Nonlinear Vibration Models for Extremes and Fatigue

TLDR

The study formulates Hermite moment models for nonlinear random vibration, developing both hardening and softening nonlinear representations. These models employ Hermite series to construct orthogonal non‑Gaussian contributions from response moments (skewness, kurtosis, etc.) and use them to analytically estimate spectral densities, crossing rates, probability distributions, and fatigue damage rates. The resulting models predict first‑yield and fatigue failure rates, outperforming conventional Charlier and Edgeworth series, and match exact results for various nonlinear oscillators and Morison wave load responses.

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.