Abstract

Resilient elements are widely applied for vibration and noise control in many areas of engineering. Their complex dynamic stiffness gives fundamental information to describe their dynamic performance and is required for predicting structure-borne sound and vibration using dynamic modeling. Many laboratory measurement methods have been developed to determine the dynamic properties of resilient elements. This paper presents a review of recent developments in the measurement methods from the perspective of force–displacement relations of the resilient element assembly rather than of their material properties. To provide context, the review begins with an introduction to modeling methods for resilient elements, especially for rubber and rubber-like isolators, and three standardized measurement methods are introduced. Recent developments are then discussed including methods to extend the frequency range, which are mainly developments of the indirect method. Mobility methods, modal-based methods, recent active frequency-based substructuring (FBS), and inverse substructuring (IS) methods to study the dynamic properties of resilient elements are also described. Laboratory test rigs and the corresponding identification methods are outlined. Methods to evaluate nonlinear dynamic properties of resilient elements by laboratory measurements are also discussed. Finally, the review is concluded by discussing the advantages and limitations of the existing methods and giving suggestions for future research.

References

1.
Lewitzke
,
C.
, and
Lee
,
P.
Application of Elastomeric Components for Noise and Vibration Isolation in the Automotive Industry, SAE Technical Paper No. 2001-01-1447.
2.
Yu
,
Y.
,
Naganathan
,
N. G.
, and
Dukkipati
,
R. V.
,
2001
, “
A Literature Review of Automotive Vehicle Engine Mounting Systems
,”
Mech. Mach. Theory
,
36
(
1
), pp.
123
142
.
3.
Eickhoff
,
B. M.
,
Evans
,
J. R.
, and
Minnis
,
A. J.
,
1995
, “
A Review of Modelling Methods for Railway Vehicle Suspension Components
,”
Vehic. Syst. Dyn.
,
24
(
6–7
), pp.
469
496
.
4.
Sol-Sánchez
,
M.
,
Moreno-Navarro
,
F.
, and
Rubio-Gámez
,
M. C.
,
2015
, “
The use of Elastic Elements in Railway Tracks: A State of the Art Review
,”
Constr. Build. Mater.
,
75
, pp.
293
305
.
5.
Housner
,
G. W.
,
Bergman
,
L. A.
,
Caughey
,
T. K.
,
Chassiakos
,
A. G.
,
Claus
,
R. O.
,
Masri
,
S. F.
,
Skelton
,
R. E.
,
Soong
,
T. T.
,
Spencer
,
B. F.
, and
Yao
,
J. T. P.
,
1997
, “
Structural Control: Past, Present, and Future
,”
J. Eng. Mech.
,
123
(
9
), pp.
897
971
.
6.
Rittweger
,
A.
,
Albus
,
J.
,
Hornung
,
E.
,
Öry
,
H.
, and
Mourey
,
P.
,
2002
, “
Passive Damping Devices for Aerospace Structures
,”
Acta Astronaut.
,
50
(
10
), pp.
597
608
.
7.
Campolina
,
B. A.
,
Atalla
,
A. N.
,
Dauchez
,
N.
, and
Neple
,
P.
,
2012
, “
Four-Pole Modelling of Vibration Isolators: Application to SEA of Aircraft Double-Wall Panels Subjected to Mechanical Excitation
,”
Noise Control Eng. J.
,
60
(
2
), pp.
158
170
.
8.
Ward
,
C. H.
The Application of a New Cab Mounting to Address Cab Shake on the 2003 Chevrolet Kodiak and GMC TopKick, SAE Technical Paper No. 2002-01-3102, 2002.
9.
Xie
,
M.
,
Wei
,
K.
,
Ren
,
J.
, and
Wang
,
P.
,
2023
, “
Theoretical and Experimental Studies on the Natural Frequencies of Fastener Clips
,”
Nonlinear Dyn.
,
111
(
6
), pp.
5125
5140
.
10.
Song
,
X.
,
Wu
,
H.
,
Jin
,
H.
, and
Cai
,
C. S.
,
2023
, “
Noise Contribution Analysis of a U-Shaped Girder Bridge With Consideration of Frequency Dependent Stiffness of Rail Fasteners
,”
Appl. Acoust.
,
205
, p.
109280
.
11.
Fragasso
,
J.
, and
Moro
,
L.
,
2022
, “
Structure-Borne Noise of Marine Diesel Engines: Dynamic Characterization of Resilient Mounts
,”
Ocean Eng.
,
261
, p.
112116
.
12.
Snowdon
,
J. C.
,
1979
, “
Vibration Isolation: Use and Characterization
,”
J. Acoust. Soc. Am.
,
66
(
5
), pp.
1245
1274
.
13.
Jeong
,
T.
, and
Singh
,
R.
,
2001
, “
Inclusion of Measured Frequency- and Amplitude-Dependent Mount Properties in Vehicle or Machinery Models
,”
J. Sound Vib.
,
245
(
3
), pp.
385
415
.
14.
Ungar
,
E. E.
, and
Dietrich
,
C. W.
,
1966
, “
High-Frequency Vibration Isolation
,”
J. Sound Vib.
,
4
(
2
), pp.
224
241
.
15.
Dal
,
H.
,
Açıkgöz
,
K.
, and
Badienia
,
Y.
,
2021
, “
On the Performance of Isotropic Hyperelastic Constitutive Models for Rubber-Like Materials: A State of the Art Review
,”
ASME Appl. Mech. Rev.
,
73
(
2
), p.
020802
.
16.
Peng
,
X.
, and
Li
,
L.
,
2020
, “
State of the Art of Constitutive Relations of Hyperelastic Materials
,”
Chin. J. Theoret. Appl. Mech.
,
52
(
5
), pp.
1221
1232
. (in Chinese).
17.
