Parametric Vibration Stability and Active Control of Nonlinear Beams

LI Feng-ming; LIU Chun-chuan

doi:10.3879/j.issn.1000-0887.2012.11.004

Volume 33 Issue 11

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LI Feng-ming, LIU Chun-chuan. Parametric Vibration Stability and Active Control of Nonlinear Beams[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1284-1293. doi: 10.3879/j.issn.1000-0887.2012.11.004

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Parametric Vibration Stability and Active Control of Nonlinear Beams

doi: 10.3879/j.issn.1000-0887.2012.11.004

LI Feng-ming^{1,2
,},
LIU Chun-chuan²

¹College of Mechanical Engineering, Beijing University of Technology,Beijing 100124, P.R.China;²School of Astronautics, Harbin Institute of Technology, P.O.Box 137, Harbin 150001, P.R.China

Received Date: 2011-08-27
Rev Recd Date: 2012-06-17
Publish Date: 2012-11-15

Abstract

Abstract

The vibration stability and active control of the parametrically excited nonlinear beam structures were studied using the piezoelectric material. The velocity feedback control algorithm was applied to obtain the active damping. The cubic nonlinear equation of motion with damping was established by employing Hamilton’ principle. The method of multiple scales was used to solve the equation of motion, and the stable region was obtained. The effects of the control gain and amplitude of the external force on the stable region and amplitudefrequency curve characteristics were analyzed numerically. From the numerical results it was seen that with the increase of the feedback control gain, the axial force to which the structure could be subjected increased, and in certain scope the structural active damping ratio also increased. With the increase of the control gain, the response amplitude decreases gradually, but the required control voltage exists peak value.
- beam,
- piezoelectric material,
- parametric vibration,
- stability,
- active control,
- method of multiple scales

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References(19)

References

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