Abstract

In a standard design practice, it is often necessary to assemble engineered structures from individually manufactured parts. Ideally, the assembled system should perform as if the connections between the components were perfect, that is, as if the system were a single monolithic piece. However, the fasteners used in those connections, such as mechanical lap joints, are imperfect and highly nonlinear. In particular, these jointed connections dissipate energy, often through friction over highly localized microscale regions near connection points, and are known to exhibit history dependent, or hysteretic behavior. As a result, while mechanical joints are one of the most common elements in structural dynamics problems, their presence implies that assembled structural systems are difficult to model and analyze. Through rigorous experimental, analytical, and numerical work over the past century, researchers from several different disciplines have developed numerous damping models that give rise to the dynamical behavior attributed to joints. This work seeks to review, compare, and contrast several linear and nonlinear damping models that are known to be relevant to modeling assembled structural systems. These models are presented and categorized to place them in the proper historical and mathematical context as well as presenting numerous examples of their applications. General properties of hysteretic friction damping models are also studied and compared analytically. Connections are drawn between the different models so as to not only identify differences between models, but also highlight commonalities not normally seen to be in association.

References

References
1.
Menq
,
C.-H.
,
Bielak
,
J.
, and
Griffin
,
J. H.
,
1986
, “
The Influence of Microslip on Vibratory Response—Part I: A New Microslip Model
,”
J. Sound Vib.
,
107
(
2
), pp.
279
293
.10.1016/0022-460X(86)90238-5
2.
Menq
,
C.-H.
,
Griffin
,
J. H.
, and
Bielak
,
J.
,
1986
, “
The Influence of Microslip on Vibratory Response—Part II: A Comparison With Experimental Results
,”
J. Sound Vib.
,
107
(
2
), pp.
295
307
.10.1016/0022-460X(86)90239-7
3.
Quinn
,
D. D.
, and
Segalman
,
D. J.
,
2005
, “
Using Series-Series Iwan-Type Models for Understanding Joint Dynamics
,”
ASME J. Appl. Mech.
,
72
(
5
), pp.
666
673
.10.1115/1.1978918
4.
Segalman
,
D. J.
,
Gregory
,
D. L.
,
Starr
,
M. J.
,
Resor
,
B. R.
,
Jew
,
M. D.
,
Lauffer
,
J. P.
, and
Ames
,
N. M.
,
2009
, “
Handbook on Dynamics of Jointed Structures
,” Sandia National Laboratories, Albuquerque, NM, Report No.
SAND2009–4164
.https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2009/094164.pdf
5.
Goodman
,
L. E.
, and
Brown
,
C. B.
,
1962
, “
Energy Dissipation in Contact Friction: Constant Normal and Cyclic Tangential Loading
,”
ASME J. Appl. Mech.
,
29
(
1
), pp.
17
22
.10.1115/1.3636453
6.
Schwingshackl
,
C. W.
,
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2012
, “
Measured and Estimated Friction Interface Parameter in a Nonlinear Dynamic Analysis
,”
Mech. Syst. Signal Process.
,
28
, pp.
574
584
.10.1016/j.ymssp.2011.10.005
7.
Kartal
,
M. E.
,
Mulvihill
,
D. M.
,
Nowell
,
D.
, and
Hills
,
D. A.
,
2011
, “
Measurements of Pressure and Area Dependent Tangential Contact Stiffness Between Rough Surfaces Using Digital Image Correlation
,”
Tribol. Int.
,
44
(
10
), pp.
1188
1198
.10.1016/j.triboint.2011.05.025
8.
Smallwood
,
D. O.
,
2000
, “
Damping Investigations of a Simplified Frictional Shear Joint
,” Sandia National Laboratories, Albuquerque, NM, Report No.
SAND2000–1929C
.https://digital.library.unt.edu/ark:/67531/metadc723091/
9.
Hartwigsen
,
C. J.
,
Song
,
Y.
,
McFarland
,
D. M.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2004
, “
Experimental Study of Non-Linear Effects in a Typical Shear Lap Joint Configuration
,”
J. Sound Vib.
,
277
(
1–2
), pp.
327
351
.10.1016/j.jsv.2003.09.018
10.
Ouyang
,
H.
,
Oldfield
,
M. J.
, and
Mottershead
,
J. E.
,
2006
, “
Experimental and Theoretical Studies of a Bolted Joint Excited by a Torsional Dynamic Load
,”
Int. J. Mech. Sci.
,
48
(
12
), pp.
1447
1455
.10.1016/j.ijmecsci.2006.07.015
11.
Deaner
,
B.
,
Allen
,
M.
,
Starr
,
M.
,
Segalman
,
D.
, and
Sumali
,
H.
,
2015a
, “
Application of Viscous and Iwan Modal Damping Models to Experimental Measurements From Bolted Structures
,”
ASME J. Vib. Acoust.
,
137
(
2
), p.
021012
.10.1115/1.4029074
12.
Brake
,
M. R. W.
,
Schwingshackl
,
C. W.
, and
Reu
,
P.
,
2019
, “
On the Observed Variability and Repeatability in Jointed Structures
,”
Mech. Syst. Signal Process.
,
129
, pp.
282
307
.10.1016/j.ymssp.2019.04.020
13.
Woodhouse
,
J.
,
Putelat
,
T.
, and
McKay
,
A.
,
2015
, “
Are There Reliable Constitutive Laws for Dynamic Friction?
,”
Philos. Trans. R. Soc. London
,
373
(
2051
), p. 20140401.10.1098/rsta.2014.0401
14.
Hassani
,
V.
,
Tjahjowidodo
,
T.
, and
Do
,
T. N.
,
2014
, “
A Survey on Hysteresis Modeling, Identification and Control
,”
Mech. Syst. Signal Process.
,
49
(
1–2
), pp.
209
233
.10.1016/j.ymssp.2014.04.012
15.
Marques
,
F.
,
Flores
,
P.
,
Claro
,
J. C. P.
, and
Lankarani
,
H. M.
,
2016
, “
A Survey and Comparison of Several Friction Force Models for Dynamic Analysis of Multibody Mechanical Systems
,”
Nonlinear Dyn.
,
86
(
3
), pp.
1407
1443
.10.1007/s11071-016-2999-3
16.
Segalman
,
D. J.
,
2006
, “
Modelling Joint Friction in Structural Dynamics
,”
Struct. Control Health Monit.
,
13
(
1
), pp.
430
453
.10.1002/stc.119
17.
Firrone
,
C. M.
, and
Zucca
,
S.
,
2011
, “
Modelling Friction Contacts in Structural Dynamics and Its Application to Turbine Bladed Disks
,”
Numerical Analysis
,
J.
Awrejcewicz
, ed.,
IntechOpen
,
Rijeka, Croatia
, Chap.
14
.10.5772/25128
18.
Mayer
,
M. H.
, and
Gaul
,
L.
,
2007
, “
Segment-to-Segment Contact Elements for Modelling Joint Interfaces in Finite Element Analysis
,”
Mech. Syst. Signal Process.
,
21
(
2
), pp.
724
734
.10.1016/j.ymssp.2005.10.006
19.
Hertz
,
H.
,
1882
, “
Ber Die Berhrung Fester Elastischer Krper (on the Contact of Elastic Solids)
,”
J. Fur Die Reine Andgewandte Math.
,
92
, pp.
156
171
.
20.
Gaul
,
L.
, and
Nitsche
,
R.
,
2001
, “
The Role of Friction in Mechanical Joints
,”
ASME Appl. Mech. Rev.
,
54
(
2
), pp.
93
106
.10.1115/1.3097294
21.
Afzal
,
M.
,
Arteaga
,
I. L.
, and
Kari
,
L.
,
2016
, “
An Analytical Calculation of the Jacobian Matrix for 3d Friction Contact Model Applied to Turbine Blade Shroud Contact
,”
Comput. Struct.
,
177
, pp.
204
217
.10.1016/j.compstruc.2016.08.014
22.
Roettgen
,
D. R.
, and
Allen
,
M. S.
,
2017
, “
Nonlinear Characterization of a Bolted, Industrial Structure Using a Modal Framework
,”
Mech. Syst. Signal Process.
,
84
, pp.
152
170
.10.1016/j.ymssp.2015.11.010
23.
Filippi
,
S.
,
Akay
,
A.
, and
Gola
,
M. M.
,
2004
, “
Measurement of Tangential Contact Hysteresis During Microslip
,”
ASME J. Tribol.
,
126
(
3
), pp.
