The Journal of the Acoustical Society of America · 1963 · 612 citations · 0 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsStochastic ProcessesNonlinear DynamicsStochastic Differential EquationsEquivalent LinearizationFokker - Planck EquationFokker-planck EquationsFokker-planck TheoryLinearizationNonlinear Dynamic ResponseNonlinear SystemsRandom Excitation Models
The method of equivalent linearization of Kryloff and Bogoliubov is generalized to the case of nonlinear dynamic systems with random excitation. The method is applied to a variety of problems, and the results are compared with exact solutions of the Fokker-Planck equation for those cases where the Fokker-Planck technique may be applied. Alternate approaches to the problem are discussed, including the characteristic function method of Rice.