The estimation of displacement and fatigue life of nonlinear structures subjected to random excitation presents several analysis complications that will be discussed. Recent nonlinear random vibration experiments performed at Wright Patterson Air Force Base (WPAFB)  have generated data that has been analyzed in the time and frequency domains to model this complicated behavior. This paper will discuss how the probability density function transform and inverse distribution function methods have been applied. Probability density function (PDF) transformations have been shown to be useful for estimating nonlinear random fatigue damage, but preliminary applications were limited . Analysis of the WPAFB data has employed additional normal PDF, peak PDF and nonlinear peak PDF transformations. These PDF transforms were used to estimate rates of zero crossings and more importantly, two-dimensional rainflow matrices (RFM) of total stress. The inverse distribution function method has been shown to be very effective for estimating linear to nonlinear functional relationships. Several functional relationships of linear to nonlinear displacement and stress are presented, illustrating the method using response and peak distribution functions. Standard closed form PDF transformation methods require the linear to nonlinear functional relationships to be both differentiable and invertible. Numerical PDF transformation methods have been developed that require only differentiable functional relationships. Examples of the numerical methods will be presented for a two-step serial application of the PDF transform. Analyses of the WPAFB data and subsequent ordinary differential equation (ODE) numerical experiments with Duffing equation systems have shown that total stress peak PDFs (or 2D RFMs) can be estimated using the PDF transform method. These estimated RFMs and the resultant time to failure will be compared to estimates using the raw WPAFB experimental results.
Date of creation, presentation, or exhibit
Department, Program, or Center
Mechanical Engineering (KGCOE)
Sweitzer, Karl and Ferguson, N.S., "Nonlinear random displacement and fatigue estimates using PDF transformations" (2006). Accessed from
RIT – Main Campus