Abstract

Starting from a recent classification of the development stages of nonlinear dynamics in mechanics, this review builds on the idea that the level of scientific maturity of the area is now such as to involve a gradual shift of its core interests from the inherent theoretical and practical findings to the application benefits that they can bring to solving dynamic problems in a variety of technological environments. First, an overview of the current state of knowledge and the achievements of the community of relevant scholars in about the last ten years is presented, distinguishing between traditional and emerging themes fully inherent to mechanics, and more hybridized scientific contexts. Then, a “vision” of expected future developments is attempted, by organizing the presentation along some main lines. (i) Identifying modeling, methodological, and computational advancements needed to address challenging, new or updated, research issues, with a view to deepening and further expanding the ranges of theoretical development and practical interest of nonlinear dynamics. (ii) Overviewing directions toward which promoting full exploitation of intrinsic or intentionally added nonlinearities, to the aim of improving and possibly optimizing specific behaviors and general operating conditions of actual systems/structures in a variety of dynamic environments, by also referring to the uncertainty quantification issue. (iii) Pursuing “novel” lines of developments of nonlinear dynamics in a fully hybridized and cross-disciplinary framework, with also possible expectation of new related phenomenologies.

References

1.
Rega
,
G.
,
2020
, “
Nonlinear Dynamics in Mechanics and Engineering: 40 Years of Developments and Ali H. Nayfeh's Legacy
,”
Nonlinear Dyn.
,
99
(
1
), pp.
11
34
.10.1007/s11071-019-04833-w
2.
Shaw
,
S. W.
, and
Balachandran
,
B.
,
2008
, “
A Review of Nonlinear Dynamics of Mechanical Systems in the Year 2008
,”
J. Syst. Des. Dyn.
,
2
(
3
), pp.
611
640
.10.1299/jsdd.2.611
3.
Lacarbonara
,
W.
,
2013
,
Nonlinear Structural Mechanics
,
Springer Science
,
New York
.
4.
Amabili
,
M.
,
2008
,
Nonlinear Vibrations and Stability of Shells and Plates
,
Cambridge University Press
,
New York
.
5.
Younis
,
M. I.
,
2011
,
MEMS Linear and Nonlinear Statics and Dynamics
,
Springer Science
,
New York
.
6.
Wagg
,
D.
, and
Neild
,
S.
,
2015
,
Nonlinear Vibration With Control
,
Springer International Publishing
, Cham, Switzerland.
7.
Awrejcewicz
,
J.
,
Krysko
,
V. A.
,
Papkova
,
I. V.
, and
Krysko
,
A. V.
,
2016
,
Deterministic Chaos in One-Dimensional Continuous Systems
,
World Scientific
,
Singapore
.
8.
Awrejcewicz
,
J.
, and
Krysko
,
V. A.
,
2020
,
Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members
,
Springer Nature
, Cham, Switzerland.
9.
Fey
,
R. H. B.
,
Nijmeijer
,
H.
, and
Shukla
,
A.
,
2011
, “
Editorial: Special Issue on Stability of Non-Linear Dynamic Structures and Systems
,”
Nonlinear Dyn.
,
66
(
3
), pp. 247–250.10.1007/s11071-011-0168-2
10.
Luongo
,
A.
,
2015
, “
Advances in Dynamics, Stability and Control of Mechanical Systems. Preface
,”
Meccanica
,
50
(
3
), pp.
591
594
.10.1007/s11012-014-0089-5
11.
Lenci
,
S.
, and
Luongo
,
A.
,
2016
, “
Dynamics, Stability, and Control of Flexible Structures. Preface
,”
Int. J. Non-Linear Mech.
,
80
, pp. 1–2.10.1016/j.ijnonlinmec.2015.12.001
12.
Mikhlin
,
Y. V.
,
Pellicano
,
F.
, and
Gendelman
,
O. V.
,
2018
, “
Multiscale Mechanics and Physics: New Approaches and Phenomena. Preface
,”
Nonlinear Dyn.
,
93
(
1
), pp.
1
3
.10.1007/s11071-018-4315-x
13.
Awrejcewicz
,
J.