482
489
.10.1115/1.1692030
24.
Mignolet
,
M. P.
,
Song
,
P.
, and
Wang
,
X. Q.
,
2015
, “
A Stochastic Iwan-Type Model for Joint Behavior Variability Modeling
,”
J. Sound Vib.
,
349
, pp.
289
298
.10.1016/j.jsv.2015.03.032
25.
Masing
,
G.
,
1923
, “
Zur Heynschen Theorie Der Verfestigung Der Metalle Durch Verborgen Elastische Spannungen
,” Wissenschaftliche Veroffentlichungen Aus Dem Siemens-Konzern, Vol.
3
, Springer, Berlin, pp.
231
239
.
26.
Chiang
,
D.
,
1999
, “
The Generalized Masing Model for Deteriorating Hysteresis and Cyclic Plasticity
,”
Appl. Math. Modell.
,
23
(
11
), pp.
847
863
.10.1016/S0307-904X(99)00015-3
27.
Skelton
,
R. P.
,
Maier
,
H. J.
, and
Christ
,
H.-J.
,
1997
, “
The Bauschinger Effect, Masing Model and the Ramberg–Osgood Relation for Cyclic Deformation in Metals
,”
Mater. Sci. Eng. A
,
238
(
2
), pp.
377
390
.10.1016/S0921-5093(97)00465-6
28.
Quinn
,
D. D.
,
2012
, “
Modal Analysis of Jointed Structures
,”
J. Sound Vib.
,
331
(
1
), pp.
81
93
.10.1016/j.jsv.2011.08.017
29.
Visintin
,
A.
,
1991
,
Differential Models of Hysteresis, Volume 111 of Applied Mathematical Sciences
,
Springer-Verlag
,
Berlin
.
30.
Dossogne
,
T.
,
Jerome
,
T. W.
,
Lancereau
,
D. P. T.
,
Smith
,
S. A.
,
Brake
,
M. R. W.
,
Pacini
,
B. R.
,
Reuss
,
P.
, and
Schwingshackl
,
C. W.
,
2017
, “
Experimental Assessment of Jointed Configuration
,”
IMAC–XXXV: A Conference and Exposition on Structural Dynamics
,
Garden Grove, CA
, Jan. 30–Feb. 2, pp.
255
261
.10.1007/978-3-319-54930-9_22
31.
Brake
,
M. R. W.
, (ed.), 2018,
The Mechanics of Jointed Structures
,
Springer International Publishing
,
Berlin
.
32.
Botto
,
D.
,
Gastadi
,
C.
,
Gola
,
M. M.
, and
Umer
,
M.
,
2018
, “
An Experimental Investigation of the Dynamics of a Blade With Two Under-Platform Dampers
,”
ASME J. Eng. Gas Turbines Power
,
140
(
3
), p.
032504
.10.1115/1.4037865
33.
Pesaresi
,
L.
,
Salles
,
L.
,
Elliott
,
R.
,
Jones
,
A.
,
Green
,
J. S.
, and
Schwingshackl
,
C. W.
,
2016
, “
Numerical and Experimental Investigation of an Underplatform Damper Test Rig
,”
Appl. Mech. Mater.
,
849
, pp.
1
12
.10.4028/www.scientific.net/AMM.849.1
34.
Bograd
,
S.
,
Schmidt
,
A.
, and
Gaul
,
L.
,
2008
, “
Joint Damping Prediction by Thin Layer Elements
,”
Proceedings of the IMAC 26th Society of Experimental Mechanics,
Orlando, FL
, Feb. 4–7, p.
21
.https://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/dynamics/bograd_schmidt_gaul.pdf
35.
Bograd
,
S.
,
Reuss
,
P.
,
Schmidt
,
A.
,
Gaul
,
L.
, and
Mayer
,
M.
,
2011
, “
Modeling the Dynamics of Mechanical Joints
,”
Mech. Syst. Signal Process.
,
25
(
8
), pp.
2801
2826
.10.1016/j.ymssp.2011.01.010
36.
Süß
,
D.
,
2016
, “
Multi-Harmonische-Balance-Methoden Zur Untersuchung Des Übertragungsverhaltens Von Strukturen Mit Fügestellen
,”
Ph.D. dissertation
,
Lehrstuhl fr Technische Mechanik, FAU
,
Erlangen, Germany
.https://opus4.kobv.de/opus4-fau/frontdoor/deliver/index/docId/7193/file/Dissertation_Suess_LTM.pdf
37.
Süß
,
D.
,
Janeba
,
A.
, and
Willner
,
K.
,
2018
, “
The Gaul Resonator: Experiments for the Isolated Investigation of a Bolted Lap Joint
,” M. Brake, ed., Springer, Berlin, pp.
59
72
.10.1007/978-3-319-56818-8_6
38.
Chen
,
W.
,
Jin
,
M.
,
Lawal
,
I.
,
Brake
,
M. R.
, and
Song
,
H.
,
2019
, “
Measurement of Slip and Separation in Jointed Structures With Non-Flat Interfaces
,”
Mech. Syst. Signal Process.
,
134
, p.
106325
.10.1016/j.ymssp.2019.106325
39.
Fantetti
,
A.
,
Tamatam
,
L. R.
,
Volvert
,
M.
,
Lawal
,
I.
,
Liu
,
L.
,
Salles
,
L.
,
Brake
,
M. R. W.
,
Schwingshackl
,
C. W.
, and
Nowell
,
D.
,
2019
, “
The Impact of Fretting Wear on Structural Dynamics: Experiment and Simulation
,”
Tribol. Int.
,
138
, pp.
111
124
.10.1016/j.triboint.2019.05.023
40.
Gaul
,
L.
, and
Lenz
,
J.
,
1997
, “
Nonlinear Dynamics of Structures Assembled by Bolted Joints
,”
Acta Mech.
,
125
(
1–4
), pp.
169
181
.10.1007/BF01177306
41.
Ewins
,
D. J.
,
Bergman
,
L. A.
, and
Segalman
,
D. J.
,
2006
, “
Report on the SNL/NSF International Workshop on Joint Mechanics
,”
National Science Foundation/Sandia National Laboratories
,
Arlington, VA
, Report No.
SAND2007–7761
.https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2007/077761.pdf
42.
Ewins
,
D. J.
,
Bergman
,
L. A.
, and
Segalman
,
D. J.
,
2009
, “
Report on the SNL/AWE/NSF International Workshop on Joint Mechanics
,”
Sandia National Laboratories/Atomic Weapons Establishment/National Science Foundation
,
Dartington, UK
, Report No.
SAND2010–5458
.https://www.osti.gov/biblio/993308
43.
Starr
,
M. J.
,
Brake
,
M. R.
,
Segalman
,
D. J.
,
Bergman
,
L. A.
, and
Ewins
,
D. J.
,
2013
, “
Proceedings of the Third International Workshop on Jointed Structures
,”
Sandia National Laboratories
,
Albuquerque, NM
, Report No.
SAND2013–6655
.https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2013/136655.pdf
44.
Brake
,
M. R. W.
,
Ewins
,
D. J.
,
Segalman
,
D. J.
,
Bergman
,
L. A.
, and
Quinn
, D.
D.
,
2006
, “
Proceedings of the Fourth International Workshop on Jointed Structures
,”
Sandia National Laboratories
,
Albuquerque, NM
, Report No.
SAND2016–9962
.10.2172/1562833
45.
Rayleigh
,
J. W. S. B.
,
1894
,
The Theory of Sound
, Vol.
1
,
Macmillan
, London.
46.
Rao
,
S. S.
,
2011
,
Mechanical Vibrations
,
Prentice Hall, Singapore.
47.
Kelly
,
S. G.
,
2012
,
Mechanical Vibrations: Theory and Applications
,
Cengage Learning
,
Stamford, CT
.
48.
Mathis
,
A. T.
, and
Quinn
,
D. D.
,
2017
, “
Analysis of Systems With Generalized Light Damping Through Method of Multiple-Scales With Emphasis on Mode-Coupling
,”
ASME
Paper No. DETC2017-67917.https://www.asme.org/wwwasmeorg/media/resourcefiles/events/fpmc/asme_idetc-cie_program17.pdf
49.
Lang
,
G. F.
,
2012
, “
Matrix Madness and Complex Confusion: A Review of Complex Modes From Multiple Viewpoints
,”
J. Sound Vib.
,
46
(
11
), pp.
8
12
.https://www.researchgate.net/publication/287229711_Matrix_Madness_and_Complex_Confusion_A_Review_of_Complex_Modes_from_Multiple_Viewpoints
50.
