Research on the transmission law of kurtosis of SDOF system under nonstationary and non-Gaussian random excitations

Vibration fatigue failure of structures under complex random excitations is a common problem in the field of engineering, and it seriously endangers the reliability and safety of major equipments and structures. It is particularly important to accurately predict the vibration fatigue life of structures under random excitations. Generally, it is assumed that the vibration excitation of engineering structures follows a stationary Gaussian distribution, but the actual excitation usually follows a nonstationary and non-Gaussian distribution, especially under harsh or variable working conditions. The vibration fatigue life of structures is closely related to the structural dynamic response characteristics, and the kurtosis of the structural response has a particularly obvious influence on the vibration fatigue life. In this paper, taking the single-degree-of-freedom system as an example and by decomposing complex random excitations in frequency segments, the dynamic response law of the system under nonstationary and non-Gaussian random excitations is studied in depth, and a mathematical model describing the transmission law of the kurtosis between the decomposed signal of excitation and response signal is established. The results show that there is a close linear relationship between the kurtosis of the structural dynamic response and the kurtosis of the decomposed signal obtained by frequency decomposition of the excitation signal by 3.2 times the half power bandwidth at the damped natural frequency of the structure. It is possible to quantitatively estimate the kurtosis of the structural response according to this relationship, which lays the foundation for accurately predicting the vibration fatigue life of structures under nonstationary and non-Gaussian random excitations.