,
Amabili
,
M.
, and
Nabarette
,
A.
,
2021
, “
Modelling and Analysis of Mechanical Systems Dynamics. Preface
,”
Meccanica
,
56
(
4
), pp.
731
733
.10.1007/s11012-021-01321-7
14.
Carillo
,
S.
, and
D'Ambrogio
,
W.
,
2017
, “
New Trends in Dynamics and Stability. Preface
,”
Meccanica
,
52
(
13
), pp.
3011
3014
.10.1007/s11012-017-0744-8
15.
Rega
,
G.
,
Daqaq
,
M. F.
,
Hajj
,
M.
, and
Bajaj
,
A.
,
2020
, “
In Memory of Professor Ali H. Nayfeh
,”
Nonlinear Dyn.
,
99
(
1
), pp. 1–9.10.1007/s11071-019-05422-7
16.
Luongo
,
A.
,
Leamy
,
M. J.
,
Lenci
,
S.
,
Piccardo
,
G.
, and
Touzé
,
C.
,
2021
, “
Advances in Stability, Bifurcations and Nonlinear Vibrations in Mechanical Systems
,”
Nonlinear Dyn.
,
103
(
4
), pp. 2993–2995.10.1007/s11071-021-06404-4
17.
Kapitaniak
,
T.
, and
Kurths
,
J.
,
2014
, “
Synchronized Pendula: From Huygens' Clocks to Chimera States
,”
Eur. Phys. J. Spec. Top.
,
223
(
4
), pp.
609
612
.10.1140/epjst/e2014-02128-8
18.
Wiercigroch
,
M.
, and
Pavlovskaia
,
E.
,
2015
, “
Nonlinear Dynamics in Engineering: Modelling, Analysis and Applications. Preface
,”
Int. J. Non-Linear Mech
,
70
, p.
1
.10.1016/j.ijnonlinmec.2014.12.002
19.
Rosenberg
,
R. M.
,
1962
, “
The Normal Modes of Nonlinear n-Degree-of-Freedom Systems
,”
ASME J. Appl. Mech.
,
29
(
1
), pp.
7
14
.10.1115/1.3636501
20.
Shaw
,
S. W.
, and
Pierre
,
C.
,
1993
, “
Normal Modes for Nonlinear Vibratory Systems
,”
J. Sound Vib.
,
164
(
1
), pp.
85
124
.10.1006/jsvi.1993.1198
21.
Vakakis
,
A. F.
,
Manevitch
,
L. I.
,
Mikhlin
,
Y. V.
,
Pilipchuk
,
V. N.
, and
Zevin
,
A. A.
,
1996
,
Normal Modes and Localization in Nonlinear Systems
,
Wiley
,
New York
.
22.
Mikhlin
,
Y. V.
, and
Avramov
,
K. V.
,
2010
, “
Nonlinear Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments
,”
ASME Appl. Mech. Rev.
,
63
(
6
), p.
060802
.10.1115/1.4003825
23.
Avramov
,
K. V.
, and
Mikhlin
,
Y. V.
,
2013
, “
Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems
,”
ASME Appl. Mech. Rev.
,
65
(
2
), p.
020801
.10.1115/1.4023533
24.
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
25.
Peeters
,
M.
,
Viguié
,
R.
,
Sérandour
,
G.
,
Kerschen
,
G.
, and
Golinval
,
J.-C.
,
2009
, “
Nonlinear Normal Modes, Part II: Toward a Practical Computation Using Numerical Continuation Techniques
,”
Mech. Syst. Signal Process.
,
23
(
1
), pp.
195
216
.10.1016/j.ymssp.2008.04.003
26.
Renson
,
L.
,
Kerschen
,
G.
, and
Cochelin
,
B.
,
2016
, “
Numerical Computation of Nonlinear Normal Modes in Mechanical Engineering
,”
J. Sound Vib.
,
364
, pp.
177
206
.10.1016/j.jsv.2015.09.033
27.
Rega
,
G.
, and
Troger
,
H.
,
2005
, “
Dimension Reduction of Dynamical Systems: Methods, Models, Applications
,”
Nonlinear Dyn.