Rosatello, M., Cooper, S.
,
M.
,
Johnson
,
K.
,
Mathis
,
A. T.
,
Brake
,
M. R. W.
,
Allen
,
M. S.
,
Ferri
,
A.
,
Roettgen
,
A. D.
,
Pacini
,
B. R.
, and
Mayes
,
R. L.
,
2017
, “
Effect of Far-Field Structure on Joint Properties
,”
Proceedings of IMAC–XXXV: A Conference and Exposition on Structural Dynamics
, Garden Grove, CA, Jan. 30–Feb. 2.10.1007/978-3-319-54930-9_7
51.
Phani
,
A. S.
, and
Woodhouse
,
J.
,
2007
, “
Viscous Damping Identification in Linear Vibration
,”
J. Sound Vib.
,
303
(
3–5
), pp.
475
500
.10.1016/j.jsv.2006.12.031
52.
Park
,
S. W.
,
2001
, “
Analytical Modeling of Viscoelastic Dampers for Structural and Vibration Control
,”
Int. J. Solids Struct.
,
38
(
44–45
), pp.
8065
8092
.10.1016/S0020-7683(01)00026-9
53.
Prandina
,
M.
,
Mottershead
,
J.
, and
Bonisoli
,
E.
,
2009
, “
An Assessment of Damping Identification Methods
,”
J. Sound Vib.
,
323
(
3–5
), pp.
662
676
.10.1016/j.jsv.2009.01.022
54.
Arora
,
V.
,
2014
, “
Structural Damping Identification Method Using Normal FRFs
,”
Int. J. Solids Struct.
,
51
(
1
), pp.
133
143
.10.1016/j.ijsolstr.2013.09.017
55.
Arruda
,
J. R. F.
, and
Santos
,
J. M. C.
,
1993
, “
Mechanical Joint Parameter Estimation Using Frequency Response Function and Component Mode Synthesis
,”
Mech. Syst. Signal Process.
,
7
(
6
), pp.
493
508
.10.1006/mssp.1993.1029
56.
Hammami
,
C.
,
Balmes
,
E.
, and
Guskov
,
M.
,
2016
, “
Numerical Design and Test on an Assembled Structure of a Bolted Joint With Viscoelastic Damping
,”
Mech. Syst. Signal Process.
,
70-71
, pp.
714
724
.10.1016/j.ymssp.2015.06.031
57.
Hong
,
S. W.
, and
Lee
,
C. W.
,
1991
, “
Identification of Linearized Joint Structural Parameter by Combined Use of Measured and Computed Frequency Responses
,”
Mech. Syst. Signal Process.
,
5
(
4
), pp.
267
277
.10.1016/0888-3270(91)90028-4
58.
Kim
,
T. R.
,
Wu
,
S. M.
, and
Eman
,
K. F.
,
1989
, “
Identification of Joint Parameters for a Taper Joint
,”
ASME J. Eng. Ind.
,
111
(
3
), pp.
282
287
.10.1115/1.3188760
59.
Kim
,
T. R.
,
Ehmann
,
K. F.
, and
Wu
,
S. M.
,
1991a
, “
Identification of Joint Structural Parameter Between Substructures
,”
ASME J. Eng. Ind.
,
113
(
4
), pp.
419
424
.10.1115/1.2899716
60.
Lee
,
D. H.
, and
Hwang
,
W. S.
,
2007
, “
An Identification Method for Joint Structural Parameters Using an FRF-Based Substructuring Method and an Optimization Technique
,”
J. Mech. Sci. Technol.
,
21
(
12
), pp.
2011
2022
.10.1007/BF03177459
61.
Zbiciak
,
A.
, and
Kozyra
,
Z.
,
2015
, “
Dynamic Analysis of a Soft-Contact Problem Using Viscoelastic and Fractional-Elastic Rheological Models
,”
Arch. Civ. Mech. Eng.
,
15
(
1
), pp.
286
291
.10.1016/j.acme.2014.03.002
62.
Petrone
,
F.
,
Lacagnina
,
M.
, and
Scionti
,
M.
,
2004
, “
Dynamic Characterization of Elastomers and Identification With Rheological Models
,”
J. Sound Vib.
,
271
(
1–2
), pp.
339
363
.10.1016/j.jsv.2003.02.001
63.
Komperod
,
M.
,
2015
, “
The Kelvin–Voigt Model's Suitability to Explain the Viscoelastic Properties of Anticorrosion Bitumen at Large Shear Strain in Subsea Cables and Umbilicals
,”
Proceedings of the 56th Conference on Simulation and Modelling
, Linkoping University, Sweeden, Oct.
7
9
.10.3384/ecp15119319
64.
Kaliske
,
M.
, and
Rothert
,
H.
,
1997
, “
Formulation and Implementation of Three-Dimensional Viscoelasticity at Small and Finite Strains
,”
Comput. Mech.
,
19
(
3
), pp.
228
239
.10.1007/s004660050171
65.
Mainardi
,
F.
, and
Spada
,
G.
,
2011
, “
Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology
,”
Eur. Phys. J. Spec. Top.
,
193
(
1
), pp.
133
160
.10.1140/epjst/e2011-01387-1
66.
Adhikari
,
S.
,
2014
,
Structural Dynamic Analysis With Generalized Damping Models: Analysis
,
Wiley
,
Hoboken, NJ
.
67.
Lakes
,
R.
,
2009
,
Viscoelastic Materials
,
Cambridge University Press
,
New York
.
68.
Woodhouse
,
J.
,
1998
, “
Linear Damping Models for Structural Vibration
,”
J. Sound Vib.
,
215
(
3
), pp.
547
569
.10.1006/jsvi.1998.1709
69.
de Lima
,
A. M. G.
,
Rade
,
D. A.
, and
Lépore Neto
,
F. P.
,
2009
, “
An Efficient Modeling Methodology of Structural Systems Containing Viscoelastic Dampers Based on Frequency Response Function Substructuring
,”
Mech. Syst. Signal Process.
,
23
(
4
), pp.
1272
1281
.10.1016/j.ymssp.2008.09.005
70.
Rouleau
,
L.
,
Deu
,
J. F.
, and
Legay
,
A.
,
2017
, “
A Comparison of Model Reduction Technique Based on Modal Projections for Structures With Frequency-Dependent Damping
,”
Mech. Syst. Signal Process.
,
90
, pp.
110
125
.10.1016/j.ymssp.2016.12.013
71.
Schwarzl
,
F.
, and
Staverman
,
A. J.
,
1952
, “
Time-Temperature Dependence of Linear Viscoelastic Behavior
,”
J. Appl. Phys.
,
23
(
8
), pp.
838
843
.10.1063/1.1702316
72.
Williams
,
M. L.
,
Landel
,
R. F.
, and
Ferry
,
J. D.
,
1955
, “
The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids
,”
J. Am. Chem. Soc.
,
77
(
14
), pp.
3701
3707
.10.1021/ja01619a008
73.
Duhem
,
P.
,
1897
, “
Die Dauernden Aenderungen Und Die Thermodynamik
,”
Z. Phys. Chem.
,
24 U
(
1
), p. 666.10.1515/zpch-1897-2436
74.
Padthe
,
A. K.
,
Drincic
,
B.
,
Oh
,
J.
,
Rizos
,
D. D.
,
Fassois
,
S. D.
, and
Bernstein
,
D. S.
,
2008
, “
Duhem Modeling of Friction-Induced Hysteresis
,”
IEEE Control Mag.
,
28
(
5
), pp.
90
107
.10.1109/MCS.2008.927331
75.
Oh
,
J.
, and
Bernstein
,
D. S.
,
2005
, “
Semilinear Duhem Model for Rate-Independent and Rate-Dependent Hysteresis
,”
IEEE Trans. Autom. Control
,
50
(
5
), pp.
631
645
.10.1109/TAC.2005.847035
76.
Naser
,
M. F. M.
,
2013
, “
Characterization of the Hysteresis Duhem Model
,”
Fifth IFAC International Workshop on Periodic Control Systems, the International Federation of Automatic Control
,
Caen, France
, July 3–5, pp.
29
34
.https://core.ac.uk/download/pdf/41773145.pdf
77.
Ikhouane
,
F.
,
2013
, “
Characterization of Hysteresis Processes
,”
Math. Control Signals Syst.
,
25
(
3
), pp.
291
310
.10.1007/s00498-012-0099-6
78.
Jayawardhana
,
B.
