The paper deals with an approach to the response limit estimation of the vibrating systems in the transient state. A gradient and perturbation methods for derivatives of the response with respect to the random parameters are shown. This sensitivity analysis can be performed for linear systems in the analytical way or in numerical way for both linear and nonlinear systems. In case of nonlinear systems it is supposed small deviations of random parameters from hyperbolic point of the system and that no bifurcations and changes of phase portrait will occur.
statistical characteristics, random vibration, nonlinear system