Stabilization of a 1/3-order subharmonic resonance using nonlinear dynamic vibration absorber |
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Authors: | Hoonhee Jo Hiroshi Yabuno |
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Institution: | (1) Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;(2) School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088, USA; |
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Abstract: | The paper proposes a stabilization method for a 1/3-order subharmonic resonance with a new type of nonlinear vibration absorber
using nonlinear coupling between a main system and the absorber. The main system with nonlinear restoring force and harmonic
excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces a 1/3-order
subharmonic resonance. A damped pendulum, whose natural frequency is tuned to be in the neighborhood of twice that of the
main system, is connected through a link to the main system as a nonlinear vibration absorber. Theoretical results using the
method of multiple scales show that only a stable nontrivial steady state is changed into an unstable one due to the effect
of absorber. In addition, we numerically confirm the validity of the proposed absorber using Runge–Kutta method. |
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