,
Ouyang
,
R.
, and
Andrieu
,
V.
,
2012
, “
Stability of Systems With the Duhem Hysteresis Operator: The Dissipativity Approach
,”
Automatica
,
48
(
10
), pp.
2657
2662
.10.1016/j.automatica.2012.06.069
79.
Ouyang
,
R.
,
Andrieu
,
V.
, and
Jayawardhana
,
B.
,
2013
, “
On the Characterization of the Duhem Hysteresis Operator With Clockwise Input–Output Dynamics
,”
Syst. Control Lett.
,
62
(
3
), pp.
286
293
.10.1016/j.sysconle.2012.11.022
80.
Ouyang
,
R.
, and
Jayawardhana
,
B.
,
2014
, “
Absolute Stability Analysis of Linear Systems With Duhem Hysteresis Operator
,”
Automatica
,
50
(
7
), pp.
1860
1866
.10.1016/j.automatica.2014.04.028
81.
Bouc
,
R.
,
1971
, “
Modle Mathmatique D'hystrsis
,”
Acoustica
,
24
(
1
), pp.
16
25
.
82.
Leine
,
R.
, and
Nijmeijer
,
H.
,
2014
,
Dynamics and Bifurcations of Non-Smooth Mechanical Systems (Lecture Notes in Applied and Computational Mechanics)
,
Springer
,
Berlin
.
83.
Wen
,
Y. K.
,
1976
, “
Method for Random Vibration of Hysteretic Systems
,”
J. Eng. Mech. Div.
,
102
(
2
), pp.
249
263
.https://cedb.asce.org/CEDBsearch/record.jsp?dockey=0006630
84.
Charalampakis
,
A. E.
, and
Koumousis
,
V. K.
,
2008
, “
On the Response and Dissipated Energy of Bouc–Wen Hysteretic Model
,”
J. Sound Vib.
,
309
(
3–5
), pp.
887
895
.10.1016/j.jsv.2007.07.080
85.
Ismail
,
M.
,
Ikhouane
,
F.
, and
Rodellar
,
J.
,
2009
, “
The Hysteresis Bouc–Wen Model, a Survey
,”
Arch. Comput. Methods Eng.
,
16
(
2
), pp.
161
188
.10.1007/s11831-009-9031-8
86.
Ikhouane
,
F.
,
Manosa
,
V.
, and
Rodellar
,
J.
,
2007
, “
Dynamic Properties of the Hysteretic Bouc–Wen Model
,”
Syst. Control Lett.
,
56
(
3
), pp.
197
205
.10.1016/j.sysconle.2006.09.001
87.
Zhu
,
X.
, and
Lu
,
X.
,
2011
, “
Parametric Identification of Bouc–Wen Model and Its Application in Mild Steel Damper Modeling
,”
Procedia Eng.
,
14
, pp.
318
324
.10.1016/j.proeng.2011.07.039
88.
Esfahani
,
A. F.
,
Dreesen
,
P.
,
Tiels
,
K.
,
Noel
,
J.
, and
Schoukens
,
J.
,
2018
, “
Parameter Reduction in Nonlinear State-Space Identification of Hysteresis
,”
Mech. Syst. Signal Process.
,
104
, pp.
884
895
.10.1016/j.ymssp.2017.10.017
89.
Ha
,
J.
,
Fung
,
R.
, and
Han
,
C.
,
2005
, “
Optimization of an Impact Drive Mechanism Based on Real-Coded Genetic Algorithm
,”
Sens. Actuators A
,
121
(
2
), pp.
488
493
.10.1016/j.sna.2005.03.001
90.
Pivovarov
,
I.
, and
Vinogradov
,
O. G.
,
1987
, “
One Application of Bouc's Model for Non-Linear Hysteresis
,”
J. Sound Vib.
,
118
(
2
), pp.
209
216
.10.1016/0022-460X(87)90521-9
91.
Sireteanu
,
T.
,
Giuclea
,
M.
, and
Mitu
,
A. M.
,
2010
, “
Identification of an Extended Bouc–Wen Model With Application to Seismic Protection Through Hysteretic Devices
,”
Comput. Mech.
,
45
(
5
), pp.
431
441
.10.1007/s00466-009-0451-y
92.
Ortiz
,
G. A.
,
Alvarez
,
D. A.
, and
Bedoya-Ruíz
,
D.
,
2015
, “
Identification of Bouc–Wen Type Models Using the Transitional Markov Chain Monte Carlo Method
,”
Comput. Struct.
,
146
, pp.
252
269
.10.1016/j.compstruc.2014.10.012
93.
Noel
,
J. P.
,
Esfahani
,
A. F.
,
Kerschen
,
G.
, and
Schoukens
,
J.
,
2017
, “
A Nonlinear State-Space Approach to Hysteresis Identification
,”
Mech. Syst. Signal Process.
,
84
(
Part B
), pp.
171
184
.10.1016/j.ymssp.2016.08.025
94.
Kyprianou
,
A.
,
Worden
,
K.
, and
Panet
,
M.
,
2001
, “
Identification of Hysteretic Systems Using the Differential Evolution Algorithm
,”
J. Sound Vib.
,
248
(
2
), pp.
289
314
.10.1006/jsvi.2001.3798
95.
Ni
,
Y. Q.
,
Ko
,
J. M.
, and
Wong
,
C. W.
,
1998
, “
Identification of Non-Linear Hysteretic Isolators From Periodic Vibration Tests
,”
J. Sound Vib.
,
217
(
4
), pp.
737
756
.10.1006/jsvi.1998.1804
96.
Zaman
,
M. A.
, and
Sikder
,
U.
,
2015
, “
Bouc–Wen Hysteresis Model Identification Using Modified Firefly Algorithm
,”
J. Magn. Magn. Mater.
,
395
, pp.
229
233
.10.1016/j.jmmm.2015.07.080
97.
Oldfield
,
M.
,
Ouyang
,
H.
, and
Mottershead
,
J. E.
,
2005
, “
Simplified Models of Bolted Joints Under Harmonic Loading
,”
Comput. Struct.
,
84
(
1–2
), pp.
25
33
.10.1016/j.compstruc.2005.09.007
98.
Charalampakis
,
A. E.
, and
Dimou
,
C. K.
,
2010
, “
Identification of Bouc–Wen Hysteretic Systems Using Particle Swarm Optimization
,”
Comput. Struct.
,
88
(
21–22
), pp.
1197
1205
.10.1016/j.compstruc.2010.06.009
99.
Charalampakis
,
A. E.
, and
Koumousis
,
V. K.
,
2008
, “
Identification of Bouc–Wen Hysteretic Systems by a Hybrid Evolutionary Algorithm
,”
J. Sound Vib.
,
314
(
3–5
), pp.
571
585
.10.1016/j.jsv.2008.01.018
100.
Wong
,
C. W.
,
Ni
,
Y. Q.
, and
Ko
,
J. M.
,
1994
, “
Steady-State Oscillation of Hysteretic Differential Model—II: Performance Analysis
,”
J. Eng. Mech.
,
120
(
11
), pp.
2299
2325
.10.1061/(ASCE)0733-9399(1994)120:11(2299)
101.
Charalampakis
,
A. E.
, and
Koumousis
,
V. K.
,
2009
, “
A Bouc–Wen Model Compatible With Plasticity Postulates
,”
J. Sound Vib.
,
322
(
4–5
), pp.
954
968
.10.1016/j.jsv.2008.11.017
102.
Biswas
,
S.
, and
Chatterjee
,
A.
,
2014
, “
A Reduced-Order Model From High-Dimensional Frictional Hysteresis
,”
Proc. R. Soc. A
,
470
(
2166
), p.
20130817
.10.1098/rspa.2013.0817
103.
Biswas
,
S.
, and
Chatterjee
,
A.
,
2015
, “
A Two-State Hysteresis Model From High-Dimensional Friction
,”
R. Soc. Open Sci.
,
2
(
7
), p.
150188
.10.1098/rsos.150188
104.
Baber
,
T. T.
, and
Wen
,
Y. K.
,
1984
, “
Random Vibration of Hysteretic Degrading Systems
,”
J. Eng. Mech.
,
110
(
7
), pp.
1036
1087
.10.1061/(ASCE)0733-9399(1984)110:7(1036)
105.
Ma
,
F.
,
Zhang
,
H.
,
Bockstedte
,
A.
,
Foliente
,
G. C.
, and
Paevere
,
P.
,
2004
, “
Parameter Analysis of the Differential Model of Hysteresis
,”
ASME J. Appl. Mech.
