This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?Lin Y.K., Probabilistic Theory of Structural Dynamics, McGraw-Hill, New York, 1967. 132. Lin Y.K., Some Observations on the Stochastic Averaging Method, Probabilistic Engineering Mechanics, 1(1), 23-27 ... Lin Y.K., Cai G.Q., Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric andanbsp;...
|Title||:||The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions|
|Publisher||:||World Scientific - 1994-01-01|