Equivalent Gaussian process in stochastic dynamics with application to along-wind response of structures

Thee principle of normal tail approximation, that is, a Gaussian rv equivalent to a non-Gaussian rv, which has been widely applied to structural reliability problems and has been extended by Grigoriu to stochastic processes for calculating the mean upcrossing rate of a non-Gaussian process, is here considered as an approximate tool for solving non-linear dynamical problems, in which the excitation is non-Gaussian. A non-Gaussian excitation is replaced by an equivalent one, so that all methods that are suitable for Gaussian agencies can be used. The method is applied to the study of the SDOF oscillator excited by wind turbulence. The oscillator is assumed to be linear, but an excitation of the form r[v(t) - i(t)] ’ introduces a non-linearity; moreover, it is no more Gaussian, even if the turbulence is. The solutions that are obtained using the equivalent Gaussian process for both the cases, in which the term z?(t) is retained or is neglected, are compared with those that are obtained by the use of Monte-Carlo simulation and of stochastic differential calculus. The agreement is satisfactory for engineering purposes.