Access the full text.
Sign up today, get DeepDyve free for 14 days.
W. Zhu, T. Soong, Y. Lei (1994)
Equivalent Nonlinear System Method for Stochastically Excited Hamiltonian SystemsJournal of Applied Mechanics, 61
W. Zhu, Y. Yang (1996)
Exact Stationary Solutions of Stochastically Excited and Dissipated Integrable Hamiltonian SystemsJournal of Applied Mechanics, 63
(1968)
Averaging principle for stochastic differential/to equations
W. Zhu (1988)
Stochastic Averaging Methods in Random VibrationApplied Mechanics Reviews, 41
J. Roberts, P. Spanos (1986)
Stochastic averaging: An approximate method of solving random vibration problemsInternational Journal of Non-linear Mechanics, 21
D. Kramer, G. Neugebauer (1969)
EXACT STATIONARY SOLUTION OF THE EINSTEIN--MAXWELL EQUATIONS.
R. Khas'minskii (1967)
Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic SystemsTheory of Probability and Its Applications
Z. Huang, W. Zhu (2000)
Lyapunov exponent and almost sure asymptotic stability of quasi-linear gyroscopic systemsInternational Journal of Non-linear Mechanics, 35
(1964)
Behavior of a conservative system with small friction and small random noise
(1995)
Probabilistic Structural Dvnamics: Advanced Theory and Applications, McGraw-Hili, Inc
W. Zhu, Z. Huang, Yi Yang (1997)
Stochastic Averaging of Quasi-Integrable Hamiltonian SystemsJournal of Applied Mechanics, 64
W. Zhu, Y. Lei (1997)
Equivalent Nonlinear System Method for Stochastically Excited and Dissipated Integrable Hamiltonian SystemsJournal of Applied Mechanics, 64
V. Oseledec (1968)
A multiplicative ergodic theorem: Lyapunov characteristic num-bers for dynamical systems
W. Zhu, Z. Huang (1999)
Stochastic Hopf bifurcation of quasi-nonintegrable-Hamiltonian systemsInternational Journal of Non-linear Mechanics, 34
W. Zhu (1996)
Recent Developments and Applications of the Stochastic Averaging Method in Random VibrationApplied Mechanics Reviews, 49
(1993)
Random Vibration ofMechanical and Structural Systems, PTR Prentice Hall, Englewood Cliffs
(1998)
Stochastic stability of quasinonintegrable-Hamiltonian systems", to appear in Journal of Sound and Vihra/ion
Z. Wei-qiu (1996)
Stochastic averaging of quasi-Hamiltonian systems
Christian Soize (1994)
The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions, 17
L. Arnold, N. Namachchivaya, K. Schenk-Hoppé (1994)
TOWARD AN UNDERSTANDING OF STOCHASTIC HOPF BIFURCATION: A CASE STUDYInternational Journal of Bifurcation and Chaos, 06
Z. Huang, W. Zhu (1997)
EXACT STATIONARY SOLUTIONS OF AVERAGED EQUATIONS OF STOCHASTICALLY AND HARMONICALLY EXCITED MDOF QUASI-LINEAR SYSTEMS WITH INTERNAL AND/OR EXTERNAL RESONANCESJournal of Sound and Vibration, 204
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.
Advances in Structural Engineering – SAGE
Published: Jul 1, 1999
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.