Stability regions for Mathieu equation with imperfect periodicity. (English) Zbl 1233.70007
Summary: We consider a mean square stability for the Mathieu equation with a random phase modulation in parametric excitation. An efficient numerical scheme is proposed for obtaining the stability charts for this equation. The influence of the random phase modulation on the shape of parametric resonance regions is studied. It is found that this influence can lead to stabilization under some conditions. A comparison with a case of Gaussian parametric excitation is presented.
MSC:
| 70K28 | Parametric resonances for nonlinear problems in mechanics |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 93E15 | Stochastic stability in control theory |
| 68Q87 | Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) |
| 34D20 | Stability of solutions to ordinary differential equations |
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