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Stochastic averaging: An approximate method of solving random vibration problems. (English) Zbl 0582.73077
Results 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:
74H50Random vibrations (dynamical problems in solid mechanics)
70L05Random vibrations (general mechanics)
60H99Stochastic analysis