Kurtosis transmission law of amplitude modulated non-Gaussian signals

There are many methods published about how to create non-Gaussian signals with given Power Spectral Density (PSD) and kurtosis, to use for vibration testing and/or fatigue life evaluation. However, some signals show significantly different fatigue damage characteristics, expressed as Fatigue Damage Spectrum (FDS), compared to others, highlighting the need for a proper understanding of their properties. A specific non-Gaussian signal generation method is studied in depth in this paper, where a Gaussian signal with defined PSD is multiplied with a slowly varying Amplitude Modulation Signal (AMS). This AMS is created by raising the absolute value of a Gaussian signal to a power p . A new algebraic expression for calculation of AMS parameter from given kurtosis is then presented. To investigate how kurtosis transmits from the excitation to the system response, simulations were conducted on single degree of freedom (SDOF) systems with varying AMS and system properties. A new kurtosis transfer model is then proposed and validated through vibration experiments on a cantilever beam. The results show that with a given input kurtosis, the response kurtosis can be accurately predicted from the SDOF resonance frequency divided by AMS cutoff frequency and SDOF system Q factor, which lays the foundation for fatigue life evaluation of structures under non-Gaussian excitations.