EQUIVALENT GAUSSIAN PROCESS IN STOCHASTIC DYNAMICS WITH APPLICATION TO ALONG-WIND RESPONSE OF STRUCTURES

The principle of normal tail approximation, that is, a Gaussian IV equ ivalent to a non-Gaussian IV, which has been widely applied to structu ral reliability problems and has been extended by Grigoriu to stochast ic processes for calculating the mean upcrossing rate of a non-Gaussia n process, is here considered as an approximate tool for solving non-l inear dynamical problems, in which the excitation is non-Gaussian. A n on-Gaussian excitation is replaced by an equivalent one, so that all m ethods that are suitable For Gaussian agencies can be used. The method is applied to the study of the SDOF oscillator excited by wind turbul ence. The oscillator is assumed to be linear, but an excitation of the form y[V(t)-x(t)](2) introduces a non-linearity; moreover, it is no m ore Gaussian, even if the turbulence is. The solutions that are obtain ed using the equivalent Gaussian process for both the cases, in which the term x(t) is retained or is neglected, are compared with those tha t are obtained by the use of Monte-Carlo simulation and of stochastic differential calculus. The agreement is satisfactory for engineering p urposes. Copyright (C) 1996 Elsevier Science Ltd.