Stochastic stability of quasi-integrable and resonant Hamiltonian systems excited by fractional Gaussian noise

Engineering structures are often subjected to random loads, where structural stability significantly impacts operational performance and even safety. This paper theoretically investigates the stochastic stability of multi-degree-of-freedom (MDOF) quasi-integrable and resonant Hamiltonian systems under fractional Gaussian noise (fGn) excitation. Due to the long-range dependence inherent in fGn, the system response exhibits non-Markovian behavior. Currently, there is no established effective theoretical method for analyzing the stability of stochastic systems under such excitation. To address this challenge, we propose a novel strategy: according to the broad power spectrum of fGn, we approximate it as wideband noise and subsequently apply the stochastic averaging method for quasi-integrable Hamiltonian systems under wideband noise excitation. This approach enables the stability analysis of MDOF integrable and resonant Hamiltonian systems driven by fGn. Numerical example demonstrates well agreement between the proposed analytical method and simulation results, validating the effectiveness of this methodology.