Abstract: A survey of stochastic averaging methods in random vibration is given. After a brief introduction to the basic ideas, the advantages and the history of the methods, three kinds of stochastic ...

Abstract: The significant advances in nonlinear stochastic dynamics and control in Hamiltonian formulation during the past decade are reviewed. The exact stationary solutions and equivalent nonlinear system ...

Abstract: An equivalent nonlinear system method is proposed to obtain the approximate probability density for the stationary response of multi-degree-of-freedom integrable Hamiltonian systems with linear and ...

Abstract: The stationary response of multi-degree-of-freedom dissipated Hamiltonian systems to random pulse trains is studied. The random pulse trains are modeled as Poisson white noises. The approximate ...

Abstract: A stochastic averaging method for predicting the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian systems (nonintegrable-Hamiltonian systems with lightly linear and (or) nonlinear ...

Abstract: It is shown that the structure and property of the exact stationary solution of a stochastically excited and dissipated n -degree-of-freedom Hamiltonian system depend upon the integrability and ...

Abstract: The averaged equations of integrable and nonresonant Hamiltonian systems of multi-degree-of-freedom subject to light damping and real noise excitations of small intensities are first derived. Then, ...

Abstract: A stochastic averaging method is proposed to predict approximately the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian systems (nonintegrable Hamiltonian systems with lightly linear ...

Abstract: A procedure for designing a feedback control to asymptotically stabilize with probability one quasi-integrable Hamiltonian system is proposed. First, a set of averaged Ito⁁ stochastic differential ...

Abstract: Physical and engineering systems are often subjected to combined harmonic and random excitations. The random excitation is often modeled as Gaussian white noise for mathematical tractability. ...