The investigation of the stability of elastic and viscoelastic rods under a stochastic excitation

stability ofelastic and viscoelastic rods subjected to a random stationary longitudinal force is considered. A numerical method of simulation of random realizations of a wide-band stationary process, corresponding to the variation of the longitudinal force in time. is employed. For each realization the numerical solution of the system of differential or integro-differential equations describing the dynamic behavior of the rods is found. With the help of Liapunov exponents which are calculated for statistical moments of the solution of the equations, the conclusion is made about the stability with respect to statistical moments. The described approach is applicable for the solution of similar stochastic problem for plates and shells under the linearized treatment. :(’ 1997 Elsevier Science Ltd. A11 rights reserved. I