,
41
(
1–3
), pp.
1
15
.10.1007/s11071-005-2790-3
28.
Mazzilli
,
C. E.
,
Gonçalves
,
P. B.
, and
Franzini
,
G. R.
,
2022
, “
Reduced-Order Modelling Based on Non-Linear Modes
,”
Int. J. Mech. Sci.
,
214
, p.
106915
.10.1016/j.ijmecsci.2021.106915
29.
Haller
,
G.
, and
Ponsioen
,
S.
,
2016
, “
Nonlinear Normal Modes and Spectral Submanifolds: Existence, Uniqueness and Use in Model Reduction
,”
Nonlinear Dyn.
,
86
(
3
), pp.
1493
1534
.10.1007/s11071-016-2974-z
30.
Manevitch
,
L. I.
,
2001
, “
The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex Variables
,”
Nonlinear Dyn.
,
25
(
1/3
), pp.
95
109
.10.1023/A:1012994430793
31.
Manevitch
,
L. I.
,
2007
, “
New Approach to Beating Phenomenon in Coupled Nonlinear Oscillatory Chains
,”
Arch. Appl. Mech.
,
77
(
5
), pp.
301
312
.10.1007/s00419-006-0081-1
32.
Vakakis
,
A. F.
,
Gendelman
,
O. V.
,
Kerschen
,
G.
,
Bergman
,
L. A.
,
McFarland
,
D. M.
, and
Lee
,
Y. S.
,
2008
,
Passive Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems
,
Springer
,
Berlin
.
33.
Lee
,
Y. S.
,
Vakakis
,
A. F.
,
Bergman
,
L. A.
,
McFarland
,
D. M.
,
Kerschen
,
G.
,
Nucera
,
F.
,
Tsakirtzis
,
S.
, and
Panagopoulos
,
P. N.
,
2008
, “
Passive Nonlinear Targeted Energy Transfer and Its Applications to Vibration Absorption: A Review
,”
Proc. Inst. Mech. Eng., Part K J. Multi-Body Dyn.
,
222
(
2
), pp.
77
134
.10.1243/14644193JMBD118
34.
Ding
,
H.
, and
Chen
,
L.-Q.
,
2020
, “
Designs, Analysis, and Applications of Nonlinear Energy Sinks
,”
Nonlinear Dyn.
,
100
(
4
), pp.
3061
3107
.10.1007/s11071-020-05724-1
35.
Gendelman
,
O. V.
, and
Vakakis
,
A. F.
,
2018
, “
Introduction to a Topical Issue ‘Nonlinear Energy Transfer in Dynamical and Acoustical Systems'
,”
Philos. Trans. R. Soc. A
,
376
, p.
20170129
.10.1098/rsta.2017.0129
36.
Babitsky
,
V.
,
Silberschmidt
,
V.
, Han, Q., and
Wen
,
B.
,
2011
, “
Dynamics of Vibro-Impact Systems. Edtorial
,”
J. Sound Vib.
,
330
(
10
), p.
2123
.10.1016/j.jsv.2010.12.024
37.
Perlikowski
,
P.
,
Woo
,
K.-C.
,
Lenci
,
S.
, and
Kapitaniak
,
T.
,
2017
, “
Dynamics of Systems With Impacts
,”
ASME J. Comput. Nonlinear Dyn.
,
12
(
6
), p.
060301
.10.1115/1.4037433
38.
Fidlin
,
A.
, and
Silberschmidt
,
V.
,
2020
, “
Specal Issue on Vibro-Impact and Friction Dynamics. Editorial
,”
J. Sound Vib.
,
468
, p.
115082
.10.1016/j.jsv.2019.115082
39.
Makarenkov
,
O.
, and
Lamb
,
J. S. W.
,
2012
, “
Dynamics and Bifurcations of Nonsmooth Systems: A Survey
,”
Phys. D
,
241
(
22
), pp.
1826
1844
.10.1016/j.physd.2012.08.002
40.
Thorin
,
A.
, and
Legrand
,
M.
,
2018
, “
Nonsmooth Modal Analysis: From the Discrete to the Continuous Settings
,”
Advanced Topics in Nonsmooth Dynamics, Transactions of the European Network for Nonsmooth Dynamics
,
R.
