Random vibration response statistics for fatigue analysis of nonlinear structures

Abstract

Statistical analysis methods are developed for determining fatigue time to failure for nonlinear structures when subjected to random loading.  The change in the response, as structures progress from a linear regime to a large amplitude nonlinear regime, is studied in both the time and frequency domains.  The analyses in the two domains are shown to compliment each other, allowing keen understanding of the physical fundamentals of the problem.

Analysis of experimental random vibration data, obtained at Wright Patterson Air Force Base, is included to illustrate the challenge for a real, multi-mode, nonlinear structure.  The reverse path frequency response identification method was used with the displacement and strain response to estimate nonlinear frequency response functions.  The coherence functions of these estimates provided insight into nonlinear models of the system.  Time domain analysis of the nonlinear data showed how the displacement and strain departed from a normal distribution.  Inverse distribution function methods were used to develop functions that related the linear to the nonlinear response of the structure.  These linear to the nonlinear functions were subsequently used to estimate probability density functions that agreed well with measured histograms.

Fatigue analysis was performed on the experimental and simulated linear and nonlinear data.  The time to failure estimates for the nonlinear results was shown to increase dramatically when compared to the linear results.  The nonlinear stresses have significant positive mean values due to membrane effects, that when used with fatigue equations that account for mean stresses, show reductions in time to failure.

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