Non-Gaussian probability density function of SDOF linear structures under wind actions

Wind velocity is usually analytically described adding a static mean term to a zero mean fluctuation stationary process. The corresponding aerodynamic alongwind force acting on a single degree of freedom (SDOF) structure can be considered as a sum of three terms proportional to the mean wind velocity, to the product between mean and fluctuating part of the wind velocity and to the square power of the fluctuating wind velocity, respectively. The latter term, often neglected in the literature, is responsible for the non-Gaussian behaviour of the response. In this paper a method for the evaluation of the stationary probability density function of SDOF structures subjected to non-Gaussian alongwind aerodynamic forces is presented. The method requires first the approximation of the non-Gaussian probability density function by means of a C-type Gram-Charlier series expansion; the coefficients of this series are then evaluated using very simple linear algebraic relationships once the response statistical moments or, alternatively, the cumulants or the quasi-moments up to a fixed order have been determined.