,
71
(
3
), pp.
342
349
.10.1115/1.1668082
106.
Park
,
Y. J.
,
Wen
,
Y. K.
, and
Ang
,
A. H.-S.
,
1986
, “
Random Vibration of Hysteretic Systems Under bi-Directional Ground Motions
,”
Earthquake Eng. Struct. Dyn.
,
14
(
4
), pp.
543
557
.10.1002/eqe.4290140405
107.
Wang
,
C.
, and
Wen
,
Y.
,
2000
, “
Evaluation of Pre-Northridge Low-Rise Steel Buildings
,”
J. Struct. Eng.
,
126
(
10
), pp.
1160
1168
.10.1061/(ASCE)0733-9445(2000)126:10(1160)
108.
Harvey
,
P. S.
, Jr.
, and
Gavin
,
H. P.
,
2014
, “
Truly Isotropic Biaxial Hysteresis With Arbitrary Knee Sharpness
,”
Earthquake Eng. Struct. Dyn.
,
43
(
13
), pp.
2051
2057
.10.1002/eqe.2436
109.
Baber
,
T. T.
, and
Noori
,
M. N.
,
1986
, “
Modeling General Hysteresis Behavior and Random Vibration Application
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
108
(
4
), pp.
411
420
.10.1115/1.3269364
110.
Song
,
J.
, and
Der Kiureghian
,
A.
,
2006
, “
Generalized Bouc–Wen Model for Highly Asymmetric Hysteresis
,”
ASCE J. Eng. Mech.
,
132
(
6
), pp.
610
618
.10.1061/(ASCE)0733-9399(2006)132:6(610)
111.
Ramrakhyani
,
D. S.
,
Lesieutre
,
G. A.
, and
Smith
,
E. C.
,
2004
, “
Modeling of Elastomeric Materials Using Nonlinear Fractional Derivative and Continuously Yielding Friction Elements
,”
Int. J. Solids Struct.
,
41
(
14
), pp.
3929
3948
.10.1016/j.ijsolstr.2004.02.034
112.
Guo
,
K.
,
Zhang
,
X.
,
Li
,
H.
,
Hua
,
H.
, and
Meng
,
G.
,
2008
, “
A New Dynamical Friction Model
,”
Int. J. Mod. Phys. B
,
22
(
08
), pp.
967
980
.10.1142/S0217979208039010
113.
Nowell
,
D.
,
Dini
,
D.
, and
Hills
,
D. A.
,
2006
, “
Recent Developments in the Understanding of Fretting Fatigue
,”
Eng. Fract. Mech.
,
73
(
2
), pp.
207
222
.10.1016/j.engfracmech.2005.01.013
114.
Iwan
,
W. D.
,
1966
, “
A Distributed-Element Model for Hysteresis and Its Steady-State Dynamic Response
,”
ASME J. Appl. Mech.
,
33
(
4
), pp.
893
900
.10.1115/1.3625199
115.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1987
, “
An Elastic-Plastic Model for the Contact of Rough Surfaces
,”
ASME J. Tribol.
,
109
(
2
), pp.
257
263
.10.1115/1.3261348
116.
Mulvihill
,
D. M.
,
Kartal
,
M. E.
,
Nowell
,
D.
, and
Hills
,
D. A.
,
2011
, “
An Elastic-Plastic Asperity Interaction Model for Sliding Friction
,”
Tribol. Int.
,
44
(
12
), pp.
1679
1694
.10.1016/j.triboint.2011.06.018
117.
Akay
,
A.
,
2015
, “
Research Need & Open Questions in Vibration Energy Transport & Dissipation
,” National Science Foundation, Arlington, VA, Report.
118.
Cherng
,
R. H.
, and
Wen
,
Y. K.
,
1991
, “
Stochastic Finite Element Analysis of Non-Linear Plane Trusses
,”
Int. J. Non-Linear Mech.
,
26
(
6
), pp.
835
849
.10.1016/0020-7462(91)90035-R
119.
Triantafyllou
,
S. P.
, and
Koumousis
,
V. K.
,
2012
, “
Bouc–Wen Type Hysteretic Plane Stress Element
,”
J. Eng. Mech.
,
138
(
3
), pp.
235
246
.10.1061/(ASCE)EM.1943-7889.0000332
120.
Mayergoyz
,
I. D.
,
2003
,
Mathematical Models of Hysteresis and Their Applications
,
Elsevier, New York.
121.
Na
,
J.
,
Chen
,
Q.
, and
Ren
,
X.
,
2018
,
Adaptive Identification and Control of Uncertain Systems With Non-Smooth Dynamics
,
Academic Press
, London.
122.
Segalman
,
D. J.
, and
Starr
,
M. J.
,
2004
, “
Relationships Among Certain Joint Constitutive Models
,”
Sandia National Laboratories
,
Albuquerque, NM
, Report No.
SAND2004–4321
.https://www.osti.gov/biblio/919196
123.
Visintin
,
A.
,
2006
, “
Mathematical Models of Hysteresis
,”
The Science of Hysteresis
, Vol.
1
,
I.
Mayergoyz
, and
G.
Bertotti
, eds.,
Elsevier
, New York, pp.
1
123
.
124.
Rakotondrabe
,
M.
,
2012
, “
Classical Prandtl–Ishlinskiĭ Modeling and Inverse Multiplicative Structure to Compensate Hysteresis in Piezoactuators
,”
2012 American Control Conference
,
Montreal, QC, Canada
, June 27–29, pp.
1646
1651
.https://hal.archives-ouvertes.fr/hal-00799726/document
125.
Jenkins
,
G. M.
,
1962
, “
Analysis of the Stress-Strain Relationships in Reactor Grade Graphite
,”
Br. J. Appl. Phys.
,
13
(
1
), pp.
30
32
.10.1088/0508-3443/13/1/307
126.
Song
,
Y.
,
Hartwigsen
,
C. J.
,
McFarland
,
D. M.
,
Vakakis
,
A. F.
, and
Bergman
,
L. A.
,
2004
, “
Simulation of Dynamics of Beam Structures With Bolted Joints Using Adjusted Iwan Beam Elements
,”
J. Sound Vib.
,
273
(
1–2
), pp.
249
276
.10.1016/S0022-460X(03)00499-1
127.
Al Janaideh
,
M.
,
Mao
,
J.
,
Rakheja
,
S.
,
Xie
,
W.
, and
Su
,
C.
,
2008
, “
Generalized Prandtl–Ishlinskiĭ Hysteresis Model: Hysteresis Modeling and Its Inverse for Compensation in Smart Actuators
,”
Proceedings of the 47th IEEE Conference on Decision and Control
, Cancun, Mexico, Dec. 9–11, pp.
5182
5187
.10.1109/CDC.2008.4739202
128.
Wang
,
D.
,
Dong
,
Z.
,
Jiao
,
N.
,
Yuan
,
S.
,
Zhou
,
L.
, and
Li
,
W. J.
,
2011
, “
An Asymmetric PI Hysteresis Model for Piezoceramics in Nanoscale AFM Imaging
,”
Proceedings of the Sixth IEEE International Conference on Nano/Micro Engineered and Molecular Systems
,
Kaohsiung, Taiwan
, Feb. 20–23, pp.
1075
1079
.10.1109/NEMS.2011.6017543
129.
Aljanaideh
,
O.
,
Habineza
,
D.
,
Rakotondrabe
,
M.
, and Al
Janaideh
,
M.
,
2016
, “
Experimental Comparison of Rate-Dependent Hysteresis Models in Characterizing and Compensating Hysteresis of Piezoelectric Tube Actuators
,”
Phys. B
,
486
, pp.
64
68
.10.1016/j.physb.2015.10.021
130.
Al
Janaideh
, M., Su,
C.-Y.
, and
Rakehja, S.
,
2008
, “
Modeling Hysteresis of Smart Actuators
,” Proceeding of the Fifth International Symposium on Mechatronics and Its Applications (
ISM08
),
Amman, Jordan
, May 27–29, pp.
1
4
.10.1109/ISMA.2008.4648805
131.
Jiang
,
H.
,
Ji
,
H.
,
Qiu
,
J. H.
, and
Chen
,
Y.
,
2010
, “
A Modified Prandtl–Ishlinskiĭ Model for Modeling Asymmetric Hysteresis of Piezoelectric Actuators
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
,
57
(
5
), pp.
1200
1210
.10.1109/TUFFC.2010.1533
132.
Al Janaideh
,
M.
