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Research Papers: Design Automation

Tuned Nonlinear Energy Sink With Conical Spring: Design Theory and Sensitivity Analysis

[+] Author and Article Information
Donghai Qiu

Changchun Institute of Optics,
Fine Mechanics and Physics,
Chinese Academy of Sciences,
Changchun 130033, China;
University of Chinese Academy of Sciences,
Beijing 100049, China;
Institut Clément Ader (ICA), CNRS,
INSA-ISAE-Mines Albi-UPS,
Université de Toulouse,
3 rue Caroline Aigle,
Toulouse F-31400, France
e-mail: donghai.qiu@insa-toulouse.fr

Sébastien Seguy

Institut Clément Ader (ICA), CNRS,
INSA-ISAE-Mines Albi-UPS,
Université de Toulouse,
3 rue Caroline Aigle,
Toulouse F-31400, France
e-mail: sebastien.seguy@insa-toulouse.fr

Manuel Paredes

Institut Clément Ader (ICA), CNRS,
INSA-ISAE-Mines Albi-UPS,
Université de Toulouse,
3 rue Caroline Aigle,
Toulouse F-31400, France
e-mail: manuel.paredes@insa-toulouse.fr

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 24, 2017; final manuscript received October 17, 2017; published online November 9, 2017. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 140(1), 011404 (Nov 09, 2017) (10 pages) Paper No: MD-17-1500; doi: 10.1115/1.4038304 History: Received July 24, 2017; Revised October 17, 2017

This paper is devoted to the study of a nonlinear energy sink (NES) intended to attenuate vibration induced in a harmonically forced linear oscillator (LO) and working under the principle of targeted energy transfer (TET). The purpose motivated by practical considerations is to establish a design criterion that first ensures that the NES absorber is activated and second provides the optimally tuned nonlinear stiffness for efficient TET under a given primary system specification. Then a novel NES design yielding cubic stiffness without a linear part is exploited. To this end, two conical springs are specially sized to provide the nonlinearity. To eliminate the linear stiffness, the concept of a negative stiffness mechanism is implemented by two cylindrical compression springs. A small-sized NES system is then developed. To validate the concept, a sensitivity analysis is performed with respect to the adjustment differences of the springs and an experiment on the whole system embedded on an electrodynamic shaker is studied. The results show that this type of NES can not only output the expected nonlinear characteristics, but can also be tuned to work robustly over a range of excitation, thus making it practical for the application of passive vibration control.

Copyright © 2017 by ASME
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Figures

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Fig. 1

Schematic of a harmonically excited LO coupled with a NES

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Fig. 2

Cubic NES under periodic forcing with parameters K = 3000, λ1 = 0.6, λ2 = 0.3, ε = 0.01, G = 0.2 mm and initial conditions x0 = 0, x˙0=0, y0=0 and y˙0=0. (a) time-displacement of LO and NES. (b) SIM structure and trace between LO and cubic NES: the thin curve represents the transient projected motion.

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Fig. 3

Frequency response function of LO with cubic NES (points) and without NES (thin line) in different types of excitation: (a) G = 0.08 mm, (b) G = 0.13 mm, (c) G = 0.18 mm, and (d) G = 0.23 mm. The points and the crosses represent stable and unstable fixed points, respectively.

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Fig. 4

Maximum amplitude of LO with the variation of (a) nonlinear stiffness and excitation amplitude, (b) nonlinear stiffness, and (c) excitation amplitude. Each point is extracted from the maximum amplitude of FRF.

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Fig. 5

Evolution of the multiplicity of periodic solutions for the system with parameters K = 3000, λ1 = 0.6, λ2 = 0.3, and ε = 0.01

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Fig. 6

Critical excitation amplitude as a function of the nonlinear stiffness, λ1 = 0.6, λ2 = 0.3, and ε = 0.01

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Fig. 7

Force characteristic of conical spring, T represents the transition point between linear and nonlinear phase

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Fig. 8

State and corresponding force of two conical springs (the dashed line): (a) and (c) at original length; (b) and (d) precompressed at the transition point. The solid line represents the composed force.

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Fig. 9

Polynomial components of the two optimized conical springs

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Fig. 10

Schematic of NES system: (a) negative stiffness mechanism, (b) conical spring, and (c) the composed system

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Fig. 11

Assembly of NES system. x and y correspond to the displacement of LO and NES, respectively.

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Fig. 12

Conical spring manufactured and measuring equipment

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Fig. 13

Experimental force–displacement relation of conical springs

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Fig. 14

Nonlinear energy sink system with linear springs of large mean diameter

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Fig. 15

Details of the experimental setup and measuring system

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Fig. 16

Force–displacement relation of the designed NES

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Fig. 17

Differences of the adjustment length for conical springs (γi) and linear springs (ηi)

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Fig. 18

The nonlinear NES force versus the response of LO and NES with G = 0.205 mm, σ = −0.2: (a) and (d) positive linear stiffness, γ1 = γ2 = 1, η1 = η2 =−1; (b) and (e) negative linear stiffness, γ1 = γ2 = −1, η1 = η2 = 1; (c) and (f) unsymmetrical stiffness, γ1 = 1, γ2 = −1, η1 = η2 = 0

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Fig. 19

Experimental setup: (a) global view of the system and (b) detailed view of LO and NES

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Fig. 20

Experimental results: (a) frequency response curve of LO with (thick line) and without (thin line) the designed NES, and (b) SMR of LO (solid line) and NES (dashed line)

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