Random Response to Periodic Excitation with Correlated Disturbances

Abstract

The paper addresses non-Gaussian stationary response of linear single-degree-of-freedom (SDOF) systems subject to a periodic excitation with correlated random amplitude and phase disturbances that are modeled as correlated Gaussian white noise processes. Correlation between amplitude and phase modulation is specified by the cross-correlation coefficient. Numerical results for the second and fourth moment responses are presented. The probability density function of the response is calculated based on the cumulant-neglect closure method. Non-Gaussian nature of the response is discussed in terms of the excess factor. The results show that the moment responses generally increase with larger random amplitude disturbance and may decrease with larger random phase modulation for a lightly damped system at resonance. The cross correlation between amplitude and phase disturbances plays an important role in the system moment response. Larger system damping results in smaller system moment responses. The moment response may approach a limiting value, depending on the intensity of the amplitude disturbance, as the relative detuning or phase modulation increases. For the case of the phase modulation alone, the response may become Gaussian in the sense of up to the fourth-order moment for sufficiently large relative detuning or random phase disturbances.