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Research Papers

Nonlinear Torsional Vibration Absorber for Flexible Structures

[+] Author and Article Information
Xiao-Ye Mao

Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China

Hu Ding

Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
149 Yan Chang Road,
Shanghai 200072, China;
Shanghai Key Laboratory of Mechanics in
Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: dinghu3@shu.edu.cn

Li-Qun Chen

Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China;
Shanghai Key Laboratory of Mechanics in
Energy Engineering,
Shanghai University,
Shanghai 200072, China;
Department of Mechanics,
Shanghai University,
Shanghai 200072, China

1Corresponding author.

Manuscript received September 11, 2018; final manuscript received November 15, 2018; published online December 7, 2018. Assoc. Editor: Ahmet S. Yigit.

J. Appl. Mech 86(2), 021006 (Dec 07, 2018) (11 pages) Paper No: JAM-18-1527; doi: 10.1115/1.4042045 History: Received September 11, 2018; Revised November 15, 2018

A new kind of nonlinear energy sink (NES) is proposed to control the vibration of a flexible structure with simply supported boundaries in the present work. The new kind of absorber is assembled at the end of structures and absorbs energy through the rotation angle at the end of the structure. It is easy to design and attached to the support of flexible structures. The structure and the absorber are coupled just with a nonlinear restoring moment and the damper in the absorber acts on the structure indirectly. In this way, all the linear characters of the flexible structure will not be changed. The system is investigated by a special perturbation method and verified by simulation. Parameters of the absorber are fully discussed to optimize the efficiency of it. For the resonance, the maximum motion is restrained up to 90% by the optimized absorber. For the impulse, the vibration of the structure could attenuate rapidly. In addition to the high efficiency, energy transmits to the absorber uniaxially. For the high efficiency, convenience of installation and the immutability of linear characters, the new kind of rotating absorber provides a very good strategy for the vibration control.

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Figures

Grahic Jump Location
Fig. 1

Mechanical model of the nonlinear absorber attached to the boundary

Grahic Jump Location
Fig. 2

Total response of the beam with nonlinear absorbers: (a) total response of the middle point and (b)efficiency of nonlinear absorber

Grahic Jump Location
Fig. 3

Total responses of nonlinear absorbers: (a) rotation of the left ring and (b) rotation of the right ring

Grahic Jump Location
Fig. 4

Efficiency of nonlinear absorbers: (a) average power of up branch and (b) average power of up branch

Grahic Jump Location
Fig. 5

Energy transmission of nonlinear absorbers: (a) transient response of the middle point with initial displacement along the beam, (b) transient response of the absorber with initial displacement along the beam, (c) transient response of the middle point with initial rotational angle in the absorber, and (d) transient response of the absorber with initial rotational angle in the absorber

Grahic Jump Location
Fig. 6

Optimization of nonlinear restoring moment: (a) effect of k1 to restoring moment and (b) effect of radius ratio to restoring moment

Grahic Jump Location
Fig. 7

Optimization of rotational inertia: (a) effect of J to the motion of middle point and (b) effect of J to the rotation of absorber

Grahic Jump Location
Fig. 8

Optimization of damping: (a) effect of c1 to the motion of middle point and (b) effect of c1 to the rotation of absorber

Grahic Jump Location
Fig. 9

Optimization of saddle-node points: (a) effect of J to SN points and (b) effect of c1 to SN points

Grahic Jump Location
Fig. 10

Optimization of upper branch range: (a) effect of c1 to upper SN point and (b) effect of c1 to lower SN point

Grahic Jump Location
Fig. 11

Optimized vibration control for the linear structure: (a) steady-state response with optimized absorber and (b) transient response with optimized absorber

Grahic Jump Location
Fig. 12

Optimization of upper branch range of the nonlinear structure: (a) effect of c1 to upper SN point and (b) effect of c1 to lower SN point

Grahic Jump Location
Fig. 13

Optimized vibration control for the nonlinear structure: (a) steady-state response with optimized absorber and (b) transient response with optimized absorber

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