The natural frequency of a rubber-damped torsional vibration absorber (TVA) depends on the excitation amplitudes and frequencies in a highly nonlinear manner. This is due to nonlinear shear properties of the rubber ring. In this study, the nonlinear static and dynamic shear characteristics of a rubber ring, and the natural frequency of a nonlinear TVA are experimentally characterized firstly. Since a rubber ring employed in a rubber-damped TVA is usually in the compression state, its static and dynamic shear properties depend upon the compression ratio and dimensions apart from the chemical ingredients in a highly complex manner. The prediction of the natural frequency of a rubber-ring TVA thus poses considerable complexities. In this study, a special fixture is designed and fabricated for characterizing shear properties of a rubber ring subject to different compression ratios. The shear properties are subsequently characterized using different constitutive models, and a methodology for identifying the model parameters is presented considering the measured properties. Second, a methodology for estimating the natural frequency of the TVA is proposed, and the effectiveness of the proposed method is demonstrated through comparisons of the estimated natural frequency with the measured values. The results of the study suggest that the model using fractional derivatives to characterize nonlinear shear properties of a rubber ring can be effectively used to obtain accurate estimation of natural frequency of a nonlinear TVA over a wide range of excitations. The natural frequency of a TVA can thus be accurately estimated before prototyping using the experimental and modeling methods developed in this paper.

References

References
1.
Mendes
,
A. S.
,
Meirelles
,
P. S.
, and
Zampieri
,
D. E.
,
2008
, “
Analysis of Torsional Vibration in Internal Combustion Engines: Modeling and Experimental Validation
,”
Inst. Mech. Eng. Part K
,
222
(
2
), pp.
155
178
.
2.
Thomson
,
W. T.
,
1981
,
Theory of Vibration With Applications
,
Prentice Hall
,
Englewood Cliffs, NJ
.
3.
Hartog Den
,
J. P.
,
1985
,
Mechanical Vibrations
,
Dover
,
New York
.
4.
Shangguan
,
W. B.
, and
Pan
,
X. Y.
,
2008
, “
Multi-Mode and Rubber-Damped Torsional Vibration Absorbers for Engine Crankshaft Systems
,”
Int. J. Veh. Des.
,
47
(
1–4
), pp.
176
188
.
5.
Sommier
,
E.
,
Fotsing
,
E. R.
,
Ross
,
A.
, and
Lavoie
,
M.
,
2014
, “
Characterization of the Injection Molding Process of Passive Vibration Isolators
,”
J. Elastomers Plast.
,
1
(
1
), pp.
1
12
.
6.
Sun
,
Y.
, and
Thomas
,
M.
,
2011
, “
Control of Torsional Rotor Vibrations Using an Electrorheological Fluid Dynamic Absorbers
,”
J. Vib. Control
,
17
(
8
), pp.
1253
1264
.
7.
Hoang
,
N.
,
Zhang
,
N.
, and
Du
,
H.
,
2009
, “
A Dynamic Absorber With a Soft Magnetorheological Elastomer for Powertrain Vibration Suppression
,”
Smart Mat Struct.
,
18
(
7
), p.
074009
.
8.
Monroe
,
R. J.
, and
Shaw
,
S. W.
,
2013
, “
Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
,”
ASME J. Vib. Acoust.
,
135
(
1
), p.
011017
.
9.
Monroe
,
R. J.
, and
Shaw
,
S. W.
,
2013
, “
Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part II: Experimental Results
,”
ASME J. Vib. Acoust.
,
135
(
1
), p.
011018
.
10.
Ishida
,
Y.
,
2012
, “
Recent Development of the Passive Vibration Control Method
,”
Mech. Syst. Signal Process.
,
29
(
1
), pp.
2
18
.
11.
Heymans
,
N.
,
2004
, “
Fractional Calculus Description of Non-Linear Viscoelastic Behavior of Polymers
,”
Nonlinear Dyn.
,
38
(
1–4
), pp.
221
231
.
12.
Pritz
,
T.
,
1996
, “
Analysis of Four-Parameter Fractional Derivative Model of Real Solid Materials
,”
J. Sound Vib.
,
195
(
1
), pp.
