# Dynamic Response of Slender Vertical Structures Subjected to Thunderstorm Outflows
## 1 Introduction  
Slender vertical structures are sensitive to wind, which usually represents their design loading condition [1] and can induce fatigue-related collapses [2]. While their assessment under stationary wind conditions, such as extra-tropical cyclones, is nowadays consolidated in codes and standards, their reliability under nonstationary conditions caused via thunderstorm outflows is still a matter of research. As shown via meteorological observations [3], experimental measurements in laboratories [4], full-scale analyses of collected wind speed time histories [5], and their comparison with stationary boundary layer winds [6], thunderstorm outflow is characterized via a nose-shaped vertical mean velocity profile and nonstationary turbulent fluctuation. Therefore, most of the models and approaches available for synoptic winds are unsuitable for their representation. In addition, the reference wind velocity provided by codes is currently defined according to statistical analyses that do not distinguish between extra-tropical cyclones and thunderstorms [7]. Indeed, the wind velocities provided by synoptic winds and thunderstorm outflows are characterized by different extreme distributions [8]; in thunderstorm-prone areas, high return period thunderstorm wind speeds can be higher than those corresponding to extra-tropical cyclones, as pointed out by [PERSON] [9] and demonstrated by [PERSON] et al. [10], who carried out statistical analyses on thunderstorm time histories collected in the High Tyrrhenian Sea. Considering that synoptic winds provide higher wind speeds at greater heights and thunderstorms at lower ones, not only can mid-low structures be under-designed, but taller buildings can be over-designed to wind actions. As a result, since current codes and standards lack a reliable and handy approach for downburst-resistant structural design, the resistance and durability of mid-low structures can be put at risk by the occurrence of such extreme wind conditions, as pointed out by [PERSON] et al. [11] and investigated by [PERSON] et al. [12], who studied the collapse of transmission towers. During the last few decades, with the aim of providing engineers with suitable tools to predict the wind loading and maximum structural response to thunderstorms, different approaches were adopted, which can be gathered into two main families: time domain analysis (TDA) and time-frequency domain approaches. Time domain analysis consists of the evaluation of the dynamic response starting from wind velocity time histories that have been recorded full scale [13], simulated in moving jet wind tunnels [14], or simulated numerically starting from suitable statistical models of the wind speed. In particular, [PERSON] et al. [15] proposed a hybrid simulation technique to generate thunderstorm time histories, subsequently adopted by [PERSON] and [PERSON] [16], which consists of the joint usage of Monte Carlo simulations and wind speed data collected at full scale. Although they represent a reliable method, they can be time-consuming, and their use is restricted by the limited set of available full-scale thunderstorm records. Starting from a wide set of thunderstorm records, the thunderstorm response spectrum (TRS) technique was proposed by [PERSON] et al. for single-degree-of-freedom (SDOF) systems [17], which was subsequently extended by [PERSON] for multi-degree-of-freedom (MDOF) systems [18], in analogy to the widely adopted earthquake response spectrum [19]. Despite its simple conceptualization and its reliability being based on a significant amount of data, the usage of the TRS approach lacks handiness due to the absence of analytical formulations and its reliance on charts. Time-frequency domain analysis makes use of advanced models such as the evolutionary power spectral density (EPSD) to account for the nonstationary characteristics of a thunderstorm outflow. In this framework, [PERSON] and [PERSON] [20] recently proposed an EPSD model for thunderstorms based on a large number of full-scale records, while [PERSON] et al.