The Journal of the Acoustical Society of America · 1963 · 182 citations · 0 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsStochastic ProcessesDissipative SystemsNonlinear DynamicsStochastic Differential EquationsDiscrete Nonlinear SystemsFokker - Planck EquationFokker-planck EquationsFokker-planck TheoryNonlinear SystemsRandom Excitation ModelsStationary SolutionsWhite Noise Excitation
The Fokker-Planck equation is derived and applied to discrete nonlinear dynamic systems subjected to white random excitation. For the class of problems in which the nonlinearities involve only the displacements of the system, it is shown that exact solutions can be constructed for the stationary Fokker-Planck equation. It is further shown that if stationary solutions exist they are unique.