Mihai
,
L. A.
, and
Goriely
,
A.
,
2017
, “
How to Characterize a Nonlinear Elastic Material? A Review on Nonlinear Constitutive Parameters in Isotropic Finite Elasticity, Proceedings of the Royal Society A: Mathematical
,”
Phys. Eng. Sci.
,
473
(
2207
), p.
20170607
.
18.
Puglisi
,
G.
, and
Saccomandi
,
G.
,
2016
, “
Multi-Scale Modelling of Rubber-Like Materials and Soft Tissues: An Appraisal, Proceedings of the Royal Society A: Mathematical
,”
Phys. Eng. Sci.
,
472
(
2187
), p.
20160060
.
19.
Muhr
,
A. H.
,
2005
, “
Modeling the Stress-Strain Behavior of Rubber
,”
Rubb. Chem. Technol.
,
78
(
3
), pp.
391
425
.
20.
Ibrahim
,
R. A.
,
2008
, “
Recent Advances in Nonlinear Passive Vibration Isolators
,”
J. Sound Vib.
,
314
(
3–5
), pp.
371
452
.
21.
ISO 10846-1 2008
.
Acoustics and Vibration—Laboratory Measurement of Vibro-Acoustic Transfer Properties of Resilient Elements—Part 1: Principles and Guidelines
.
22.
ISO 10846-2 2008
.
Acoustics and Vibration—Laboratory Measurement of Vibro-Acoustic Transfer Properties of Resilient Elements—Part 2: Direct Method for Determination of the Dynamic Stiffness of Resilient Supports for Translatory Motion
.
23.
ISO 10846-3 2002
.
Acoustics and Vibration—Laboratory Measurement of Vibro-Acoustic Transfer Properties of Resilient Elements—Part 3: Indirect Method for Determination of the Dynamic Stiffness of Resilient Supports for Translatory Motion
.
24.
ISO 10846-5:2009
,
2009
,
Acoustics and Vibration—Laboratory Measurement of Vibro-Acoustic Transfer Properties of Resilient Elements, Part 5: Driving Point Method for Determination of the Low-Frequency Transfer Stiffness of Resilient Supports for Translatory Motion
.
26.
High-Frequency Dynamic Stiffness Test Rig for Elastomer Mounts m + p HFDST-3000-E. https://mpihome.com/files/pdf/data-mp-high-frequency-test-rig-en.pdf,
2019
.
27.
Herron
,
D.
,
Bongini
,
E.
,
Faure
,
B.
,
Potvin
,
R.
,
Cox
,
S.
, et al
,
2018
, “Development of a Test Procedure for Stiffness Measurements Appropriate to Ground-Borne Noise Modelling,”
Noise and Vibration Mitigation for Rail Transportation Systems. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 139
,
D.
Anderson
, ed.,
Springer
,
Cham
, pp.
619
631
.
28.
Gejguš
,
T.
,
Schröder
,
J.
,
Loos
,
K.
,
Lion
,
A.
, and
Johlitz
,
M.
,
2022
, “
Advanced Characterisation of Soft Polymers Under Cyclic Loading in Context of Engine Mounts
,”
Polymers
,
14
(
3
), p.
429
.
29.
Liu
,
X.-A.
,
Zhang
,
J.
,
Jia
,
X.
,
Xiao
,
S.
,
Chen
,
D.
, and
Shangguan
,
W.-B.
,
2022
, “
Modeling and Analysis of Dynamic Characteristics of Rubber Isolators for Electric Vehicles Under High-Frequency Excitation
,”
Proc. Inst. Mech. Eng., Part D: J. Autom. Eng.
,
237
(
12
), p.
09544070221114683
.
30.
Sanderson
,
M. A.
,
1996
, “
Vibration Isolation: Moments and Rotations Included
,”
J. Sound Vib.
,
198
(
2
), pp.
171
191
.
31.
Ohlrich
,
M.
,
2011
, “
Predicting Transmission of Structure-Borne Sound Power From Machines by Including Terminal Cross-Coupling
,”
J. Sound Vib.
,
330
(
21
), pp.
5058
5076
.
32.
Verheij
,
J. W.
,
1982
, “
Multi-Path Sound Transfer From Resiliently Mounted Shipboard Machinery
,”
Doctoral thesis
,
TNO Institute of Applied Physics
,
Delft, The Netherlands
, (Ph.D. thesis).
33.
van der Seijs
,
M. V.
,
de Klerk
,
D.
, and
Rixen
,
D. J.
,
2016
, “
General Framework for Transfer Path Analysis: History, Theory and Classification of Techniques
,”
Mech. Syst. Signal Process.
,
68–69
, pp.
217
244
.
34.
Thompson
,
D.
,
2008
,
Railway Noise and Vibration: Mechanisms, Modelling and Means of Control
,
Elsevier
,
Oxford
.
35.
Alonso
,
A.
,
Gil-Negrete
,
N.
,
Nieto
,
J.
, and
Giménez
,
J. G.
,
2013
, “
Development of a Rubber Component Model Suitable for Being Implemented in Railway Dynamic Simulation Programs
,”
J. Sound Vib.
,
332
(
12
), pp.
3032
3048
.
36.
Li
,
Q.
,
Dai
,
B.
,
Zhu
,
Z.
, and
Thompson
,
D. J.
,
2021
, “
Improved Indirect Measurement of the Dynamic Stiffness of a Rail Fastener and its Dependence on Load and Frequency
,”
Constr. Build. Mater.
,
304
, p.
124588
.
37.
Makris
,
N.
, and
Constantinou
,
M. C.
,
1991
, “
Fractional-Derivative Maxwell Model for Viscous Dampers
,”
J. Struct. Eng.
,
117
(
9
), pp.
2708
2724
.
38.
Makris
,
N.
