Research on Dynamic Characteristics of Serial-Parallel-Ⅱ Inerter Nonlinear Energy Sink

WU Ziying; ZHU Rongxian; JANG Donggui; CHAO Guoqiang; ZHANG Yuxuan

doi:10.21656/1000-0887.440350

Volume 45 Issue 7

Jul. 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(7): 907-921

WU Ziying, ZHU Rongxian, JANG Donggui, CHAO Guoqiang, ZHANG Yuxuan. Research on Dynamic Characteristics of Serial-Parallel-Ⅱ Inerter Nonlinear Energy Sink[J]. Applied Mathematics and Mechanics, 2024, 45(7): 907-921. doi: 10.21656/1000-0887.440350

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Research on Dynamic Characteristics of Serial-Parallel-Ⅱ Inerter Nonlinear Energy Sink

doi: 10.21656/1000-0887.440350

School of Mechanical and Precision Instrument Engineering, Xi'an Univercity of Technology, Xi'an 710048, P.R.China

Received Date: 2023-12-08
Rev Recd Date: 2024-02-17
Publish Date: 2024-07-01

Abstract

Abstract

A serial-parallel-Ⅱ inerter nonlinear energy sink was proposed through replacement of the linear restoring force and linear damping with the nonlinear restoring force and nonlinear damping in inertial vibration reduction systems, in view of the effects of friction. The dynamic equation for the main system was established, the amplitude-frequency response curves of the system under the base simple harmonic excitation were solved with the harmonic balance method. The effects of the inertia ratio, nonlinear damping, nonlinear stiffness and friction on the vibration damping performance of the system were studied with the arc length algorithm and the numerical method. The results show that, with the increase of the nonlinear stiffness and nonlinear damping, the peak value will first decrease and then increase. The difference is that the amplitude-frequency response curve of the former gradually bends to the upper right direction, and the position of the peak value of the latter shifts to the lower frequency band. The actions of 3 parameters of the inertial ratio, nonlinear damping and nonlinear stiffness, on the damping effects of the system were analyzed. The research indicates that, with an excitation amplitude of 0.005 m, the vibration reduction effect will be the best when the inertia ratio and damping change simultaneously. For ε=0.1, the minimum value of the peak displacement of the main structure of the system will be about 0.01 m, while for ε=0.001, the maximum value within the overall value range will be approximately 0.061 m, and the amplitude damping ratio will be 97.1% and 82.1%, respectively. When the inertia ratio reaches optimal value 0.1, the nonlinear damping range and nonlinear stiffness κ₂₁ will grow larger. Under friction, the maximum amplitude of the system will have different degrees of increases. The research results provide a reference for the study on structural vibration reduction.
- harmonic balance method,
- nonlinear,
- inerter,
- vibration control

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References(31)

References

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