Auxiliary harmonic excitation generalized method for random vibration analysis of linear structures under non-stationary Gaussian excitation

Frequency-domain methods are the most fundamental and effective methods for non-stationary random vibration analysis. However, the existing frequency-domain methods often involve truncation for degree of mode or decomposition of the power spectrum in multi-correlation conditions, which may have impact on the computational accuracy and efficiency of the methods. To avoid the truncation for degree of mode and the decomposition of the power spectrum, an accurate and efficient auxiliary harmonic excitation generalized method is proposed for random vibration analysis of linear structures under non-stationary Gaussian excitation. First, several existing frequency-domain analysis methods are investigated and discussed. Second, the generalized impulse response function, the generalized frequency response function, and the evolutionary generalized frequency response function are proposed. Meanwhile, the physical meaning of the evolutionary frequency response function is re-investigation, in which the response for the evolutionary harmonic excitation and the evolutionary frequency response function proves equivalent. Subsequently, according to the physical meaning, a novel and easy-to-implement algorithm of the response PSD is proposed. The response for the evolutionary auxiliary harmonic excitation can be quickly evaluated based on the time-domain explicit formulation method. Finally, two examples are investigated to verify the accuracy and efficiency of the proposed method.