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.

References

References
1.
Jiang
,
J.
, and
Iwai
,
Y.
,
2009
, “
Improving the B-Spline Method of Dynamically-Compensated Cam Design by Minimizing or Restricting Vibrations in High-Speed Cam-Follower Systems
,”
ASME J. Mech. Des.
,
131
(
4
), p.
041003
.
2.
Kim
,
S.
,
Dean
,
R.
,
Flowers
,
G.
, and
Chen
,
C.
,
2009
, “
Active Vibration Control and Isolation for Micromachined Devices
,”
ASME J. Mech. Des.
,
131
(
9
), p.
091002
.
3.
Trimble
,
A. Z.
,
Lang
,
J. H.
,
Pabon
,
J.
, and
Slocum
,
A.
,
2010
, “
A Device for Harvesting Energy From Rotational Vibrations
,”
ASME J. Mech. Des.
,
132
(
9
), p.
091001
.
4.
Okwudire
,
C. E.
,
2012
, “
Reduction of Torque-Induced Bending Vibrations in Ball Screw-Driven Machines Via Optimal Design of the Nut
,”
ASME J. Mech. Des.
,
134
(
11
), p.
111008
.
5.
Moeenfard
,
H.
, and
Awtar
,
S.
,
2014
, “
Modeling Geometric Nonlinearities in the Free Vibration of a Planar Beam Flexure With a Tip Mass
,”
ASME J. Mech. Des.
,
136
(
4
), p.
044502
.
6.
Vakakis
,
A. F.
,
Gendelman
,
O. V.
,
Bergman
,
L. A.
,
McFarland
,
D. M.
,
Kerschen
,
G.
, and
Lee
,
Y. S.
,
2008
,
Targeted Energy Transfer in Mechanical and Structural Systems
, Vol.
156
,
Springer Science & Business Media
,
Berlin
.
7.
Vakakis
,
A. F.
, and
Gendelman
,
O. V.
,
2001
, “
Energy Pumping in Nonlinear Mechanical Oscillators: Part II: Resonance Capture
,”
ASME J. Appl. Mech.
,
68
(
1
), pp.
42
48
.
8.
Lee
,
Y.
,
Vakakis
,
A. F.
,
Bergman
,
L.
,
McFarland
,
D.
,
Kerschen
,
G.
,
Nucera
,
F.
,
Tsakirtzis
,
S.
, and
Panagopoulos
,
P.
,
2008
, “
Passive Non-Linear Targeted Energy Transfer and Its Applications to Vibration Absorption: A Review
,”
Proc. Inst. Mech. Eng. Part K J. Multibody Dyn.
,
222
(
2
), pp.
77
134
.
9.
Gourdon
,
E.
,
Alexander
,
N.
,
Taylor
,
C.
,
Lamarque
,
C.
, and
Pernot
,
S.
,
2007
, “
Nonlinear Energy Pumping Under Transient Forcing With Strongly Nonlinear Coupling: Theoretical and Experimental Results
,”
J. Sound. Vib
,
300
(
35
), pp.
522
551
.
10.
Gourc
,
E.
,
Michon
,
G.
,
Seguy
,
S.
, and
Berlioz
,
A.
,
2014
, “
Experimental Investigation and Design Optimization of Targeted Energy Transfer Under Periodic Forcing
,”
ASME J. Vib. Acoust
,
136
(
2
), p.
021021
.
11.
Gourc
,
E.
,
Michon
,
G.
,
Seguy
,
S.
, and
Berlioz
,
A.
,
2015
, “
Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments
,”
ASME J. Vib. Acoust
,
137
(
3
), p.
031008
.
12.
Lamarque
,
C.-H.
,
Gendelman
,
O. V.
,
Savadkoohi
,
A. T.
, and
Etcheverria
,
E.
,
2011
, “
Targeted Energy transfer in mechanical Systems by Means of Non-Smooth Nonlinear Energy Sink
,”
Acta Mech.
,
221
(
1–2
), p.
175
.
13.
Sigalov
,
G.
,
Gendelman
,
O.
,
Al-Shudeifat
,
M.
,
Manevitch
,
L.
,
Vakakis
,
A.
, and
Bergman
,
L.
,
2012
, “
Resonance Captures and Targeted Energy Transfers in an Inertially-Coupled Rotational Nonlinear Energy Sink
,”
Nonlinear Dyn.
,
69
(
4
), pp.
1693
1704
.
14.
Jutte
,
C. V.
, and
Kota
,
S.
,
2008
, “
Design of Nonlinear Springs for Prescribed Load-Displacement Functions
,”
ASME J. Mech. Des.
,
130
(
8
), p.
081403
.
15.