,
1992
, “
Theoretical and Experimental Investigation of Viscous Dampers in Applications of Seismic and Vibration Isolation
,”
Ph.D. thesis
,
State University of New York at Buffalo
, Amherst
USA
.
39.
Oregui
,
M.
,
de Man
,
A.
,
Woldekidan
,
M. F.
,
Li
,
Z.
, and
Dollevoet
,
R.
,
2016
, “
Obtaining Railpad Properties via Dynamic Mechanical Analysis
,”
J. Sound Vib.
,
363
, pp.
460
472
.
40.
Penas
,
R.
,
Balmes
,
E.
, and
Gaudin
,
A.
,
2022
, “
A Unified non-Linear System Model View of Hyperelasticity, Viscoelasticity and Hysteresis Exhibited by Rubber
,”
Mech. Syst. Signal Process.
,
170
, p.
108793
.
41.
Feng
,
X.
,
Xu
,
P.
, and
Zhang
,
Y.
,
2018
, “
Filled Rubber Isolator’s Constitutive Model and Application to Vehicle Multi-Body System Simulation: A Literature Review
,”
SAE Int. J. Vehic. Dyn. Stab. NVH
,
2
(
2
), pp.
101
119
.
42.
Sun
,
X.
, and
Yang
,
Y.
,
2023
, “
Modelling Comparison for Harmonic Dynamic Characteristics of a Silicone-oil-Filled Rubber Isolator and Response Analysis of a Single DOF System
,”
Int. J. Heavy Vehic. Syst.
,
30
(
4
), pp.
401
425
.
43.
Harris
,
J.
, and
Stevenson
,
A.
,
1987
, “
On the Role of Non–Linearity in the Dynamic Behaviour of Rubber Components
,”
Int. J. Vehic. Des.
,
8
(
4–6
), pp.
553
577
.
44.
Sjöberg
,
M.
, and
Kari
,
L.
,
2003
, “
Testing of Nonlinear Interaction Effects of Sinusoidal and Noise Excitation on Rubber Isolator Stiffness
,”
Polym. Test.
,
22
(
3
), pp.
343
351
.
45.
Carleo
,
F.
,
Barbieri
,
E.
,
Whear
,
R.
, and
Busfield
,
J. J. C.
,
2018
, “
Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates
,”
Polymers
,
10
(
9
), p.
988
.
46.
Somanath
,
S.
,
Marimuthu
,
R.
, and
Krishnapillai
,
S.
,
2023
, “
Frequency Domain Analysis of Pre-Stressed Elastomeric Vibration Isolators
,”
Defence Technol.
,
25
, pp.
33
47
.
47.
Noll
,
S. A.
,
Joodi
,
B.
,
Dreyer
,
J.
, and
Singh
,
R.
,
2015
, “
Volumetric and Dynamic Performance Considerations of Elastomeric Components
,”
SAE Int. J. Mater. Manuf.
,
8
(
3
), pp.
953
959
.
48.
Liu
,
X.
,
Thompson
,
D.
,
Squicciarini
,
G.
,
Rissmann
,
M.
,
Bouvet
,
P.
,
Xie
,
G.
,
Martínez-Casas
,
J.
, et al
,
2021
, “
Measurements and Modelling of Dynamic Stiffness of a Railway Vehicle Primary Suspension Element and its use in a Structure-Borne Noise Transmission Model
,”
Appl. Acoust.
,
182
, p.
108232
.
49.
Dickens
,
J. D.
,
1998
, “
Dynamic Characterisation of Vibration Isolators
,”
Ph.D. thesis
,
University of New South Wales, Australia
,
Sydney, Australia
.
50.
Du
,
Y.
,
Burdisso
,
R. A.
,
Nikolaidis
,
E.
, and
Tiwari
,
D.
,
2003
, “
Effects of Isolators Internal Resonances on Force Transmissibility and Radiated Noise
,”
J. Sound Vib.
,
268
(
4
), pp.
751
778
.
51.
Kim
,
S.
, and
Singh
,
R.
,
2001
, “
Multi-Dimensional Characterization of Vibration Isolators Over a Wide Range of Frequencies
,”
J. Sound Vib.
,
245
(
5
), pp.
877
913
.
52.
Gardonio
,
P.
, and
Elliott
,
S. J.
,
2000
, “
Passive and Active Isolation of Structural Vibration Transmission Between Two Plates Connected by a Set of Mounts
,”
J. Sound Vib.
,
237
(
3
), pp.
483
511
.
53.
Gardonio
,
P.
,
Elliott
,
S. J.
, and
Pinnington
,
R. J.
,
1997
, “
Active Isolation of Structural Vibration on a Multiple-Degree-of-Freedom System, Part I: The Dynamics of the System
,”
J. Sound Vib.
,
207
(
1
), pp.
61
93
.
54.
Kim
,
S.
, and
Singh
,
R.
,
2001
, “
Vibration Transmission Through an Isolator Modelled by Continuous System Theory
,”
J. Sound Vib.
,
248
(
5
), pp.
925
953
.
55.
Fredette
,
L.
, and
Singh
,
R.
,
2017
, “
High Frequency, Multi-Axis Dynamic Stiffness Analysis of a Fractionally Damped Elastomeric Isolator Using Continuous System Theory
,”
J. Sound Vib.
,
389
, pp.
468
483
.
56.
Kari
,
L.
,
2001
, “
On the Waveguide Modelling of Dynamic Stiffness of Cylindrical Vibration Isolators. Part I: The Model, Solution and Experimental Comparison
,”
J. Sound Vib.
,
244
(
2
), pp.
211
233
.
57.
Kari
,
L.
,
2001
, “
On the Waveguide Modelling of Dynamic Stiffness of Cylindrical Vibration Isolators. Part II: The Dispersion Relation Solution, Convergence Analysis and Comparison With Simple Models
,”
J. Sound Vib.
,
244
(
2
), pp.