,
Davino
,
D. D.
,
Krejci
,
P.
, and
Visone
,
C.
,
2016
, “
Comparison of Prandtl–Ishlinskiĭ and Preisach Modeling for Smart Devices Applications
,”
Phys. B
, 486, pp.
155
159
.https://www.infona.pl/resource/bwmeta1.element.elsevier-07a7e5d9-16d5-3bee-bc13-3a2dcedd2e88
133.
Al Janaideh
,
M.
, and
Aljanaideh
,
O.
,
2018
, “
Further Results on Open-Loop Compensation of Rate-Dependent Hysteresis in a Magnetostrictive Actuator With the Prandtl–Ishlinskiĭ Model
,”
Mech. Syst. Signal Process.
,
104
, pp.
835
850
.10.1016/j.ymssp.2017.09.004
134.
Al Janaideh
,
M.
,
Naldi
,
R.
,
Marconi
,
L.
, and
Krejci
,
P.
,
2013
, “
A Hybrid Model for the Play Hysteresis Operator
,”
Phys. B
,
430
, pp.
95
98
.10.1016/j.physb.2013.07.002
135.
Krejci
,
P.
, and
Kuhnen
,
K.
,
2001
, “
Inverse Control of Systems With Hysteresis and Creep
,”
IEEE Proc. Control Theory Appl.
,
148
(
3
), pp.
185
192
.10.1049/ip-cta:20010375
136.
Ko
,
Y.
,
Hwang
,
Y.
,
Chae
,
M.
, and
Kim
,
T.
,
2017
, “
Direct Identification of Generalized Prandtl–Ishlinskiĭ Model Inversion for Asymmetric Hysteresis Compensation
,”
ISA Trans.
,
70
, pp.
209
218
.10.1016/j.isatra.2017.07.004
137.
Masing
,
G.
,
1926
, “
Eigenspannungen Und Vertfestigung Beim Messing
,”
Proceedings of the Second International Congress of Applied Mechanics,
Zurich, Switzerland
, Sept. 12–17, pp.
332
335
.https://www.semanticscholar.org/paper/Eigenspannungen-und-Verfestigung-beim-Messing-Masing/6c9ee1bf62309dbe9d14b26ef62d87a895f07761
138.
Awrejcewicz
,
J.
,
Dzyubak
,
L.
, and
Lamarque
,
C.-H.
,
2008
, “
Modelling of Hysteresis Using Masing–Bouc–Wen's Framework and Search of Conditions for the Chaotic Responses
,”
Commun. Nonlinear Sci. Numer. Simul.
,
13
(
5
), pp.
939
958
.10.1016/j.cnsns.2006.09.003
139.
Tjahjowidodo
,
T.
,
Al-Bender
,
F.
,
Van Brussel
,
H.
, and
Symens
,
W.
,
2007
, “
Friction Characterization and Compensation in Electro-Mechanical Systems
,”
J. Sound Vib.
,
308
(
3–5
), pp.
632
646
.10.1016/j.jsv.2007.03.075
140.
Iwan
,
W. D.
,
1967
, “
On a Class of Model for the Yielding Behavior of Continuous Composite Systems
,”
ASME J. Appl. Mech.
,
34
(
3
), pp.
612
617
.10.1115/1.3607751
141.
Bauschinger
,
J.
,
1886
, “
On the Change of the Position of the Elastic Limit of Iron and Steel Under Cyclic Variations of Stress
,”
Mitteilung XV Aus Dem Mechanisch-Technischen Laboratorium Der Kniglichen Technischen Hochschule Mnchen
,
13
(
1
), pp.
1
116
.
142.
Segalman
,
D. J.
, and
Starr
,
M. J.
,
2012
, “
Iwan Models and Their Provenance
,”
ASME Paper No.
DETC2012-71534. 10.1115/DETC2012-71534
143.
Segalman
,
D. J.
,
2001
, “
An Initial Overview of Iwan Modeling for Mechanical Joints
,”
Sandia National Laboratories
,
Albuquerque, NM
, Report No.
SAND2001–0811
.https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2001/010811.pdf
144.
Segalman
,
D. J.
,
2005
, “
A Four-Parameter Iwan Model for Lap-Type Joints
,”
Trans. ASME
,
72
(
5
), pp.
752
760
.10.1115/1.1989354
145.
Brake
,
M. R. W.
,
2017
, “
A Reduced Iwan Model That Includes Pinning for Bolted Joint Mechanics
,”
Nonlinear Dyn.
,
87
(
2
), pp.
1335
1349
.10.1007/s11071-016-3117-2
146.
Dong
,
W.
,
Chao
,
X.
,
Xuanhua
,
F.
, and
Qiang
,
W.
,
2018
, “
Reduced-Order Modeling Approach for Frictional Stick-Slip Behavior of Joint Interface
,”
Mech. Syst. Signal Process.
,
103
, pp.
131
138
.10.1016/j.ymssp.2017.10.001
147.
Eriten
,
M.
,
Kurt
,
M.
,
Luo
,
G.
,
McFarland
,
D. M.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2013
, “
Nonlinear System Identification of Frictional Effects in a Beam With a Bolted Joint Connection
,”
Mech. Syst. Signal Process.
,
39
(
1–2
), pp.
245
264
.10.1016/j.ymssp.2013.03.003
148.
Lacayo
,
R. M.
,
Deaner
,
B. J.
, and
Allen
,
M. S.
,
2017
, “
A Numerical Study on the Limitations of Modal Iwan Models for Impulsive Excitations
,”
J. Sound Vib.
,
390
, pp.
118
140
.10.1016/j.jsv.2016.11.038
149.
Argatov
,
I. I.
, and
Butcher
,
E. A.
,
2011
, “
On the Iwan Models for the Lap-Type Bolted Joints
,”
Int. J. Non-Linear Mech.
,
46
(
2
), pp.
347
356
.10.1016/j.ijnonlinmec.2010.09.018
150.
Moore
,
K. J.
,
Kurt
,
M.
,
Eriten
,
M.
,
Dodson
,
J. C.
,
Foley
,
J. R.
,
Wolfson
,
J. C.
,
McFarland
,
D. M.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2017
, “
Nonlinear Parameter Identification of a Mechanical Interface Based on Primary Wave Scattering
,”
Exp. Mech.
,
57
(
9
), pp.
1495
1508
.10.1007/s11340-017-0320-0
151.
Lacayo
,
R. M.
, and
Allen
,
M. S.
,
2019
, “
Updating Structural Models Containing Nonlinear Iwan Joints Using Quasi-Static Modal Analysis
,”
Mech. Syst. Signal Process.
,
118
, pp.
133
157
.10.1016/j.ymssp.2018.08.034
152.
Balaji
,
N. N.
, and
Brake
,
M. R. W.
,
2019
, “
The Surrogate System Hypothesis for Joint Mechanics
,”
Mech. Syst. Signal Process.
,
126
, pp.
42
64
.10.1016/j.ymssp.2019.02.013
153.
Ahmadian
,
H.
, and
Rajaei
,
M.
,
2014
, “
Identification of Iwan Distribution Density Function in Frictional Contacts
,”
J. Sound Vib.
,
333
(
15
), pp.
3382
3393
.10.1016/j.jsv.2014.03.021
154.
Bonney
,
M. S.
,
Robertson
,
B. A.
,
Mignolet
,
M.
,
Schempp
,
F.
, and
Brake
,
M. R.
,
2016
, “
Experimental Determination of Frictional Interface Models
,”
Dynamics of Coupled Structures
, Vol.
4
, M. A. Allen, R. L.
Mayes,
and D.
Rixen
,
eds.,
Springer International Publishing
,
Berlin
, pp.
473
490
.
155.
Singh
,
B.
, and
Nanda
,
B. K.
,
2013
, “
Investigation Into the Effect of Surface Roughness on the Damping of Tack-Welded Structures Using the Response Surface Methodology Approach
,”
J. Vib. Control
,
19
(
4
), pp.
547
559
.10.1177/1077546311429056
156.
Bonney
,
M. S.
, and
Brake
,
M. R.
,
2014
, “
Utilizing Soize's Approach to Identify Parameter and Model Uncertainties
,”
Sandia National Laboratories
,
Albuquerque, NM
, Report No.
SAND2014–19209
.https://www.researchgate.net/publication/318468915_Utilizing_Soize's_Approach_to_Identify_Parameter_and_Model_Uncertainties
157.
Rajaei
,
M.
, and
Ahmadian
,
H.
