Stochastic stability of narrow moving bands under random tension fluctuation is investigated within the concept of the Lyapunov exponent. The moment Lyapunov exponents and Lyapunov exponents are important characteristics determining the moment and almost-sure stability boundaries of a stochastic dynamical system. Galerkin’s method is used to reduce the partial differential equation of motion to a corresponding ordinary differential equation with randomly varying stiffness. We obtain explicit stability conditions based on the asymptotic expansion series for the moment Lyapunov exponent g(p), and the Lyapunov exponent λ for a two-dimensional linear stochastic system.
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