THE NONSTATIONARY RESPONSE PROBABILITY DENSITY-FUNCTIONS OF NONLINEARLY DAMPED OSCILLATORS SUBJECTED TO WHITE-NOISE EXCITATIONS

The non-stationary random response analysis of non-linear systems is of interest in many areas of vibration. In this paper an estimate is made of the non-stationary response probability density function (pdf) of non-linearly damped oscillators by applying non-Gaussian closure. This approximate technique is believed to be capable of handling strong non-linearities. The time dependent solution, which explores the transition of pdfs from a given initial state to the stationary state, is numerically obtained in different time steps. The investigation shows that the response pdfs of displacement and velocity may have quite different shapes and are often very unlike Gaussian. In addition to the pdfs, some important response statistics can also be directly acquired by the approach. © 1990.