Estimation of Overhead Power Line Support Vibration Frequency
DOI:
https://doi.org/10.24160/1993-6982-2022-5-150-156Keywords:
power line support, number of panels, lower frequency estimate, truss spatial model, Dunkerley's methodAbstract
The aim of the study is to obtain formulas for assessing the overhead power line support truss spatial model fundamental vibration frequency. A spatial statically determinate model of the structure is proposed. To calculate the truss stiffness matrix, the forces in the bars are determined by cutting out nodes in a program compiled in the Maple symbolic mathematics environment. The system of equilibrium equations in projections on the coordinate axes has a matrix form. The stiffness matrix coefficients are calculated using the Maxwell–Mohr formula. The hinges are taken to be ideal, and the truss weight is uniformly distributed over the truss nodes. Horizontal vibrations of the masses are considered. To estimate the natural vibration fundamental frequency, the Dunkerley method was used, which reduces the problem with many degrees of freedom to the calculation of partial frequencies. The coefficients in the solution formula are determined using the induction method by generalizing a number of formulas for trusses with a sequentially increasing number of panels along the height of supports. The general terms of the sequences of coefficients satisfy linear homogeneous recurrent equations of no higher than eleventh degree. The solutions of the equations give the final formula for the dependence of the lowest natural vibration frequency of the support truss with the mass distributed over the nodes on the number of panels. A comparison of the analytical solution with the numerical one has shown that the error of the obtained estimate does not exceed 6%. The results can be used in engineering calculations of power line supports.
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Для цитирования: Кирсанов М.Н. Оценка частоты колебаний опоры линии электропередач // Вестник МЭИ. 2022. № 5. С. 150—156. DOI: 10.24160/1993-6982-2022-5-150-156
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Работа выполнена при поддержке: Российского научного фонда (проект № 22-21-00473)
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For citation: Kirsanov M.N. Estimation of Overhead Power Line Support Vibration Frequency. Bulletin of MPEI. 2022;5:150—156. (in Russian). DOI: 10.24160/1993-6982-2022-5-150-156
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The work is executed at support: Russian Science Foundation (Project No. 22-21-00473)
