Efficient fatigue life assessment strategy via generalizing the Lyapunov equation method by Hilbert transform

Abstract

In this paper, an effective strategy is proposed for high-cycle fatigue life assessment under random excitation, with the generalized Lyapunov equation method (GLEM). Firstly, the Lyapunov equation method is generalized for odd spectral moments, which can be expressed in the Hilbert transform of the auto-correlation function. Then, a semi-analytic coefficient matrix of the Lyapunov equation is deduced as the excitation power spectral density (PSD) is discretized, based on which the GLEM is extended to deal with arbitrary excitation PSD form. Finally, combined with the Palmgren-Miner rule and frequency-domain methods, a convenient high-cycle fatigue assessment strategy is constructed based on the GLEM. In this way, the spectral moments can be obtained by a low-dimensional linear algebraic equation, avoiding the derivation of the response PSD. The correctness and efficiency of the proposed method are verified by numerical examples, as well as the effects of damping ratio, excitation PSD, modal truncations, and frequency points number.