A closed form solution for a class of non-stationary nonlinear random vibration problems. (English) Zbl 0667.70034
Nonlinear stochastic dynamic engineering systems, Proc. IUTAM Symp., Innsbruck/Igls/Austria 1987, 393-403 (1988).
[For the entire collection see Zbl 0658.00017.]
A Markov approximation of the energy of a class of lightly damped, nonlinear, single-degree-of-freedom oscillators subjected to modulated white noise excitation is derived using the stochastic averaging method. The solution of the associated forward Kolmogorov equation for the transition probability density function is presented. The merit of this solution is demonstrated by deriving the spectral density of the oscillator stationary response to step modulated white noise.
A Markov approximation of the energy of a class of lightly damped, nonlinear, single-degree-of-freedom oscillators subjected to modulated white noise excitation is derived using the stochastic averaging method. The solution of the associated forward Kolmogorov equation for the transition probability density function is presented. The merit of this solution is demonstrated by deriving the spectral density of the oscillator stationary response to step modulated white noise.
MSC:
| 70L05 | Random vibrations in mechanics of particles and systems |
