Access the full text.
Sign up today, get DeepDyve free for 14 days.
WQ Zhu ZL Huang (1999)
Stochastic Hopf bifurcation of quasi-non-int systemsInternational Journal of Nonlinear Mechanics, 34
M. Wang, G. Uhlenbeck (1945)
On the Theory of the Brownian Motion IIReviews of Modern Physics, 17
Zhu WQ. Stochastic averaging of the energy envelope of nearly Lyapunov systems. In (1982)
Hennig K ed. Proceedings of the IUTAM Symposium on Random Vibrations and ReliabilityHennig K ed
L. Bergman, B. Spencer (1983)
SOLUTION OF THE FIRST PASSAGE PROBLEM FOR SIMPLE LINEAR AND NONLINEAR OSCILLATORS BY THE FINITE ELEMENT METHOD.
J. Franklin, E. Rodemich (1968)
Numerical Analysis of an Elliptic-Parabolic Partial Differential EquationSIAM Journal on Numerical Analysis, 5
W. Zhu, Z. Huang (1999)
Stochastic Hopf bifurcation of quasi-nonintegrable-Hamiltonian systemsInternational Journal of Non-linear Mechanics, 34
M Kac (1963)
Some results related to reliability of engineering structures
W. Schütz (1979)
The prediction of fatigue life in the crack initiation and propagation stages—a state of the art surveyEngineering Fracture Mechanics, 11
Heinrich JC. Solution of the first-passage problem for simple linear and nonlinear oscillators by the finite element method. T & M Report Bergman LA (1983)
Bergman LA, Heinrich JC. Solution of the first-passage problem for simple linear and nonlinear oscillators by the finite element method. T & M Report 461, 1983
GE Uhlenbeck MC Wang (1945)
On the theory of Brown motion IIReview of Modern Physics, 17
M. Wehner (1983)
Numerical Evaluation of Path Integral Solutions to Fokker-Planck Equations with Application to Void Formation.
J. Roberts (1986)
First-passage time for randomly excited non-linear oscillatorsJournal of Sound and Vibration, 109
L. Bergman, J. Heinrich (1981)
On the moments of time to first passage of the linear oscillatorEarthquake Engineering & Structural Dynamics, 9
J. Yu, G. Cai, Y. Lin (1997)
A new path integration procedure based on Gauss-Legendre schemeInternational Journal of Non-linear Mechanics, 32
J. Roberts (1978)
First passage time for oscillators with non-linear restoring forcesJournal of Sound and Vibration, 56
RZ Khasminskii (1968)
On the averaging principle for stochastic differential Ito equationsKibernetica, 4
W. Zhu, Z. Huang (1998)
STOCHASTIC STABILITY OF QUASI-NON-INTEGRABLE-HAMILTONIAN SYSTEMSJournal of Sound and Vibration, 218
A. Freudenthal (1974)
New aspects of fatigue and fracture mechanics
L. Bergman, J. Heinrich (1982)
On the reliability of the linear oscillator and systems of coupled oscillatorsInternational Journal for Numerical Methods in Engineering, 18
Yu-Kweng Lin, G. Cai (1967)
Probabilistic Structural Dynamics: Advanced Theory and Applications
Cox Pdf (1977)
The Theory Of Stochastic ProcessesThe Mathematical Gazette, 61
YQ Yang WQ Zhu (1997)
Stochastic averaging of quasi-non-integrable-Hamiltonian systemsASME Journal of Applied Mechanics, 64
GQ Cai YK Lin (1996)
Some results related to failures of statistic systems. Fields Institute CommunicationsAmerican Mathematical Society, 19
G. Cai, Y. Lin (1998)
FAILURES OF STOCHASTICALLY EXCITED SYSTEMS
J. Roberts (1986)
Response of an oscillator with non-linear damping and a softening spring to non-white random excitationProbabilistic Engineering Mechanics, 1
M Tabor (1989)
Chaos and Integrability in Nonlinear Dynamics
G. Cai, Y. Lin (1994)
On Statistics of First-Passage FailureJournal of Applied Mechanics, 61
Abstract Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure.
"Acta Mechanica Sinica" – Springer Journals
Published: May 1, 2000
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.