The Stability of a Moving Elastic Strip Subjected to Random Parametric Excitation

The dynamic stability of a thin strip, traveling axially, at a constant speed between two roller supports is investigated for the case of zero mean random in-plane loading. Galerkin’s method is used to reduce the equations of motion to a set of fourth-order stochastic equations. An extention of the method first proposed by Wu and Kozin is developed which allows determination of the sufficiency conditions to guarantee Almost Sure Asymptotic Stability of stochastic systems of order greater than two. Using this method, results in terms of the variance of the random loadings on the moving strip are derived. It is found that the critical noise level to guarantee stability of the strip decreases with increasing mode, approaching asymptotically a level determined solely by the strip stiffness.