Probability of first passage failure for lightly damped oscillators
Abstract
The theory of Markov processes is applied to the case of a lightly damped, singledegreeoffreedom oscillator subjected to normal, stationary whitenoise excitation. It is found that the energy envelope of the oscillator can be modeled satisfactorily by a onedimensional Markov process. The discretetime Markov envelope method gives accurate estimates of the probability of firstpassage failure for both singlesided and doublesided barriers in typical cases. Results obtained by the continuoustime Markov envelope method deviate considerably in general from the corresponding discretetime results.
 Publication:

In: Stochastic problems in dynamics; Proceedings of the Symposium
 Pub Date:
 1977
 Bibcode:
 1977spd..proc..256R
 Keywords:

 Failure Modes;
 Oscillators;
 Probability Theory;
 Vibration Damping;
 White Noise;
 Discrete Functions;
 Distribution Moments;
 FokkerPlanck Equation;
 Markov Processes;
 Probability Density Functions;
 Random Noise;
 Random Vibration;
 Physics (General)