Filter approach to the stochastic analysis of MDOF wind-excited structures

In this paper, an approach useful for stochastic analysis of the Gaussian a nd non-Gaussian behavior of the response of multi-degree-of-freedom (MDOF) wind-excited structures is presented. This approach is based on a particula r model of the multivariate stochastic wind field based upon a particular d iagonalization of the power spectral density (PSD) matrix of the fluctuatin g part of wind velocity. This diagonalization is performed in the space of eigenvectors and eigenvalues that are called here wind-eigenvalues and wind -eigenvectors, respectively. From the examination of these quantities it ca n be recognized that the wind-eigenvectors change slowly with frequency whi le the first wind-eigenvalue dominates all the others in the low-frequency range. It is shown that the wind field can be modeled in a satisfactory way by taking the first wind-eigenvector as constant and by retaining only the first eigenvalue in the calculations. The described model is then used for stochastic analysis in the time domain of MDOF wind-excited structures. Th is is accomplished by modeling each element of the diagonalized wind-PSD ma trix as the velocity PSD function of a set of second-order digital filters with viscous damping driven by white noise of selected intensity. This appr oach makes it easy to obtain in closed form the statistical moments of ever y order of the structural response, taking full advantage of the Ito calcul us. Moreover, in the proposed approach, it is possible to reduce the comput ational effort by appropriately selecting the number of wind modes retained in the calculation. (C) 1998 Elsevier Science Ltd. All rights reserved.