A stationary model for periodic excitation with uncorrelated random disturbances

The paper presents a stationary model for periodic excitations with random amplitude and phase disturbances for linear and nonlinear random vibration analysis. The disturbances are modeled as uncorrelated stationary white noise processes. Application of the model is demonstrated by stationary moment response of a linear single-degree-of-freedom system subject to such excitations. To find moment responses, an equivalent augmented system subject to parametric white noise excitations under certain constraint conditions is studied. Numerical results for the second and fourth-order moment responses are presented. The probability density function of the response is calculated based on thhe cumulant-neglect closure method. NonGaussianity of the response is discussed in terms of the excess factor. The results show that the random amplitude disturbance can significantly increase system moment response. The random phase modulation may increase or reduce the system moment response, depending on the value of relative detuning berween the system natural frequency and the mean excitation frequency. The response may become Gaussian in the sense of up to the fourth-order moment for sufficiently large random phase or relative detuning.