First-Passage Time in a Random Vibrational System

@article{Gray1966FirstPassageTI,
  title={First-Passage Time in a Random Vibrational System},
  author={Augustine H. Gray},
  journal={Journal of Applied Mechanics},
  year={1966},
  volume={33},
  pages={187-191}
}
  • A. Gray
  • Published 1 March 1966
  • Mathematics
  • Journal of Applied Mechanics
20 Citations

Figures from this paper

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process
TLDR
The widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main resul...
Title Response Spectra of Quasi-Stationary Random Excitations
One of the most important problems in the field of earthquake ngineering is to suppose reasonable arthquake excitation patterns for the dynamic analysis of structures. In particular, in the response
Ideal and physical barrier problems for non-linear systems driven by normal and Poissonian white noise via path integral method
Abstract In this paper, the probability density evolution of Markov processes is analyzed for a class of barrier problems specified in terms of certain boundary conditions. The standard case of
Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise
Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the
First-passage failure of MDOF nonlinear oscillator
First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise
First-passage time probability of non-linear stochastic systems by generalized cell mapping method
In this paper, the first-passage time probability of linear and non-linear dynamical systems subjected to white noise excitation is studied by the generalized cell mapping method. A wide range of the
Distribution of the first-passage time of mast antenna structures to non-stationary random excitation
The distribution of the first-passage time for normal stationary random processes provided by Vanmarcke has been extended to cases involving Gaussian non-stationary random processes. The
First-passage probabilities for randomly excited systems: Diffusion methods
Abstract For systems driven by wide-band random excitation processes it is possible to model the response as a multi-dimensional continuous Markov, or diffusion, process. This approach enables, in
Stochastic averaging: An approximate method of solving random vibration problems
Abstract Results obtained by applying the method of stochastic averaging to random vibration problems are discussed. This method is applicable to a variety of problems involving the response of
Energy Fluctuation Scale and Diffusion Models
The energy fluctuation scale, θE, of a narrow‐band Gaussian response is introduced. It is shown that E and associated bandwidth measures (e.g., 1/vOθE) are: (1) Simply related to both the spectral
...
1
2
...