Time-Frequency Buffeting Responses of Transmission Lines Excited by Two-Dimensional Turbulent Wind: Closed-Form Solution

Currently, the buffeting analysis for transmission lines (TLs) only involves the excitation of horizontal turbulence, while numerous investigations have proven that significant vertical turbulence exists in many wind fields. Additionally, overhead conductors generally exhibit nonlinear behavior, rendering the conventional multidimensional wind-excited model based on linear theories no longer applicable. To address these challenges and avoid relying on the extremely time-consuming nonlinear finite-element method, this paper proposes a closed-form solution (CFS) for predicting time-frequency buffeting responses of TLs excited by two-dimensional turbulent wind. First, the static response is determined through nonlinear static analysis. Then a two-dimensional influence line method, employed to evaluate the turbulent wind effect, is developed by decoupling the buffeting responses in two directions. Power spectral density functions for various responses are further derived, considering the cross-correlation between horizontal and vertical turbulence. Moreover, the impact of wind attack angle on various responses is revealed through parametric analyses. Finally, an amplification factor is introduced to modify the vertical wind effect on equivalent static wind load (ESWL), and the corresponding fitting formula is provided to facilitate the design. Numerical verification illustrates the high accuracy and efficiency of the CFS. Although the wind attack angle is time-varying, it is controlled by the mean wind. As it increases, the RMS of transverse and longitudinal reactions decrease, while the RMS of the vertical reaction increases. Neglecting vertical turbulence underestimates the horizontal ESWL, with the amplification factor exceeding 1.35 when a wind attack angle of 50 degrees is considered.