-span is demonstrated by the consistency of the results determined by the ABAQUS. Meanwhile, the dynamic stiffness and natural frequency are discussed under variation of the span lengths ratio, Irvine parameter, and insulator string length. Moreover, the modal shape function corresponding natural frequency is derived, and the contribution of localization mode is studied. The results show that the contribution is either sensitive to or independent of transmission line parameters in certain parameter ranges. Finally, generalizing the work of two-span, the dynamic stiffness of arbitrary span number is obtained.

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Analysis of High Codimensional Bifurcation and Chaos for the Quad Bundle Conductor's Galloping

Cited by 4 publications

References 17 publications

Free vibration analysis of transmission lines based on the dynamic stiffness method

Free vibration analysis of transmission lines based on the dynamic stiffness method

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

Calculation Method for Dynamic Stiffness of Multispan Overhead Transmission Lines

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