Investigation of internal resonance of a three-degree-of-freedom system under random excitation

A three-degree-of-freedom system, with cubic nonlinearity, was investigated. The system consists of two masses attached by nonlinear springs and linear dampers. The lower mass was excited, through similar attachment elements, by a random excitation. The excitation was assimied to be narrow band white noise. Since the statistical moments of this nonlinear system responding to random excitation are governed by an infinite hierarchy of equations, truncation or closure schemes are necessary to approximately compute the important lower order moments. For this research, the Gaussian closure scheme and the non- Gaussian closure scheme were used. The non-Gaussian closure scheme was in the cumulant neglect sense, whereby only the cumulants up to the sixth order were considered. The mean-square response was the main system statistical property used to investigate the system behavior. The system response was investigated in the vicinity of the combination resonance conditions. The results obtained by the two methods were compared on the basis of the prediction of the system response around the combination resonance condition. An effort was made to account for the differences of the system prediction as achieved from the respective closure schemes.