Jutte
,
C. V.
, and
Kota
,
S.
,
2010
, “
Design of Single, Multiple, and Scaled Nonlinear Springs for Prescribed Nonlinear Responses
,”
ASME J. Mech. Des.
,
132
(
1
), p.
011003
.
16.
Wu
,
Y.-S.
, and
Lan
,
C.-C.
,
2014
, “
Linear Variable-Stiffness Mechanisms Based on Preloaded Curved Beams
,”
ASME J. Mech. Des.
,
136
(
12
), p.
122302
.
17.
Sönmez
,
Ü.
,
2007
, “
Introduction to Compliant Long Dwell Mechanism Designs Using Buckling Beams and Arcs
,”
ASME J. Mech. Des.
,
129
(
8
), pp.
831
843
.
18.
Sönmez
,
Ü.
, and
Tutum
,
C. C.
,
2008
, “
A Compliant Bistable Mechanism Design Incorporating Elastica Buckling Beam Theory and Pseudo-Rigid-Body Model
,”
ASME J. Mech. Des.
,
130
(
4
), p.
042304
.
19.
Chen
,
Y.-H.
, and
Lan
,
C.-C.
,
2012
, “
An Adjustable Constant-Force Mechanism for Adaptive End-Effector Operations
,”
ASME J. Mech. Des.
,
134
(
3
), p.
031005
.
20.
Al-Shudeifat
,
M. A.
,
2017
, “
Nonlinear Energy Sinks With Nontraditional Kinds of Nonlinear Restoring Forces
,”
ASME J. Vib. Acoust
,
139
(
2
), p.
024503
.
21.
Gendelman
,
O.
,
Starosvetsky
,
Y.
, and
Feldman
,
M.
,
2008
, “
Attractors of Harmonically Forced Linear Oscillator With Attached Nonlinear Energy Sink I: Description of Response Regimes
,”
Nonlinear Dyn.
,
51
(
1–2
), pp.
31
46
.
22.
Starosvetsky
,
Y.
, and
Gendelman
,
O.
,
2007
, “
Attractors of Harmonically Forced Linear Oscillator With Attached Nonlinear Energy Sink II: Optimization of a Nonlinear Vibration Absorber
,”
Nonlinear Dyn.
,
51
(
1
), p.
47
.
23.
Starosvetsky
,
Y.
, and
Gendelman
,
O.
,
2008
, “
Strongly Modulated Response in Forced 2DOF Oscillatory System With Essential Mass and Potential Asymmetry
,”
Phys. D: Nonlinear Phenom.
,
237
(
13
), pp.
1719
1733
.
24.
Rodriguez
,
E.
,
Paredes
,
M.
, and
Sartor
,
M.
,
2006
, “
Analytical Behavior Law for a Constant Pitch Conical Compression Spring
,”
ASME J. Mech. Des.
,
128
(
6
), pp.
1352
1356
.
25.
Paredes
,
M.
,
2013
, “
Analytical and Experimental Study of Conical Telescoping Springs With Nonconstant Pitch
,”
ASME J. Mech. Des.
,
135
(
9
), p.
094502
.
26.
Patil
,
R. V.
,
Reddy
,
P. R.
, and
Laxminarayana
,
P.
,
2014
, “
Comparison of Cylindrical and Conical Helical Springs for Their Buckling Load and Deflection
,”
Int. J. Adv. Sci. Technol.
,
73
, pp.
33
50
.
27.
Qiu
,
D.
,
Seguy
,
S.
, and
Paredes
,
M.
,
2017
, “
A Novel Design of Cubic Stiffness for a Nonlinear Energy Sink (NES) Based on Conical Spring
,”
Advances on Mechanics, Design Engineering and Manufacturing
,
Springer
, Berlin, pp.
565
573
.
28.
Harne
,
R.
,
Thota
,
M.
, and
Wang
,
K.
,
2013
, “
Concise and High-Fidelity Predictive Criteria for Maximizing Performance and Robustness of Bistable Energy Harvesters
,”
Appl. Phys. Lett.
,
102
(
5
), p.
053903
.
29.
Yamamoto
,
Y.
,
1999
, “
Spring's Effective Mass in Spring Mass System Free Vibration
,”
J. Sound. Vib
,
220
(
3
), pp.
564
570
.
30.
Opgenoord
,
M. M.
,
Allaire
,
D. L.
, and
Willcox
,
K. E.
,
2016
, “
Variance-Based Sensitivity Analysis to Support Simulation-Based Design Under Uncertainty
,”
ASME J. Mech. Des.
,
138
(
11
), p.
111410
.
31.
Romeo
,
F.
,
Sigalov
,
G.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2015
, “
Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Numerical Study
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
1
), p.
011007
.
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