Abstract
Perturbation method is a commonly used method to solve galloping equation of iced transmission lines, but few scholars have studied the influences of perturbation method on the accuracy of approximate solutions of the galloping equation. In order to analyze the accuracy of approximate solutions obtained by perturbation method for galloping equation of iced transmission lines, the partial differential galloping equation of iced transmission lines with quadratic and cubic nonlinear terms is obtained firstly. Then, the partial differential galloping equation is transformed into ordinary differential galloping equation by Galerkin method. Finally, the approximate solutions of the partial differential galloping equation are obtained by averaging method and first-order, second-order, third-order, and fourth-order multiple scales methods, and the results obtained by these methods are compared systematically. By comparing the numerical solutions and the approximate solutions obtained by averaging method, it can be found that, with the increasing in wind velocity and Young’s modulus of iced transmission lines, the nonlinearity of the system would strengthen and the drift of the vibration center of the system would also increase. The larger the drift is, the greater the error between the approximate solutions obtained by averaging method and the numerical solutions will be. And when the wind velocity reaches 32 m/s, the error would arrive at 17.321%. By comparing the numerical solutions and the approximate solutions obtained by the first-order, the second-order, the third-order, and the fourth-order multiple scales methods, it can be concluded that the first-order multiple scales method is less complex computationally. The accuracy of approximate solutions obtained by the fourth-order multiple scales method is better than that obtained by the first-order, the second-order, and the third-order multiple scales methods, and the error between the approximate solutions obtained by the fourth-order multiple scales method and the numerical solutions is less than 0.639%. The conclusions obtained in this paper would be helpful to the solutions of galloping equation of iced transmission lines and could also give some references to practical engineering.
Highlights
As an important energy transmission channel, high-voltage transmission lines are related to national social and economic development as well as people’s lives closely, so it is necessary to ensure the effective and normal operation of high-voltage transmission lines [1]. e galloping of iced transmission lines has always been a hot topic and iced transmission lines study is of great application value [2, 3]
In order to investigate the galloping of iced transmission lines, as early as 1932, Den Hartog [9] proposed the vertical galloping mechanism and found that the horizontal vibration amplitude of iced transmission lines was much smaller than the vertical amplitude, indicating that galloping mainly occurred in the vertical direction
Only the galloping in the vertical direction for iced transmission lines is considered in this paper
Summary
As an important energy transmission channel, high-voltage transmission lines are related to national social and economic development as well as people’s lives closely, so it is necessary to ensure the effective and normal operation of high-voltage transmission lines [1]. e galloping of iced transmission lines has always been a hot topic and iced transmission lines study is of great application value [2, 3]. Luongo [23, 24] established a model of cable with two DOFs considering the effects of static swing and dynamic torsion and used second-order multiple scales method to solve the corresponding nonlinear ordinary differential vibration equation of the model. Benedettini [28] used the fourth-order multiple scales method to solve the nonlinear partial differential equation of shallow cable under weak periodic excitation and analyzed the multivalue effect of the amplitude-frequency function of shallow cable. Rough the above analysis, this paper studied the influence of quadratic restoring force (q2) on the galloping system of transmission lines for the first time and found that the quadratic restoring force makes the vibration center of the system shift and the magnitude of the restoring force is directly related to drift of the system It is found in this paper that the existence of quadratic restoring force has affected the use of the perturbation method. The conclusions obtained in this paper would be helpful to the solutions of galloping equation of iced transmission lines and could give some references to practical engineering
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
