Abstract
The problem of simulating undisturbed behavior of a nonlinear system subjected to the action of deterministic and stochastic parametrical load is examined and the stability of undisturbed motion of the system is analyzed. It has been revealed that the trajectory motion of points changes greatly, if we take into account one or several components in deflection expansion while examining the deterministic and stochastic parametrical problem. In this case it is possible to stabilize the unstable undisturbed motion of the rod by superimposing the stochastic component in the form of a stationary Gaussian process with hidden periodicity to the deterministic load. By stability we mean the almost certain stability and average stability and mean square stability (stability with respect to the first- and second-order statistic moments).
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