,
2014
, “
Development of Generalized Iwan Model to Simulate Frictional Contacts With Variable Normal Loads
,”
Appl. Math. Modell.
,
38
(
15–16
), pp.
4006
4018
.10.1016/j.apm.2014.01.008
158.
Li
,
D.
,
Xu
,
C.
,
Liu
,
T.
,
Gola
,
M. M.
, and
Wen
,
L.
,
2019
, “
A Modified Iwan Model for Micro-Slip in the Context of Dampers for Turbine Blade Dynamics
,”
Mech. Syst. Signal Process.
,
121
, pp.
14
30
.10.1016/j.ymssp.2018.11.002
159.
Segalman
,
D. J.
,
2010
, “
A Modal Approach to Modeling Spatially Distributed Vibration Energy Dissipation
,”
Sandia National Laboratories
,
Albuquerque, NM
, Report No.
SAND2010–4763
.https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2010/104763.pdf
160.
Roettgen
,
D. R.
,
Allen
,
M. S.
,
Osgood
,
D.
,
2014
, “
Feasibility of Describing Joint Nonlinearity in Exhaust Components With Modal Iwan Models
,”
ASME
Paper No. DETC2014–35359.10.1115/DETC2014-35359
161.
Allen
,
M. S.
,
Deaner
,
B. J.
, and
Segalman
,
D. J.
,
2018
, “
Modal Iwan Models for Structures With Bolted Joints
,” M. Brake, ed., Springer, Berlin, pp.
255
278
.10.1007/978-3-319-56818-8_17
162.
Hollkamp
,
J. J.
, and
Gordon
,
R. W.
,
2008
, “
Reduced-Order Models for Nonlinear Response Prediction: Implicit Condensation and Expansion
,”
J. Sound Vib.
,
318
(
4–5
), pp.
1139
1153
.10.1016/j.jsv.2008.04.035
163.
Dahl
,
P. R.
,
1968
, “
A Solid Friction Model
,”
The Aerospace Corporation
,
El Segundo, CA
, Report No.
SAMSO-TR-77-131
.https://apps.dtic.mil/dtic/tr/fulltext/u2/a041920.pdf
164.
Dahl
,
P. R.
,
1976
, “
A Solid Friction Damping of Mechanical Vibrations
,”
AIAA J.
,
14
(
12
), pp.
1675
1682
.10.2514/3.61511
165.
Canudas de Wit
,
C.
,
Olsson
,
H.
,
Astrom
,
K. J.
, and
Lischinsky
,
P.
,
1995
, “
A New Model for Control of Systems With Friction
,”
IEEE Trans. Autom. Control
,
40
(
3
), pp.
419
425
.10.1109/9.376053
166.
Segalman
,
D. J.
, and
Starr
,
M. J.
,
2008
, “
Inversion of Masing Models Via Continuous Iwan Systems
,”
Int. J. Non-Linear Mech.
,
43
(
1
), pp.
74
80
.10.1016/j.ijnonlinmec.2007.10.005
167.
Hutchings
,
I. M.
,
2016
, “
Leonardo da Vinci's Studies of Friction
,”
Wear
,
360–361
, pp.
51
66
.10.1016/j.wear.2016.04.019
168.
Amontons
,
G.
,
1699
, “
De la Resistance Cause'e Dans Les Machines (About Resistance and Force in Machines)
,”
Mem. Aced.
, pp.
257
282
.
169.
Coulomb
,
C. A.
,
1821
,
Theorie Des Machines Simple (Theory of Simple Machines)
,
Bachelier
,
Paris, France
.
170.
Popova
,
E.
, and
Popov
,
V. L.
,
2015
, “
The Research Works of Coulomb and Amontons and Generalized Laws of Friction
,”
Friction
,
3
(
2
), pp.
183
190
.10.1007/s40544-015-0074-6
171.
Starr
,
M. J.
, and
Segalman
,
D. J.
,
2018
, “
Assessment of Coulomb Friction in Modeling Joint Mechanics Via a Parameter Study of Dissipation
,” M. Brake, ed., Springer, Berlin, pp.
223
229
.10.1007/978-3-319-56818-8_15
172.
Stribeck
,
R.
,
1902
, “
Die Wesentlichen Eigenschaften Der Gleit-Und Rollenlager
,”
Z. Des Ver. Dtsch. Ing.
,
46
, pp.
1341
1348
.https://books.google.co.in/books/about/Die_wesentlichen_Eigenschaften_der_Gleit.html?id=nZssnQEACAAJ&redir_esc=y
173.
Armstrong-Hélouvry
,
B.
,
Dupont
,
P.
, and
De Wit
,
C. C.
,
1994
, “
A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction
,”
Automatica
,
30
(
7
), pp.
1083
1138
.10.1016/0005-1098(94)90209-7
174.
Filippov
,
A. F.
,
1967
, “
Classical Solutions of Differential Equations With Multi-Valued Right-Hand Side
,”
SIAM J. Control
,
5
(
4
), pp.
609
621
.10.1137/0305040
175.
Arscott
,
F. M.
, and
Filippov
,
A. F.
,
1988
,
Differential Equations With Discontinuous Righthand Sides: Control Systems (Mathematics and Its Applications)
,
Springer
,
Dordrecht, The Netherlands
.
176.
Quinn
,
D. D.
,
2004
, “
A New Regularization of Coulomb Friction
,”
ASME J. Vib. Acoust.
,
126
(
3
), pp.
391
397
.10.1115/1.1760564
177.
Armstrong-Hélouvry
,
B.
,
1991
,
Control of Machines With Friction, Volume 128 of the Springer International Series in Engineering and Computer Science
,
Springer
,
New York
.
178.
Zeng
,
H.
, and
Sepehri
,
N.
,
2007
, “
Dynamic Surface Control of Cooperating Hydraulic Manipulators in the Presence of Friction
,”
Proceedings of the American Control Conference
,
New York
, July 9–13, pp.
94
99
.10.1109/ACC.2007.4282713
179.
Freidovich
,
L.
,
Robertsson
,
A.
,
Shiriaev
,
A.
, and
Johansson
,
R.
,
2010
, “
LuGre–Model-Based Friction Compensation
,”
IEEE Trans. Control Syst. Technol.
,
18
(
1
), pp.
194
200
.10.1109/TCST.2008.2010501
180.
Lu
,
L.
,
Yao
,
B.
,
Wang
,
Q.
, and
Chen
,
Z.
,
2009
, “
Adaptive Robust Control of Linear Motors With Dynamic Friction Compensation Using Modified LuGre Model
,”
Automatica
,
45
(
12
), pp.
2890
2896
.10.1016/j.automatica.2009.09.007
181.
Saha
,
A.
,
Wahi
,
P.
,
Wiercigroch
,
M.
, and
Stefański
,
A.
,
2016
, “
A Modified LuGre Friction Model for an Accurate Prediction of Friction Force in the Pure Sliding Regime
,”
Int. J. Non-Linear Mech.
,
80
, pp.
122
131
.10.1016/j.ijnonlinmec.2015.08.013
182.
Rahman
,
R. A.
,
He
,
L.
, and
Sepehri
,
N.
,
2016
, “
Design and Experimental Study of a Dynamic Adaptive Backstepping-Sliding Mode Control Scheme for Position Tracking and Regulating of a Low-Cost Pneumatic Cylinder
,”
Int. J. Robust Nonlinear Control
,
26
(
4
), pp.
853
875
.10.1002/rnc.3341
183.
Piatkowski
,
T.
,
2014
, “
Dahl and LuGre Dynamic Friction Models the Analysis of Selected Properties
,”
Mech. Mach. Theory
,
73
, pp.
91
100
.10.1016/j.mechmachtheory.2013.10.009
184.
Yanada
,
H.
, and
Sekikawa
,
Y.
,
2008
, “
Modeling of Dynamic Behavior of Friction
,”
Mechatronics
,
18
(
7
), pp.
330
339
.10.1016/j.mechatronics.2008.02.002
185.
Ahmed
,
F. S.
,
Laghrouche
,
S.
, and
Harmouche
,
M.
,
2015
, “
Adaptive Backstepping Output Feedback Control of DC Motor Actuator With Friction and Load Uncertainty Compensation
,”
Int. J. Robust Nonlinear Control
,
25
(
13
), pp.
1967
1992
.10.1002/rnc.3184
186.
Dupont
,
P.
,
Armstrong-Hlouvry
,
B.
, and
Hayward
,
V.
