Some new developments in nonlinear stochastic structural dynamics recently made by the present author and his co-workers are reviewed. A nonlinear structure under random loading is modeled as a stochastically excited and dissipated Hamiltonian system of finite degree-of-freedom (DOF). The functional form of the exact stationary solution, the equivalent nonlinear system and the stochastic averaging equations of a stochastically excited and dissipated Hamiltonian system are constructed based on the integrability and resonance of the associated Hamiltonian system, and thus the response of the system is predicted. The stochastic stability, stochastic bifurcation and optimal nonlinear feedback control of the system are treated by using the stochastic averaging method for quasi-Hamiltonian systems. It is pointed out that the theory is promising and deserves further development.
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