Random Imperfections for Dynamic Pulse Buckling

Abstract

White noise and wavelength‐dependent random imperfections, each represented by Fourier series having random coefficients with Gaussian distributions, are explored as representations of imperfections to be used in numerical investigations of dynamic pulse buckling. Results from a closed form solution show the relationship between these imperfections and previously used single‐mode imperfections, and demonstrate the statistics of typical buckled forms. Example random imperfection shapes and growing buckle forms show the advantage of using “gray” noise (standard deviation σ of the coefficients decreases as n-1/2) rather than pure white‐noise (constant σ) imperfections. The statistics of buckle amplitudes from buckled forms with 15 or more waves are shown to give good estimates for the statistics of a large population of random buckle shapes. This is an important result for finite element calculations, in which Monte Carlo calculations would be time consuming and expensive.