235
257
.
58.
Kari
,
L.
,
2017
, “
Dynamic Stiffness of Chemically and Physically Ageing Rubber Vibration Isolators in the Audible Frequency Range: Part 2—Waveguide Solution
,”
Cont. Mech. Thermodyn.
,
29
(
5
), pp.
1047
1059
.
59.
Östberg
,
M.
, and
Kari
,
L.
,
2011
, “
Transverse, Tilting and Cross-Coupling Stiffness of Cylindrical Rubber Isolators in the Audible Frequency Range—The Wave-Guide Solution
,”
J. Sound Vib.
,
330
(
13
), pp.
3222
3244
.
60.
Coja
,
M.
, and
Kari
,
L.
,
2021
, “
Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators
,”
Polymers
,
13
(
11
), p.
1703
.
61.
Östberg
,
M.
,
Coja
,
M.
, and
Kari
,
L.
,
2013
, “
Dynamic Stiffness of Hollowed Cylindrical Rubber Vibration Isolators—The Wave-Guide Solution
,”
Int. J. Solids Struct.
,
50
(
10
), pp.
1791
1811
.
62.
Mofakhami
,
M. R.
,
Toudeshky
,
H. H.
, and
Hashemi
,
S. H.
,
2006
, “
Finite Cylinder Vibrations With Different End Boundary Conditions
,”
J. Sound Vib.
,
297
(
1–2
), pp.
293
314
.
63.
Gaul
,
L.
,
1991
, “
Dynamical Transfer Behaviour of Elastomer Isolators; Boundary Element Calculation and Measurement
,”
Mech. Syst. Signal Process.
,
5
(
1
), pp.
13
24
.
64.
Lee
,
J.
, and
Thompson
,
D. J.
,
2001
, “
Dynamic Stiffness Formulation, Free Vibration and Wave Motion of Helical Springs
,”
J. Sound Vib.
,
239
(
2
), pp.
297
320
.
65.
Singh
,
R.
,
Kim
,
G.
, and
Ravindra
,
P. V.
,
1992
, “
Linear Analysis of Automotive Hydro-Mechanical Mount With Emphasis on Decoupler Characteristics
,”
J. Sound Vib.
,
158
(
2
), pp.
219
243
.
66.
Fan
,
R.
, and
Lu
,
Z.
,
2007
, “
Fixed Points on the Nonlinear Dynamic Properties of Hydraulic Engine Mounts and Parameter Identification Method: Experiment and Theory
,”
J. Sound Vib.
,
305
(
4–5
), pp.
703
727
.
67.
Zhou
,
D.
,
Zuo
,
S.
, and
Wu
,
X.
,
2019
, A Lumped Parameter Model Concerning the Amplitude-Dependent Characteristics for the Hydraulic Engine Mount With a Suspended Decoupler, SAE Technical Paper No. 2019-01-0936.
68.
Shangguan
,
W.-B.
,
Guo
,
Y.
,
Wei
,
Y.
,
Rakheja
,
S.
, and
Zhu
,
W.
,
2016
, “
Experimental Characterizations and Estimation of the Natural Frequency of Nonlinear Rubber-Damped Torsional Vibration Absorbers
,”
ASME J. Vib. Acoust.
,
138
(
5
), p.
051006
.
69.
Thompson
,
D. J.
,
van Vliet
,
W. J.
, and
Verheij
,
J. W.
,
1998
, “
Developments of the Indirect Method for Measuring the High Frequency Dynamic Stiffness of Resilient Elements
,”
J. Sound Vib.
,
213
(
1
), pp.
169
188
.
70.
Kari
,
L.
,
2001
, “
Dynamic Transfer Stiffness Measurements of Vibration Isolators in the Audible Frequency Range
,”
Noise Control Eng. J.
,
49
(
2
), pp.
88
102
.
71.
Kari
,
L.
,
2003
, “
On the Dynamic Stiffness of Preloaded Vibration Isolators in the Audible Frequency Range: Modeling and Experiments
,”
J. Acoust. Soc. Am.
,
113
(
4
), pp.
1909
1921
.
72.
Herron
,
D.
,
2009
, “
Vibration of Railway Bridges in the Audible Frequency Range
,”
Ph.D. thesis
,
University of Southampton, Institute of Sound and Vibration Research
,
Southampton, UK
.
73.
Lin
,
T. R.
,
Farag
,
N. H.
, and
Pan
,
J.
,
2005
, “
Evaluation of Frequency Dependent Rubber Mount Stiffness and Damping by Impact Test
,”
Appl. Acoust.
,
66
(
7
), pp.
829
844
.
74.
Ooi
,
L. E.
, and
Ripin
,
Z. M.
,
2011
, “
Dynamic Stiffness and Loss Factor Measurement of Engine Rubber Mount by Impact Test
,”
Mater. Des.
,
32
(
4
), pp.
1880
1887
.
75.
Thompson
,
D. J.
, and
Verheij
,
J. W.
,
1997
, “
The Dynamic Behaviour of Rail Fasteners at High Frequencies
,”
Appl. Acoust.
,
52
(
1
), pp.
1
17
.
76.
Poojary
,
U. R.
,
Hegde
,
S.
, and
Gangadharan
,
K. V.
,
2016
, “
Dynamic Blocked Transfer Stiffness Method of Characterizing the Magnetic Field and Frequency Dependent Dynamic Viscoelastic Properties of MRE
,”
Korea-Australia Rheol. J.
,
28
(
4
), pp.
301
313
.
77.
Kim
,
G.
, and
Singh
,
R.
,
1995
, “
A Study of Passive and Adaptive Hydraulic Engine Mount Systems With Emphasis on non-Linear Characteristics
,”
J. Sound Vib.
,
179
(
3
), pp.
