Stochastic averaging: An approximate method of solving random vibration problems.

*(English)*Zbl 0582.73077Results obtained by applying the method of stochastic averaging to random vibration problems are discussed. This method is applicable to a variety of problems involving the response of lightly damped systems to broad- band random excitations. Solutions pertaining to both linear and nonlinear vibrations are reviewed, and it is shown that the technique enables, in the case of parametric excitation, stability criteria to be established. Some results which have been obtained relating to the first- passage reliability problems are also surveyed. Various applications of the theory to engineering problems are outlined.

##### MSC:

74H50 | Random vibrations in dynamical problems in solid mechanics |

70L05 | Random vibrations in mechanics of particles and systems |

60H99 | Stochastic analysis |