Kurtosis transfer in MDOF systems under amplitude-modulated Non-Stationary Non-Gaussian Excitations: A Frequency-Domain decomposition approach

Non-stationary non-Gaussian random vibrations, frequently encountered in aerospace, mechanical, and civil systems, often induce transient structural responses with complex and unpredictable dynamics. Kurtosis, a key statistical measure of signal impulsiveness, plays a dual role in characterizing such transient behaviors and assessing vibration fatigue damage. This study develops a kurtosis transfer model for multi-degree-of-freedom (MDOF) systems under amplitude-modulated non-stationary non-Gaussian excitations, assuming the excitation spectrum sufficiently covers the system’s modal frequencies to induce resonance-dominated responses. The proposed framework reveals how kurtosis is selectively transmitted through specific modal pathways by establishing a mathematical relationship between frequency-domain excitation substructures and the resulting response kurtosis. In addition, a phase modulation strategy is introduced to adjust the non-Gaussian properties of decomposed excitation signals, thereby enabling active control of the system’s response kurtosis. Numerical simulations and experimental validations confirm the model’s predictive accuracy. The resulting methodology offers a physically interpretable and computationally efficient framework for known vibration systems, supporting both dynamic analysis and the design of excitation signals with targeted kurtosis levels for accelerated vibration fatigue testing.