427
453
.
78.
Ewins
,
D. J.
,
2000
,
Modal Testing: Theory, Practice and Application (Second Edition)
,
Research Studies Press
,
Baldock, Herts
.
79.
Li
,
Q.
,
Corradi
,
R.
,
Di Gialleonardo
,
E.
,
Bionda
,
S.
, and
Collina
,
A.
,
2021
, “
Testing and Modelling of Elastomeric Element for an Embedded Rail System
,”
Materials
,
14
(
22
), p.
6968
.
80.
Morison
,
C.
,
Wang
,
A.
, and
Bewes
,
O.
,
2005
, “
Methods for Measuring the Dynamic Stiffness of Resilient Rail Fastenings for Low Frequency Vibration Isolation of Railways, Their Problems and Possible Solutions, Journal of Low Frequency Noise
,”
Vib. Active Control
,
24
(
2
), pp.
107
116
.
81.
Vahdati
,
N.
, and
Saunders
,
L. K. L.
,
2002
, “
High Frequency Testing of Rubber Mounts
,”
ISA Trans.
,
41
(
2
), pp.
145
154
.
82.
Fenander
,
Å
,
1997
, “
Frequency Dependent Stiffness and Damping of Railpads
,”
Proc. Inst. Mech. Eng., Part F: J. Rail Rapid transit
,
211
(
1
), pp.
51
62
.
83.
Zhang
,
X.
,
Thompson
,
D.
,
Jeong
,
H.
,
Toward
,
M.
,
Herron
,
D.
,
Jones
,
C.
, and
Vincent
,
N.
,
2020
, “
Measurements of the High Frequency Dynamic Stiffness of Railway Ballast and Subgrade
,”
J. Sound Vib.
,
468
, p.
115081
.
84.
Gao
,
X.
,
Feng
,
Q.
,
Wang
,
A.
,
Sheng
,
X.
, and
Cheng
,
G.
,
2021
, “
Testing Research on Frequency-Dependent Characteristics of Dynamic Stiffness and Damping for High-Speed Railway Fastener
,”
Eng. Failure Anal.
,
129
, p.
105689
.
85.
Gao
,
X.
,
Feng
,
Q.
,
Wang
,
Z.
,
Liu
,
L.
, and
Wang
,
A.
,
2023
, “
Study on Dynamic Characteristics and Wide Temperature Range Modification of Elastic Pad of High-Speed Railway Fastener
,”
Eng. Failure Anal.
,
151
, p.
107376
.
86.
Dickens
,
J. D.
, and
Norwood
,
C. J.
,
2001
, “
Universal Method to Measure Dynamic Performance of Vibration Isolators Under Static Load
,”
J. Sound Vib.
,
244
(
4
), pp.
685
696
.
87.
Moorhouse
,
A. T.
, and
Gibbs
,
B. M.
,
1995
, “
Measurement of Structure-Borne Sound Emission From Resiliently Mounted Machines In situ
,”
J. Sound Vib.
,
180
(
1
), pp.
143
161
.
88.
Lee
,
H.
,
Kim
,
K.
,
Lee
,
B.
, and
Jin
,
S.
,
2001
, “
Multi-Dimensional Vibration Power Path Analysis With Rotational Terms Included: Application to a Compressor
,”
Proceedings of the Asia-Pacific Vibration Conference
,
Hangzhou, China
,
Oct. 28
.
89.
Bregar
,
T.
,
Holeček
,
N.
,
Čepon
,
G.
,
Rixen
,
D. J.
, and
Boltežar
,
M.
,
2020
, “
Including Directly Measured Rotations in the Virtual Point Transformation
,”
Mech. Syst. Signal Process.
,
141
, p.
106440
.
90.
Huras
,
L.
,
Zembaty
,
Z.
,
Bońkowski
,
P. A.
, and
Bobra
,
P.
,
2021
, “
Quantifying Local Stiffness Loss in Beams Using Rotation Rate Sensors
,”
Mech. Syst. Signal Process.
,
151
, p.
107396
.
91.
Mirza
,
W. I. I. W. I.
,
Kyprianou
,
A.
,
da Silva
,
T. A. N.
, and
Rani
,
M. N. A.
,
2023
, “
Frequency Based Substructuring and Coupling Enhancement Using Estimated Rotational Frequency Response Functions
,”
Experimental Techn.
, pp.
1
15
.
92.
Saeed
,
Z.
,
Klaassen
,
S. W. B.
,
Firrone
,
C. M.
,
Berruti
,
T. M.
, and
Rixen
,
D. J.
,
2020
, “
Experimental Joint Identification Using System Equivalent Model Mixing in a Bladed Disk
,”
ASME J. Vib. Acoust.
,
142
(
5
), p.
051001
.
93.
Ji
,
Y.
,
Chen
,
Y.
,
Zhang
,
S.
,
Bi
,
Q.
, and
Wang
,
Y.
,
2022
, “
Multi-Point Substructure Coupling Method to Compensate Multi-Accelerometer Masses in Measuring Rotation-Related Frequency Response Functions
,”
ASME J. Manuf. Sci. Eng.
,
144
(
1
), p.
011009
.
94.
van der Seijs
,
M. V.
,
2016
, “
Experimental Dynamic Substructuring: Analysis and Design Strategies for Vehicle Development
,”
Ph.D. thesis
,
Delft University of Technology
,
Delft, The Netherlands
.
95.
Meggitt
,
J. W. R.
, and
Moorhouse
,
A. T.
,
2020
, “
Finite Element Model Updating Using In-situ Experimental Data
,”
J. Sound Vib.
,
489
, p.
115675
.
96.
de Klerk
,
D.
,
Rixen
,
D. J.
, and
Voormeeren
,
S. N.
,
2008
, “
General Framework for Dynamic Substructuring: History, Review and Classification of Techniques
,”
AIAA J.
