Nonlinear Vibration Models for Extremes and Fatigue

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Abstract
Hermite moment models of nonlinear random vibration are formulated. These models use response moments (skewness, kurtosis, etc.) to form non‐Gaussian contributions, made orthogonal through a Hermite series. First‐yield and fatigue failure rates are predicted from these moments, which are often simpler to estimate (from either a time. history or analytical model). Both hardening and softening nonlinear models are developed. These are shown to be more flexible than the conventional Charlier and Edgeworth series, with the ability to reflect wider ranges of nonlinear behavior. Analytical moment‐based estimates of spectral densities, crossing rates, probability distributions of the response and its extremes, and fatigue damage rates are formed. These are found to compare well with exact results for various nonlinear models, including nonlinear oscillator responses and quasi‐static responses to Morison wave loads.

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