Three-dimensional dynamic analysis of transmission tower based on separation of background and resonant components of non-stationary downburst-induced response

Abstract

Transmission towers are vulnerable to the downburst, which highlights the importance of the investigation into the dynamic response of the structure suffering the non-stationary downburst action. Compared to the stationary downburst, the non-stationary downburst would raise the concerns that more wind parameters and substantial random samples of stochastic excitation would be involved in the time-domain dynamic analysis, leading to more attention to be paid on the computational efficiency. Therefore, this study aims to achieve a reliable approach for quickly approximating the time-varying variance of the transmission tower response under the non-stationary downburst, based on the separation of background and resonant components. Using the deterministic stochastic hybrid model (DSHM), the modulation function of the non-stationary downburst-induced wind loads is first derived in an analytical manner, and found to be composed of both the part resulting from the amplitude-modulated fluctuating wind and the part originating from the time-varying wind incidence angle due to the downburst’s motion. In association with the modal superposition method, the frequency-domain analysis method based on the reduced-order (in modal space) system is presented with consideration of the stochastic evolutionary spectrum, and the obtained variance response results agree well with the corresponding time-domain results obtained via the full-order system (finite element model). By implementing the theory of equivalent band-pass filter, the stochastic evolutionary spectrum-based background-resonance method is derived, which is found to be valid in the context of well separated natural frequencies, i.e., the equivalent bandwidths are not overlapped. Furthermore, it is revealed in theory that the background response is essentially the quasi-static fluctuating response of the structure under the fluctuating wind loads, which is corroborated by the numerical results. In addition, a closed-form formula is proposed for approximating the covariance of the stochastic wind velocity that is in compliance with Kaimal’s spectrum. Thereby, all the calculations in the background-resonance method would be algebraic, which makes it easy to compute the variance response. Note that the application of the background-resonance approach presented herein to the transmission towers can be easily extended to that to the other complex structures. Finally, the validation of the methodologies presented herein is verified by the case study.