,
46
(
5
), pp.
1169
1181
.
97.
Gardonio
,
P.
, and
Brennan
,
M. J.
,
2002
, “
On the Origins and Development of Mobility and Impedance Methods in Structural Dynamics
,”
J. Sound Vib.
,
249
(
3
), pp.
557
573
.
98.
Forrest
,
J. A.
, “
Free-Free Dynamics of Some Vibration Isolators
,”
Proceedings of the Annual Conference of the Australian Acoustical Society
,
Adelaide, Australia
,
Nov. 13–15
, pp.
406
416
.
99.
Kim
,
S.
, and
Singh
,
R.
Examination of High Frequency Characterization Methods for Mounts, SAE Technical Paper No. 2001.
100.
Fahy
,
F.
, and
Gardonio
,
P.
,
2007
,
Sound and Structural Vibration: Radiation, Transmission and Response
,
Elsevier/Academic
,
Boston, MA
.
101.
Huang
,
X.
,
Zhang
,
Z.
,
Hua
,
H.
, and
Xu
,
S.
,
2014
, “
Hybrid Modeling of Floating Raft System by FRF-Based Substructuring Method With Elastic Coupling, Dynamics of Coupled Structures
,”
Volume 1: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics
,
Springer International Publishing
, pp.
83
89
.
102.
Forrest
,
J. A.
,
2006
, “
Experimental Modal Analysis of Three Small-Scale Vibration Isolator Models
,”
J. Sound Vib.
,
289
(
1–2
), pp.
382
412
.
103.
Ooi
,
L. E.
, and
Ripin
,
Z. M.
,
2014
, “
Impact Technique for Measuring Global Dynamic Stiffness of Engine Mounts
,”
Int. J. Autom. Technol.
,
15
(
6
), pp.
1015
1026
.
104.
Noll
,
S.
,
Dreyer
,
J. T.
, and
Singh
,
R.
,
2013
, “
Identification of Dynamic Stiffness Matrices of Elastomeric Joints Using Direct and Inverse Methods
,”
Mech. Syst. Signal Process.
,
39
(
1–2
), pp.
227
244
.
105.
Noll
,
S.
,
Dreyer
,
J.
, and
Singh
,
R.
,
2013
, “
Comparative Assessment of Multi-Axis Bushing Properties Using Resonant and non-Resonant Methods
,”
SAE Int. J. Passeng. Cars—Mech. Syst.
,
6
(
2
), pp.
1217
1223
.
106.
Noll
,
S.
,
Dreyer
,
J.
, and
Singh
,
R.
,
2014
, “
Application of a Novel Method to Identify Multi-Axis Joint Properties, Dynamics of Coupled Structures
,”
Volume 1: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics
,
Springer International Publishing
, pp.
203
208
.
107.
Joodi
,
B.
,
Noll
,
S. A.
,
Dreyer
,
J.
, and
Singh
,
R.
,
2015
, “
Comparative Assessment of Frequency Dependent Joint Properties Using Direct and Inverse Identification Methods
,”
SAE Int. J. Mater. Manuf.
,
8
(
3
), pp.
960
968
.
108.
Ramesh
,
R. S.
,
Fredette
,
L.
, and
Singh
,
R.
,
2019
, “
Identification of Multi-Dimensional Elastic and Dissipative Properties of Elastomeric Vibration Isolators
,”
Mech. Syst. Signal Process.
,
118
, pp.
696
715
.
109.
Haeussler
,
M.
,
Klaassen
,
S. W. B.
, and
Rixen
,
D. J.
,
2020
, “
Experimental Twelve Degree of Freedom Rubber Isolator Models for Use in Substructuring Assemblies
,”
J. Sound Vib.
,
474
, p.
115253
.
110.
Haeussler
,
M.
,
Kobus
,
D. C.
, and
Rixen
,
D. J.
,
2021
, “
Parametric Design Optimization of e-Compressor NVH Using Blocked Forces and Substructuring
,”
Mech. Syst. Signal Process.
,
150
, p.
107217
.
111.
Oltmann
,
J.
,
Hartwich
,
T.
, and
Krause
,
D.
,
2020
, “
Optimizing Lightweight Structures With Particle Damping Using Frequency Based Substructuring
,”
Des. Sci.
,
6
, p.
e17
.
112.
Meggitt
,
J. W. R.
,
2017
, “
On In-situ Methodologies for the Characterisation and Simulation of Vibro-Acoustic Assemblies
,”
Ph.D. thesis
,
University of Salford
,
Salford, UK
.
113.
Meggitt
,
J. W. R.
, and
Moorhouse
,
A. T.
,
2019
, “
In-situ Sub-Structure Decoupling of Resiliently Coupled Assemblies
,”
Mech. Syst. Signal Process.
,
117
, pp.
723
737
.
114.
Keersmaekers
,
L.
,
Mertens
,
L.
,
Penne
,
R.
,
Guillaume
,
P.
, and
Steenackers
,
G.
,
2015
, “
Decoupling of Mechanical Systems Based on In-situ Frequency Response Functions: The Link-Preserving, Decoupling Method
,”
Mech. Syst. Signal Process.
,
58–59
, pp.
340
354
.
115.
Wang
,
Z.
,
Cheng
,
L.
,
Lei
,
S.
,
Yang
,
Y.
, and
Ding
,
L.
,
2022
, “
An In-situ Decoupling Method for Discrete Mechanical Systems With Rigid and Resilient Coupling Links
,”
Appl. Acoust.
,
195
, p.
108853
.
116.
Meggitt
,
J. W. R.
,
Elliott
,
A. S.
,
Moorhouse
,
A. T.
, and
Lai
,
H. K.
,
2016
, “
In situ Determination of Dynamic Stiffness for Resilient Elements
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
230
(
6
), pp.