Leine
,
V.
Acary
,
O.
Brüls
, eds.,
Springer Nature
, Cham, Switzerland, pp.
191
234
.
41.
Noël
,
J.
, 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
42.
Xue
,
Q.
,
Huang
,
W.
,
Leung
,
H.
, and
Wang
,
Z.
,
2021
, “
Nonlinear Dynamics in Drilling Engineering. Editorial
,”
Shock Vib.
,
2021
, p.
9831740
.
43.
Dohnal
,
F.
,
Hagedorn
,
P.
, and
Thomsen
,
J. J.
, eds.,
2012
,
Time-Periodic Systems: Current Trends in Theory and Application
,
Book of Abstracts, Euromech Colloquium 532
,
Frankfurt, Germany
.
44.
Wauer
,
J.
, and
Ishida
,
Y.
,
2009
, “
Special Issue on Recent Advances in Nonlinear Rotordynamics
,”
Nonlinear Dyn.
,
57
(
4
), p. 479.10.1007/s11071-009-9576-y
45.
Kalmar-Nagy
,
T.
,
Olgac
,
N.
, and
Stepan
,
G.
,
2010
, “
Time Delay Systems. Preface
,”
J. Vib. Control
,
16
(
7–8
), p.
941
.10.1177/1077546309341138
46.
Wang
,
Z.
,
Insperger
,
T.
, and
Zhang
,
L.
, eds.,
2017
,
Nonlinear and Delayed Dynamics of Mechatronic Systems
, Procedia IUTAM, Vol.
22
,
Elsevier
, Amsterdam, The Netherlands.
47.
Coutier-Delgosha
,
O.
,
Roger
,
M.
, and Legrand, M.,
2019
, “
Aeroacoustics and Non-Linear Structural Dynamics in Turbomachines. Editorial to Special Issue ISROMAC 2017
,”
J. Sound Vib.
,
453
, pp.
41
42
.10.1016/j.jsv.2019.04.013
48.
Sumali
,
H.
,
Younis
,
M. I.
, and
Abdel-Rahman
,
E. M.
,
2008
, “
Special Issue on Micro- and Nano Electromechanical Systems
,”
Nonlinear Dyn.
,
54
(
1–2
), pp.
1
2
.10.1007/s11071-008-9387-6
49.
Rhoads
,
J. F.
,
Shaw
,
S. W.
, and
Turner
,
K. L.
,
2010
, “
Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators
,”
ASME J. Dyn. Syst. Meas. Control
,
132
(
3
), p.
034001
.10.1115/1.4001333
50.
Rhoads
,
J. F.
,
Cho
,
H.
,
Judge
,
J.
,
Krylov
,
S.
,
Shaw
,
S. W.
, and
Younis
,
M.
,
2017
, “
Special Section on the Dynamics of MEMS and NEMS
,”
ASME J. Vib. Acoust.
,
139
(
4
), p.
040301
.10.1115/1.4036699
51.
Hierold
,
C.
,
Seshia
,
A.
, and
Elata
,
D.
, eds.,
2017
, “J-MEMS Special Topical Focus Nonlinear Phenomena in MEMS and NEMS Call for Papers,”
J. Microelectromech. Syst.
, 26(5), p. C3.10.1109/JMEMS.2017.2755198
52.
Ribeiro
,
P.
,
Lenci
,
S.
, and
Adhikari
,
S.
, eds.,
2020
, “
Non-Linear Dynamics of Micro- and Nano- Electro-Mechanical Systems, Article Collection
,”
Int. J. Non-Linear Mech
.
53.
Hajjaj
,
A. Z.
,
Jaber
,
N.
,
Ilyas
,
S.
,
Alfosail
,
F. K.
, and
Younis
,
M. I.
,
2020
, “
Linear and Nonlinear Dynamics of Micro and Nanoresonators: Review of Recent Advances
,”
Int. J. Non-Linear Mech.
,
119
, p.
103328
.10.1016/j.ijnonlinmec.2019.103328
54.
Wiercigroch
,
M.