,
2000
, “
Elasto-Plastic Friction Model: Contact Compliance and Stiction
,”
Proceedings of the American Control Conference
,
Chicago, IL
, June 28-30, pp.
1072
1077
.10.1109/ACC.2000.876665
187.
Swevers
,
J.
,
Al-Bender
,
F.
,
Ganseman
,
C. G.
, and
Projogo
,
T.
,
2000
, “
An Integrated Friction Model Structure With Improved Presliding Behavior for Accurate Friction Compensation
,”
IEEE Trans. Autom. Control
,
45
(
4
), pp.
675
686
.10.1109/9.847103
188.
Lampaert
,
V.
,
Swevers
,
J.
, and
Al-Bender
,
F.
,
2002
, “
Modification of the Leuven Integrated Friction Model Structure
,”
IEEE Trans. Autom. Control
,
47
(
4
), pp.
683
687
.10.1109/9.995050
189.
Valanis
,
K. C.
,
1970
,
A Theory of Viscoplasticity Without a Yield Surface. Part 1. General Theory
,
Defense Technical Information Center
,
Fort Belvoir, VA
.
190.
Valanis
,
K. C.
,
1978
, “Fundamental Consequences of a New Intrinsic Time Measure. Plasticity as a Limit of the Endochronic Theory,”
Defense Technical Information Center
,
Fort Belvoir, VA
, Report No.
G224-DME-78-001
.https://apps.dtic.mil/dtic/tr/fulltext/u2/a302661.pdf
191.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
,
1995
,
Nonlinear Oscillations
,
Wiley, New York.
192.
Lacarbonara
,
W.
, and
Vestroni
,
F.
,
2003
, “
Nonclassical Response of Oscillators With Hysteresis
,”
Nonlinear Dyn.
,
32
(
3
), pp.
235
258
.10.1023/A:1024423626386
193.
Casalotti
,
A.
, and
Lacarbonara
,
W.
,
2017
, “
Tailoring of Pinched Hysteresis for Nonlinear Vibration Absorption Via Asymptotic Analysis
,”
Int. J. Non-Linear Mech.
,
94
, pp.
59
71
.10.1016/j.ijnonlinmec.2017.02.015
194.
Feldman
,
M.
,
1994
, “
Non-Linear System Vibration Analysis Using Hilbert Transform – i. free Vibration Analysis Method ‘Freevib
,”
Mech. Syst. Signal Process.
,
8
(
2
), pp.
119
127
.10.1006/mssp.1994.1011
195.
Noël
,
J. P.
, and
Kerschen
,
G.
,
2017
, “
Nonlinear System Identification in Structural Dynamics: 10 More Years of Progress
,”
Mech. Syst. Signal Process.
,
83
, pp.
2
35
.10.1016/j.ymssp.2016.07.020
196.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2003
, “
Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks
,”
ASME J. Turbomach.
,
125
(
2
), pp.
364
371
.10.1115/1.1539868
197.
Krack
,
M.
,
Salles
,
L.
, and
Thouverez
,
F.
,
2017
, “
Vibration Prediction of Bladed Disks Coupled by Friction Joints
,”
Arch. Comput. Methods Eng.
,
24
(
3
), pp.
589
636
.10.1007/s11831-016-9183-2
198.
Pesaresi
,
L.
,
Armand
,
J.
,
Schwingshackl
,
C. W.
,
Salles
,
L.
, and
Wong
,
C.
,
2018
, “
An Advanced Underplatform Damper Modelling Approach Based on a Microslip Contact Model
,”
J. Sound Vib.
,
436
, pp.
327
340
.10.1016/j.jsv.2018.08.014
199.
Gustafson
,
P. A.
, and
Waas
,
A. M.
,
2009
, “
The Influence of Adhesive Constitutive Parameters in Cohesive Zone Finite Element Models of Adhesively Bonded Joints
,”
Int. J. Solids Struct.
,
46
(
10
), pp.
2201
2215
.10.1016/j.ijsolstr.2008.11.016
200.
Allen
,
M. S.
,
Lacayo
,
R. M.
, and
Brake
,
M. R.
,
2016
, “
Quasi-Static Modal Analysis Based on Implicit Condensation for Structures With Nonlinear Joints
,”
ISMA 2016, International Conference on Noise and Vibration Engineering,
Leuven, Belgium
, Sept. 7–9, pp.
731
746
.
201.
Ascher
,
U. M.
, and
Petzold
,
L. R.
,
1998
,
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
, Vol.
61
,
SIAM, Philadelphia
, PA.
202.
Xiong
,
X.
,
Kikuuwe
,
R.
, and
Yamamoto
,
M.
,
2013
, “
A Differential Algebraic Method to Approximate Nonsmooth Mechanical Systems by Ordinary Differential Equations
,”
J. Appl. Math.
,
2013
, pp.
1
13
.10.1155/2013/320276
203.
Urabe
,
M.
, and
Reiter
,
A.
,
1966
, “
Numerical Computation of Nonlinear Forced Oscillations by Galerkin's Procedure
,”
J. Math. Anal. Appl.
,
14
(
1
), pp.
107
140
.10.1016/0022-247X(66)90066-7
204.
Festjens
,
H.
,
Chevallier
,
G.
, and
Dion
,
J.-L.
,
2013
, “
A Numerical Tool for the Design of Assembled Structures Under Dynamic Loads
,”
Int. J. Mech. Sci.
,
75
, pp.
170
177
.10.1016/j.ijmecsci.2013.06.013
205.
Siewert
,
C.
,
Panning
,
L.
,
Wallaschek
,
J.
, and
Richter
,
C.
,
2010
, “
Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces
,”
ASME J. Eng. Gas Turbines Power
,
132
(
8
), p.
082501
.10.1115/1.4000266
206.
Ewins
,
D. J.
,
2018
, “
A Survey of Contact Hysteresis Measurement Techniques
,” M. Brake, ed., Springer, Berlin, pp.
149
179
.10.1007/978-3-319-56818-8_12
207.
Gola
,
M. M.
, and
Gastaldi
,
C.
,
2018
, “
Under-Platform Damper Measurements at Politecnico di Torino
,” M. Brake, ed., Springer, Berlin, pp.
181
204
.10.1007/978-3-319-56818-8_13
208.
Peter
,
S.
,
Scheel
,
M.
,
Krack
,
M.
, and
Leine
,
R. I.
,
2018
, “
Synthesis of Nonlinear Frequency Responses With Experimentally Extracted Nonlinear Modes
,”
Mech. Syst. Signal Process.
,
101
, pp.
498
515
.10.1016/j.ymssp.2017.09.014
209.
Scheel
,
M.
,
Kleyman
,
G.
,
Tatar
,
A.
,
Brake
,
M. R. W.
,
Peter
,
S.
,
Nol
,
J.-P.
,
Allen
,
M. S.
, and
Krack
,
M.
,
2019
, “
System Identification of Jointed Structures: Nonlinear Modal Testing vs. State-Space Model Identification
,”
Nonlinear Dynamics
, Vol.
1
,
K.
Gaetan
, ed.,
Springer International Publishing
,
Berlin
, pp.
159
161
.10.1007/978-3-319-74280-9_15
210.
Kerschen
,
G.
,
Peeters
,
M.
,
Golinval
,
J. C.
, and
Vakakis
,
A. F.
,
2009
, “
Nonlinear Normal Modes—Part I: A Useful Framework for the Structural Dynamicist
,”
Mech. Syst. Signal Process.
,
23
(
1
), pp.
170
194
.10.1016/j.ymssp.2008.04.002
211.
Szalai
,
R.
,
Ehrhardt
,
D.
, and
Haller
,
G.
,
2017
, “
Nonlinear Model Identification and Spectral Submanifolds for Multi-Degree-of-Freedom Mechanical Vibrations
,”
Proc. R. Soc. A
,
473
(
2202
), p.
20160759
.10.1098/rspa.2016.0759
212.
Moore
,
K. J.
,
Kurt
,
M.
,
Eriten
,
M.
,
McFarland
,
D. M.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2018
, “
Wavelet-Bounded Empirical Mode Decomposition for Measured Time Series Analysis
,”
Mech. Syst. Signal Process.
,
99
, pp.
14
29
.10.1016/j.ymssp.2017.06.005
213.
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
.10.1016/j.ymssp.2005.04.008
214.
Worden
,
K.
, and
Tomlinson
,
G. R.
,
2000
,
Nonlinearity in Structural Dynamics: Detection, Identification and Modelling
,
Taylor & Francis
, London.
You do not currently have access to this content.