986
993
.
117.
Moorhouse
,
A.
,
Elliot
,
A. S.
, and
Heo
,
Y. H.
,
2013
, “
Intrinsic Characterisation of Structure-Borne Sound Sources and Isolators From In-situ Measurements, Proceedings of Meetings on Acoustics ICA2013
,”
Acoust. Soc. Am.
,
19
(
1
), p.
065053
.
118.
Elliott
,
A. S.
,
Moorhouse
,
A. T.
, and
Pavić
,
G.
,
2012
, “
Moment Excitation and the Measurement of Moment Mobilities
,”
J. Sound Vib.
,
331
(
11
), pp.
2499
2519
.
119.
Reichart
,
R.
,
Cho
,
M.
,
Song
,
D. P.
, and
Klaassen
,
S. W. B.
,
2023
, “
How Virtual Points, Component TPA, and Frequency-Based Substructuring Disrupted the Vehicle Suspension Development Process
,”
Proceedings of the Society for Experimental Mechanics Annual Conference and Exposition, Dynamic Substructures 4
, pp.
67
72
,
Cham
:
Springer Nature Switzerland
.
120.
Wagner
,
P.
,
Hülsmann
,
A. P.
, and
van der Seijs
,
M. V.
, “
Application of Dynamic Substructuring in NVH Design of Electric Drivetrains
,”
Proceedings of the 29th International Conference on Noise and Vibration Engineering, ISMA 2020 and 8th International Conference on Uncertainty in Structural Dynamics (USD)
,
Leuven, Belgium
,
Sept. 7–9
, pp.
3365
3381
.
121.
van der Kooij
,
M. W.
,
Klaassen
,
S. W. B.
, and
Huelsmann
,
A. P.
, Using Dynamic Substructuring and Component TPA to Shape the NVH Experience of a Full-Electric Vehicle, SAE Technical Paper No. 2022-01-0988.
122.
de Brett
,
M.
,
Butlin
,
T.
,
Andrade
,
L.
, and
Nielsen
,
O. M.
,
2022
, “
Experimental Investigation Into the Role of Nonlinear Suspension Behaviour in Limiting Feedforward Road Noise Cancellation
,”
J. Sound Vib.
,
516
, p.
116532
.
123.
Gusmano
,
P.
, and
Fredette
,
L.
, Experimental Validation of Vibration Isolation in Quasi-Zero Stiffness Mount Concept, SAE Technical Paper No. 2023-01-1066, 2023.
124.
Salim
,
M. A.
,
Putra
,
A.
,
Thompson
,
D.
,
Ahmad
,
N.
, and
Abdullah
,
M. A.
,
2013
, “Transmissibility of a Laminated Rubber-Metal Spring: A Preliminary Study,”
Applied Mechanics and Materials
, Vol.
393
,
Trans Tech Publications Ltd.
,
Switzerland
, pp.
661
665
.
125.
Sun
,
X.
,
Zhang
,
C.
,
Fu
,
Q.
,
Zhang
,
H.
, and
Dong
,
H.
,
2020
, “
Measurement and Modelling for Harmonic Dynamic Characteristics of a Liquid-Filled Isolator With a Rubber Element and High-Viscosity Silicone Oil at Low Frequency
,”
Mech. Syst. Signal Process.
,
140
, p.
106659
.
126.
Bian
,
J.
, and
Jing
,
X.
,
2020
, “
Analysis and Design of a Novel and Compact X-Structured Vibration Isolation Mount (X-Mount) With Wider Quasi-Zero-Stiffness Range
,”
Nonlinear Dyn.
,
101
(
4
), pp.
2195
2222
.
127.
On
,
S. Y.
,
Moon
,
H.
,
Park
,
S. Y.
,
Ohm
,
T. W.
,
Kim
,
W.
,
Hong
,
H.
, and
Kim
,
S. S.
,
2022
, “
Design of Periodic Arched Structures Integrating the Structural Nonlinearity and Band Gap Effect for Vibration Isolation
,”
Mater. Des.
,
224
, p.
111397
.
128.
Kerschen
,
G.
,
Worden
,
K.
,
Vakakis
,
A. F.
, and
Golinval
,
J. C.
,
2006
, “
Past, Present and Future of Nonlinear System Identification in Structural Dynamics
,”
Mech. Syst. Signal Process.
,
20
(
3
), pp.
505
592
.
129.
Lapčı´k Jr
,
L.
,
Augustin
,
P.
,
Pı´štěk
,
A.
, and
Bujnoch
,
L.
,
2001
, “
Measurement of the Dynamic Stiffness of Recycled Rubber Based Railway Track Mats According to the DB-TL 918.071 Standard
,”
Appl. Acoust.
,
62
(
9
), pp.
1123
1128
.
130.
Kari
,
L.
,
2003
, “
Audible-Frequency Stiffness of a Primary Suspension Isolator on a High-Speed Tilting Bogie
,”
Proc. Inst. Mech. Eng., Part F: J. Rail Rapid Transit
,
217
(
1
), pp.
47
62
.
131.
Fredette
,
L.
,
Dreyer
,
J. T.
,
Rook
,
T. E.
, and
Singh
,
R.
,
2016
, “
Harmonic Amplitude Dependent Dynamic Stiffness of Hydraulic Bushings: Alternate Nonlinear Models and Experimental Validation
,”
Mech. Syst. Signal Process.
,
75
, pp.
589
606
.
132.
Shaska
,
K.
,
Ibrahim
,
R. A.
, and
Gibson
,
R. F.
,
2007
, “
Influence of Excitation Amplitude on the Characteristics of Nonlinear Butyl Rubber Isolators
,”
Nonlinear Dyn.
,
47
(
1
), pp.
83
104
.
