scholarly journals First-passage failure of linear oscillator with non-classical inelastic impact

2018 ◽  
Vol 54 ◽  
pp. 284-297 ◽  
Author(s):  
Ming Xu
Keyword(s):  
Linear Oscillator ◽  
First Passage ◽  
Inelastic Impact ◽  
First Passage Failure

Probability of First-Passage Failure for Nonstationary Random Vibration

1975 ◽  
Vol 42 (3) ◽  
pp. 716-720 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
White Noise ◽  
Barrier Height ◽  
Random Vibration ◽  
Series Solution ◽  
Short Pulse ◽  
Random Excitation ◽  
Numerical Results ◽  
Linear Oscillator ◽  
First Passage ◽  
First Passage Failure

The problem of calculating the probability of first-passage failure, Pf, is considered, for systems responding to a short pulse of nonstationary random excitation. It is shown, by an analysis based on the “in and exclusion” series, that, under certain conditions, Pf tends to Pf*, the probability calculated by assuming Poisson distributed barrier crossings, as the barrier height, b, tends to infinity. The first three terms in the series solution provide bounds to Pf which converge when b is large. Methods of estimating Pf from these terms are presented which are useful even when the series is divergent. The theory is illustrated by numerical results relating to a linear oscillator excited by modulated white noise.

First-passage failure of preisach hysteretic systems

2014 ◽  
Vol 27 (5) ◽  
pp. 477-485 ◽  
Author(s):  
Ming Xu ◽  
Xiaoling Jin ◽  
Yong Wang ◽  
Zhilong Huang
Keyword(s):  
First Passage ◽  
Hysteretic Systems ◽  
First Passage Failure

Break-out of dynamic balance of nonlinear ecosystems using first passage failure theory

2015 ◽  
Vol 80 (3) ◽  
pp. 1403-1411 ◽  
Author(s):  
S. L. Wang ◽  
X. L. Jin ◽  
Z. L. Huang ◽  
G. Q. Cai
Keyword(s):  
Dynamic Balance ◽  
First Passage ◽  
Failure Theory ◽  
First Passage Failure

First-Passage Time for Oscillators With Nonlinear Damping

1978 ◽  
Vol 45 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
First Passage Time ◽  
Digital Simulation ◽  
Planck Equation ◽  
Passage Time ◽  
Nonlinear Damping ◽  
First Passage ◽  
One Dimensional ◽  
Fokker Planck Equation ◽  
First Passage Failure ◽  
Fokker Planck

A simple numerical scheme is proposed for computing the probability of first passage failure, P(T), in an interval O-T, for oscillators with nonlinear damping. The method depends on the fact that, when the damping is light, the amplitude envelope, A(t), can be accurately approximated as a one-dimensional Markov process. Hence, estimates of P(T) are found, for both single and double-sided barriers, by solving the Fokker-Planck equation for A(t) with an appropriate absorbing barrier. The numerical solution of the Fokker-Planck equation is greatly simplified by using a discrete time random walk analog of A(t), with appropriate statistical properties. Results obtained by this method are compared with corresponding digital simulation estimates, in typical cases.

Sign in / Sign up

Export Citation Format

Share Document