103
115
.
13.
Pritz
,
T.
,
2003
, “
Five-Parameters Fractional Derivative Model for Polymeric Damping Materials
,”
J. Sound Vib.
,
265
(
5
), pp.
935
952
.
14.
Wu
,
J.
, and
Shangguan
,
W. B.
,
2008
, “
Modeling and Applications of Dynamic Characteristics for Rubber Isolators Using Viscoelastic Fractional Derivative Model
,”
Eng. Mech.
,
25
(
1
), pp.
161
166
(in Chinese).
15.
Bahraini
,
S. M. S.
, and
Eghtesad
,
M.
,
2013
, “
Large Deflection of Viscoelastic Beams Using Fractional Derivative Model
,”
J. Mech. Sci. Technol.
,
27
(
4
), pp.
1063
1070
.
16.
Berg
,
M.
,
1998
, “
A Non-Linear Rubber Spring Model for Rail Vehicle Dynamics Analysis
,”
Veh. Syst. Dyn.
,
30
(
4
), pp.
197
212
.
17.
Sjoberg
,
M.
, and
Kari
,
L.
,
2002
, “
Non-Linear Behavior of a Rubber Isolator System Using Fractional Derivatives
,”
Veh. Syst. Dyn.
,
37
(
3
), pp.
217
236
.
18.
Sjoberg
,
M.
, and
Kari
,
L.
,
2003
, “
Nonlinear Isolator Dynamics at Finite Deformations: An Effective Hyperelastic, Fractional Derivate, Generalized Friction Model
,”
Nonlinear Dyn.
,
33
(
3
), pp.
323
336
.
19.
Wu
,
J.
, and
Shangguan
,
W. B.
,
2010
, “
Dynamic Optimization for Vibration Systems Including Hydraulic Engine Mounts
,”
J. Vib. Control
,
16
(
11
), pp.
1577
1590
.
20.
Shangguan
,
W. B.
, and
Wu
,
J.
,
2008
, “
Modeling of Dynamic Performances for Hydraulic Engine Mounts Using Fractional Derivative and Optimisation of Powertrain Mounting Systems
,”
Int. J. Veh. Des.
,
47
(
1–4
), pp.
215
233
.
21.
Honda
,
Y.
, and
Saito
,
T.
,
1987
, “
Dynamic Characteristics of Torsional Rubber Dampers and Their Optimum Tuning
,”
SAE
Technical Paper No. 870580.
22.
Shangguan
,
W. B.
, and
Lu
,
Z. H.
,
2004
, “
Experimental Study and Simulation of a Hydraulic Engine Mount With Fully Coupled Fluid Structure Interaction Finite Element Analysis Model
,”
Comput. Struct.
,
82
(
22
), pp.
1751
1771
.
23.
Amin
,
A. F. M. S.
,
Lion
,
A.
,
Sekita
,
S.
, and
Okui
,
Y.
,
2006
, “
Nonlinear Dependence of Viscosity in Modeling the Rate-Dependent Response of Natural and High Damping Rubbers in Compression and Shear: Experimental Identification and Numerical Verification
,”
Int. J. Plast.
,
22
(
9
), pp.
1610
1657
.
24.
Yeoh
,
O. H.
,
1990
, “
Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates
,”
Rubber Chem. Technol.
,
63
(
5
), pp.
792
805
.
25.
Garcia
,
T. M. J.
,
Kari
,
L.
,
Vinolas
,
J.
, and
Gil-Negrete
,
N.
,
2007
, “
Torsion Stiffness of a Rubber Bushing: A Simple Engineering Design Formula Including the Amplitude Dependence
,”
J. Strain Anal. Eng. Des.
,
42
(
1
), pp.
13
21
.
26.
Wang
,
L.
,
Wang
,
J.
, and
Hagiwara
,
I.
,
2005
, “
An Integrated Characteristic Simulation Method for Hydraulically Damped Rubber Mount of Vehicle Engine
,”
J. Sound Vib.
,
286
(
4
), pp.
673
696
.
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