133.
Mallik
,
A. K.
,
Kher
,
V.
,
Puri
,
M.
, and
Hatwal
,
H.
,
1999
, “
On the Modeling of Non-Linear Elastomeric Vibration Isolators
,”
J. Sound Vib.
,
219
(
2
), pp.
239
253
.
134.
Chen
,
X.
,
Shen
,
Z.
,
He
,
Q.
,
Du
,
Q.
, and
Liu
,
X.
,
2016
, “
Influence of Uncertainty and Excitation Amplitude on the Vibration Characteristics of Rubber Isolators
,”
J. Sound Vib.
,
377
, pp.
216
225
. .
135.
Roncen
,
T.
,
Sinou
,
J. J.
, and
Lambelin
,
J. P.
,
2019
, “
Experiments and Nonlinear Simulations of a Rubber Isolator Subjected to Harmonic and Random Vibrations
,”
J. Sound Vib.
,
451
, pp.
71
83
.
136.
Yang
,
P.
,
Tan
,
Y.
,
Yang
,
J.
, and
Sun
,
N.
,
2006
, “
Measurement, Simulation on Dynamic Characteristics of a Wire Gauze-Fluid Damping Shock Absorber
,”
Mech. Syst. Signal Process.
,
20
(
2
), pp.
745
756
.
137.
Pu
,
Y.
,
Sumali
,
H.
, and
Gaillard
,
C. L.
Modeling of Nonlinear Elastomeric Mounts. Part 1: Dynamic Testing and Parameter Identification, SAE Technical Paper No. 2001-01-0042, 2001.
138.
Sjöberg
,
M. M.
, and
Kari
,
L.
,
2002
, “
Non-Linear Behavior of a Rubber Isolator System Using Fractional Derivatives
,”
Vehic. Syst. Dyn.
,
37
(
3
), pp.
217
236
.
139.
Yang
,
S. Y.
,
Han
,
C.
,
Shin
,
C. S.
,
Choi
,
S. B.
,
Jung
,
J. Y.
,
Kim
,
S. J.
, and
Kim
,
I. D.
,
2019
, “
Dynamic Characteristics of Passive and Semi-Active Cabin Mounts for Vibration Control of a Wheel Loader
,”
Int. J. Heavy Vehic. Syst.
,
26
(
2
), pp.
239
261
.
140.
Hu
,
J.
,
Ren
,
J.
,
Zhe
,
Z.
,
Xue
,
M.
,
Tong
,
Y.
,
Zou
,
J.
,
Zheng
,
Q.
, and
Tang
,
H.
,
2020
, “
A Pressure, Amplitude and Frequency Dependent Hybrid Damping Mechanical Model of Flexible Joint
,”
J. Sound Vib.
,
471
, p.
115173
.
141.
Jrad
,
H.
,
Renaud
,
F.
,
Dion
,
J. L.
,
Tawfiq
,
I.
, and
Hadder
,
M.
,
2013
, “
Experimental Characterization, Modeling and Parametric Identification of the Hysteretic Friction Behavior of Viscoelastic Joints
,”
Int. J. Appl. Mech.
,
5
(
02
), p.
1350018
.
142.
Jrad
,
H.
,
Dion
,
J. L.
,
Renaud
,
F.
,
Tawfiq
,
I.
, and
Haddar
,
M.
,
2013
, “
Experimental Characterization, Modeling and Parametric Identification of the Non Linear Dynamic Behavior of Viscoelastic Components
,”
Eur. J. Mech. A/Solids
,
42
, pp.
176
187
.
143.
Harris
,
J. A.
,
1987
, “
Dynamic Testing Under Nonsinusoidal Conditions and the Consequences of Nonlinearity for Service Performance
,”
Rubb. Chem. Technol.
,
60
(
5
), pp.
870
887
.
144.
Lakes
,
R.
,
2009
,
Viscoelastic Materials, United States of America
,
Cambridge University Press
,
New York
.
145.
Meram
,
A.
,
2019
, “
Dynamic Characterization of Elastomer Buffer Under Impact Loading by Low-Velocity Drop Test Method
,”
Polym. Test.
,
79
, p.
106013
.
146.
Adiguna
,
H.
,
Tiwari
,
M.
,
Singh
,
R.
,
Tseng
,
H. E.
, and
Hrovat
,
D.
,
2003
, “
Transient Response of a Hydraulic Engine Mount
,”
J. Sound Vib.
,
268
(
2
), pp.
217
248
.
147.
He
,
S.
, and
Singh
,
R.
,
2007
, “
Discontinuous Compliance Nonlinearities in the Hydraulic Engine Mount
,”
J. Sound Vib.
307
(
3–5
), pp.
545
563
.
148.
Zucchini
,
A.
,
Naets
,
F.
, and
Hülsmann
,
A.
,
2023
, “
Characterization of Rubber Mounts Through Virtual Point Transformation Using Different Boundary Conditions in the Context of Dynamic Substructuring
,”
Proceedings of the Society for Experimental Mechanics Annual Conference and Exposition, Dynamic Substructures 4
, pp,
11
21
.
Cham
:
Springer Nature Switzerland
.
149.
Anastasio
,
D.
,
2020
, “
Modeling and Experimental Identification of Vibrating Structures: Localized and Distributed Nonlinearities
,”
Ph.D. thesis
,
Politecnico di Torino
,
Turin, Italy
.
150.
Gimpl
,
V.
,
Fantetti
,
A.
,
Klaassen
,
S. W. B.
,
Schwingshackl
,
C. W.
, and
Rixen
,
D. J.
,
2022
, “
Contact Stiffness of Jointed Interfaces: A Comparison of Dynamic Substructuring Techniques With Frictional Hysteresis Measurements
,”
Mech. Syst. Signal Process.
,
171
, p.
108896
.
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