Abstract
The asymptotic stability, almost sure also in the mean square, of a viscoelastic system subjected to a load in the form of a random stationary broadband ergodic process is investigated. The behaviour of this system is described by integro-differential equations with stochastic parameters. The stability is considered with respect to the perturbation of the initial conditions. The governing relation is taken in an integral form with a creep (or relaxation) kernel of convolution type, which satisfies the condition of limited creep of the material. Using the fundamental solution of the corresponding deterministic integro-differential equation and its maximum Lyapunov exponent, the sufficient condition for stability of the zero solution of the initial equation or, which is the same thing, the equilibrium position of the viscoelastic system, is obtained.
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