Suppression of chaos in nonlinear oscillators using a linear vibration absorber

This paper proposes a nonfeedback control to suppress the chaotic response of nonlinear oscillators. A linear vibration absorber is used as nonfeedback method, whose key idea is to find conditions under which the nonlinear oscillator response converges to an equilibrium point or stay oscillating around it. Theoretical results show that if the ratio between the natural frequencies of the primary system (omega(1)) and the undamped absorber (omega(2)), that is, omega(r) = omega(2)omega(1) is tuned to be equal to the excitation frequency (omega), then the chaotic behavior of a nonlinear oscillator is driven to a stable hyperbolic equilibrium point. Numerical results are presented for the Duffing oscillator shown that if omega(r) is tuned close to excitation frequency, then the chaotic response of the Duffing oscillator is driven to periodic orbits. In the case of damped absorber, omega(r) to be tuned close to the excitation frequency does not guarantee that the response of the primary system is periodic, it is also necessary to take into account the amplitude of the excitation.

Automated summary

This paper proposes a nonfeedback control method using a linear vibration absorber to suppress chaotic responses of nonlinear oscillators. Theoretical results show that adjusting the ratio of natural frequencies between the oscillator and the absorber can drive chaotic behavior to a stable equilibrium point. Numerical results demonstrate that tuning the ratio close to the excitation frequency can drive chaotic responses to periodic orbits in some cases, but taking into account the excitation amplitude is also necessary for periodic responses.