A stochastic model for nonlinear oscillators of Duffing type
Abstract
A nonlinear model for random oscillators, which includes a stochastic version of the Duffing oscillator in both cases of hard and soft spring, is studied in the diffusion limit. This is an asymptotic limit involving random fluctuations of small size and long time. The nonlinearity is also assumed to be small. One of the main results is that the effect of the type and size of nonlinearity under investigation does not affect appreciably the qualitative long-time behavior of the moments of the displacement of the oscillator, in both the hard and the soft spring models. It is also proved that there are no stationary distributions. Finally, a numerical study for the first two moments is performed and plots are given.
- Publication:
-
SIAM Journal of Applied Mathematics
- Pub Date:
- December 1985
- Bibcode:
- 1985SJAM...45..990S
- Keywords:
-
- Duffing Differential Equation;
- Nonlinear Systems;
- Oscillators;
- Random Vibration;
- Springs (Elastic);
- Stochastic Processes;
- Asymptotic Methods;
- Boundary Value Problems;
- Free Vibration;
- Limits (Mathematics);
- Moment Distribution;
- Parabolic Differential Equations;
- Physics (General)