Almost Sure Stability of a Moving Elastic Band

Abstract

In this paper, the stochastic stability problem of a moving elastic band subjected to action in-plane acting forces is investigated. Each force consists of a constant part and a time-dependent zero mean stochastic function. By using the direct Liapunov functional method, almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, damping coefficient, and geometric and physical parameters of the band. Numerical calculations are performed for infinite mode and compared with known results. Almost sure stability regions are shown for infinite and first mode the two-dimensional density probability function, and for higher modes when the edge load Gaussian or harmonic process is known.