Simulation of Nonstationary and Nonhomogeneous Wind Velocity Field by Using Frequency–Wavenumber Spectrum

P Hong,H P Hong

doi:10.3389/fbuil.2021.636815

Abstract

The time history analysis is used to estimate the peak responses of structures subjected to stationary and nonstationary winds. The time histories of the fluctuating wind processes at multiple points can be simulated based on the spectral representation method for given target auto and cross power spectral density (PSD) functions. As the number of the processes of interest increases, the computation time for the simulation increases drastically. For the stationary homogeneous or nonhomogeneous wind fields, this problem can be overcome by using the frequency-wavenumber PSD function to simulate the stochastic propagating waves or fields. In the present study, a technique to simulate the amplitude modulated and frequency modulated nonstationary and nonhomogeneous stochastic propagating wind fields is presented. The technique relies on representing the nonstationary wind velocity by amplitude modulating a process that is time transformed from a stationary process. It is based on the established relations between the PSD functions of the nonstationary and of the stationary wind velocity. Simple to use and implement equations to carry out the simulation for one-dimensional line wind velocity field and two-dimensional nonstationary and nonhomogeneous wind velocity field are presented. The use of the developed technique and its adequacy is illustrated through numerical examples.

Highlights

AND BACKGROUNDStructures such as tall buildings, long bridges, and wind turbines are sensitive to wind actions (Simiu and Scanlan, 1996; Strommen, 2010)
The fluctuating winds can be characterized by using the power spectral density (PSD) function such as the Davenport spectrum, Kaimal spectrum, and von Karman spectrum
A common characteristic of these spectra is that they can be expressed in terms of reduced frequency or Monin coordinate, which is proportional to the turbulence length scale and inversely proportional to the mean wind velocity

Summary

INTRODUCTION

Structures such as tall buildings, long bridges, and wind turbines are sensitive to wind actions (Simiu and Scanlan, 1996; Strommen, 2010). For the fluctuating wind modelled as a stationary process defined by its PSD function, the most popular method to simulate the time histories of wind velocity is SRM. To avoid the difficulty in dealing with this position-dependent inhomogeneity, as a simple pragmatic approach to simulate two-dimensional wind velocity field, one could replace (1/x2j + 1/x2k) by 2/zav, where zav represents a weighted average height for a considered exposure area of a structure for a wind engineering application where the vertical dimension is much smaller than the horizontal dimension. Example 1, spectral analysis carried out by using the simulated samples of the propagating wind field indicates that the auto and cross PSD function calculated using the samples in the τ-domain match well their target values. The total wind velocity of the propagating wind field at a given time is equal to the mean wind component plus the fluctuating wind component (as shown in Figures 6, 7)

CONCLUSION

DATA AVAILABILITY STATEMENT