, and
Rega
,
G.
, eds.,
2013
,
Nonlinear Dynamics for Advanced Technologies and Engineering Design
(IUTAM Bookseries, Vol.
32
),
Springer
, Dordrecht, The Netherlands.
55.
Kovacic
,
I.
, and
Lenci
,
S.
, eds.,
2019
,
Exploiting Nonlinear Dynamics for Engineering Systems
(IUTAM Bookseries, Vol.
37
),
Springer Nature
, Cham, Switzerland.
56.
Vakakis
,
A. F.
, ed.,
2011
,
Advanced Nonlinear Strategies for Vibration Mitigation and System Identification
(CISM Courses and Lectures, Vol.
518
),
Springer
,
New York
.
57.
Wagg
,
D. J.
, and
Virgin
,
L.
, eds.,
2012
,
Exploiting Nonlinear Behavior in Structural Dynamics
(CISM Courses and Lectures, Vol.
536
),
Springer
,
New York
.
58.
Kerschen
,
G.
, ed.,
2014
,
Modal Analysis of Nonlinear Mechanical Systems
(CISM Courses and Lectures, Vol.
555
),
Springer
,
New York
.
59.
Lenci
,
S.
, and
Rega
,
G.
, eds.,
2018
,
Global Nonlinear Dynamics for Engineering Design and System Safety
(CISM Courses and Lectures, Vol.
588
),
Springer Nature
, Cham, Switzerland.
60.
Warminski
,
J.
, and
Wiercigroch
,
M.
,
2010
, “
Special Issue on Dynamics, Control and Design of Nonlinear Systems With Smart Structures. Preface
,”
Int. J. Non-Linear Mech.
,
45
(
9
), pp.
835
836
.10.1016/j.ijnonlinmec.2010.08.001
61.
Litak
,
G.
, and
Manoach
,
E.
,
2013
, “
Dynamics of Composite Nonlinear Systems and Materials for Engineering Applications and Energy Harvesting—The Role of Nonlinear Dynamics and Complexity in New Developments. Editorial
,”
Eur. Phys. J. Spec. Top.
,
222
(
7
), pp. 1479–1482.10.1140/epjst/e2013-01939-3
62.
Lenci
,
S.
, and
Warminski
,
J.
,
2014
, “
Nonlinear Dynamics and Control of Composites for Smart Engineering Design
,”
Meccanica
,
49
(
8
), pp.
1721
1722
.10.1007/s11012-014-0006-y
63.
Dragoni
,
E.
,
Harne
,
R. L.
, and
Daqaq
,
M. F.
,
2015
, “
Special Issue on Modeling and Control of Adaptive Dynamic Systems and Structures
,”
ASME J. Vib. Acoust.
,
137
(
1
), p.
010201
.10.1115/1.4028884
64.
Emam
,
S. A.
, and
Inman
,
D. J.
,
2015
, “
A Review on Bistable Composite Laminates for Morphing and Energy Harvesting
,”
ASME Appl. Mech. Rev.
,
67
(
6
), p.
060803
.10.1115/1.4032037
65.
Clark
,
W. W.
,
Daqaq
,
M. F.
,
Quinn
,
D. D.
,
2011
, “
Special Issue on Energy Harvesting
,”
ASME J. Vib. Acoust.
,
133
(
1
), p.
010201
.10.1115/1.4002839
66.
Litak
,
G.
,
Manoach
,
E.
, and
Halvorsen
,
E.
,
2015
, “
Nonlinear and Multiscale Dynamics of Smart Materials in Energy Harvesting. Editorial
,”
Eur. Phys. J. Spec. Top.
,
224
(
14–15
), pp.
2671
2673
.10.1140/epjst/e2015-02581-9
67.
Daqaq
,
M. F.
,
Masana
,
R.
,
Erturk
,
A.
, and
Quinn
,
D. D.
,
2014
, “
On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion
,”
ASME Appl. Mech. Rev.
,
66
(
4
), p.
040801
.10.1115/1.4026278
68.
Pakrashi
,
V.
, and
Litak
,
G.
,
2019
, “
Energy Harvesting and Applications. Editorial
,”
Eur. Phys. J. Spec. Top.
