Аналитические оценки деформаций и собственных частот опор линий электропередач

Abstract

The purpose of the study is to derive analytical expressions for estimating the lower vibration frequency of the power line support truss flat models. The forces in the bars of statically determinate structures are determined by the method of cutting out nodes in a program written in the Maple symbolic mathematics language. To find deformations, the Maxwell-Mohr's formula is used under the assumption that all rods are elastic, and that the supports are modeled by rigid rods. It is supposed that the hinges are ideal, and the mass of the structure in the form of point loads is distributed over the truss nodes, and only horizontal load displacements are considered. In comparison with similar problem statements with analytical forms of solution, the present study takes into account the masses at all nodes of the structure. For two-sided estimation of the fundamental frequency, the methods of Dunkerley and Rayleigh are used. The coefficients of the formulas in the solutions obtained for trusses with different numbers of panels form sequences, the common terms of which from the solution of linear recurrent equations give the final formula for the frequency dependence on the number of panels. As a result of the study, formulas for deflection and estimation of the fundamental frequency of truss natural vibration depending on the number of panels and dimensions of the structure have been derived. The obtained formulas can be used in carrying out engineering analyses of power transmission line supports. The formulas for the deflection and frequencies of the studied trusses have a form simple and convenient for use (in particular, for assessing the accuracy of numerical solutions). The frequency obtained by the Rayleigh method is much closer to the fundamental natural frequency than its value estimated using the Dunkerley method.