PULL-DOWN INSTABILITY OF THE QUADRATIC NONLINEAR OSCILLATORS

A nonlinear vibration system, over a span of convincing periodic motion, might break out abruptly a catastrophic instability, but the lack of a theoretical tool has obscured the prediction of the outbreak. This paper deploys the amplitude-frequency formulation for nonlinear oscillators to reveal the critically important mechanism of the pseudo-periodic motion, and finds the quadratic nonlinear force contributes to the pull-down phenomenon in each cycle of the periodic motion, when the force reaches a threshold value, the pull-down instability occurs. A criterion for prediction of the pull-down instability is proposed and verified numerically.

Automated summary

This paper uses the amplitude-frequency formulation for nonlinear oscillators to reveal the critical mechanism of pseudo-periodic motion and discover that the quadratic nonlinear force contributes to the pull-down phenomenon in each cycle. When the force reaches a threshold value, the pull-down instability occurs. A criterion for predicting the pull-down instability is proposed and numerically verified.