Mathematical model of ice-covered wires galloping phenomenon


DOI: 10.34759/trd-2020-114-02

Аuthors

Shavnya R. A.

Institute of Applied Mechanics of Russian Academy of Science, IPRIM RAS, 7, Leningradskiy Prospekt, Moscow, 125040, Russia

e-mail: shavnya.ruslan@yandex.ru

Abstract

The article considers the problem on aeroelastic fluctuations of power transmission line ice-covered wires under the wind loading (this phenomenon is also known as wires galloping). The sought quantities are the generalized coordinates of the problem: the coefficients of the approximating functions of the Ritz method and local displacements. A rigid connection between cross section of the ice and cross section of the wire is assumed. It is regarded also that while moving the wire cross section remains in the same plane. The equations describing the process dynamics are being obtained using the D’Alembert-Lagrange principle equations. The summarizing system of nonlinear differential equations, obtained by grouping the terms at variations of work and latent energy, describes the process dynamics. The system should be integrated numerically using appropriate methods (Runge–Kutta, linear multistep methods in case of high stiffness of the system, etc.). Initial conditions for the dynamics problem integrating may be obtained from the solution of the statics problem. The equations for the static problem can be obtained by excluding all inertial terms (terms with a time derivative) from the equations of the dynamic problem. The problem of statics is also being solved numerically, for example method of continuing by the parameter. The phenomenon described in the article is similar to the aviation flutter phenomenon, and, correspondingly, the described model with certain add-ons can be applied to solve this type of problem. Besides, the model of the elastic tensile wire, described in the article, can be employed in other tasks with tether systems (aircraft fuel hoses, space tether systems, etc.).

Keywords:

conductor galloping, aeroelastic fluctuations, deformable solid mechanics, flutter.

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