Random vibration response statistics for fatigue analysis of nonlinear structures

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Title: Random vibration response statistics for fatigue analysis of nonlinear structures
Author: Sweitzer, Karl
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. Numerical simulations of a nonlinear single degree of freedom system were produced to study other aspects of the large deflection structural response. Very large sample size data sets of displacement, velocity, acceleration and stress were used to quantify the rate of convergence of several random response statistics. The inverse distribution function method was also applied to the simulation results to estimate normal and peak linear to nonlinear functions. These functions were shown to be useful for probability density function estimates and for estimating rates of response zero crossings. 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. Further studies of the nonlinear increase in the frequency of stress response are included in the fatigue analysis
Record URI: http://hdl.handle.net/1850/5082
Date: 2006-03

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