,
228
(
7
), pp.
1535
1536
.10.1140/epjst/e2019-900118-y
69.
Tenreiro Machado
,
J. A.
, and
Luo
,
A.
,
2008
, “
Special Issue on Discontinuous and Fractional Dynamical Systems. Editorial
,”
ASME J. Comput. Nonlinear Dyn
,
3
(
2
), p. 020201.10.1115/1.2834905
70.
Tenreiro Machado
,
J. A.
, and
Barbosa
,
R. S.
,
2008
, “
Introduction to the Special Issue on Fractional Differentiation and Its Applications
,”
J. Vib. Control
,
14
(
9–10
), p. 1253.
71.
Baleanu
,
D.
,
O'Regan
,
D.
, and
Trujillo
,
J. J.
,
2013
, “
Special Issue on Nonlinear Fractional Differential Equations and Their Applications in Honour of Ravi P. Agarwal on His 65th Birthday.
Preface,”
Nonlinear Dyn
,
71
(
4
), p. 603.10.1007/s11071-013-0788-9
72.
Klatt
,
D.
,
Magin
,
R. L.
,
and Mainardi
,
F.
,
2014
, “
Special Section: Fractional Calculus in Vibration and Acoustics, Special Section. Editorial
,”
ASME J. Vib. Acoust
,
136
(
5
), p. 050301.10.1115/1.4027482
73.
Tenreiro Machado
,
J. A.
,
Baleanu
,
D.
,
Chen
,
W.
, and
Sabatier
,
J.
,
2014
, “
New Trends in Fractional Dynamics. Editorial
,”
J. Vib. Control
,
20
(
7
), p. 963.10.1177/1077546313507652
74.
Zhou
,
Y.
,
Ionescu
,
C.
, and
Tenreiro Machado
,
J. A.
,
2015
, “
Fractional Dynamics and Its Applications. Editorial
,”
Nonlinear Dyn.
,
80
(
4
), pp.
1661
1664
.10.1007/s11071-015-2069-2
75.
Ionescu
,
C.
,
Zhou
,
Y.
, and
Tenreiro Machado
,
J. A.
,
2016
, “
Special Issue: Advances in Fractional Dynamics and Control. Editorial
,”
J. Vib. Control
,
22
(
8
), pp. 1969–1971.10.1177/1077546315609273
76.
Baleanu
,
D.
,
Caponetto
,
R.
, and
Tenreiro Machado
,
J. A.
,
2016
, “
Challenges in Fractional Dynamics and Control Theory. Editorial
,”
J. Vib. Control
,
22
(
9
), pp. 2151–2152.10.1177/1077546315609262
77.
Baleanu
,
D.
,
Kalmar-Nagy
,
T.
,
Sapsis
,
T. P.
, and
Yabuno
,
H.
,
2018
, “Special Issue:
Nonlinear Dynamics: Models, Behavior, and Techniques. Guest Editorial
,”
ASME J. Comput. Nonlinear Dyn.
,
13
(
9
), p. 090301.10.1115/1.4040569
78.
Janson
,
N. B.
,
2012
, “
Non-Linear Dynamics of Biological Systems
,”
Contemp. Phys.
,
53
(
2
), pp.
137
168
.10.1080/00107514.2011.644441
79.
Lu
,
Q.
, and
Wiercigroch
,
M.
,
2010
, “
Special Issue on Nonlinear Dynamics of Biological Systems. Preface
,”
Int. J. Non-Linear Mech
,
45
(
6
), pp. 601–602.10.1016/j.ijnonlinmec.2010.04.006
80.
Zhao
,
X.
,
Tolkacheva
,
E. G.
, and
Ying
,
W.
, eds.,
2012
, “
Special Issue: Nonlinear Dynamics in Medicine and Biology
,”
Nonlinear Dyn.
,
68
(
3
).
81.
Ziebert
,
F.
, and
Aranson
,
I. S.
,
2016
, “
Nonlinear Models in Molecular and Cell Biology. Editorial
,”
Phys. D
,
318–319
, pp. 1–2.10.1016/j.physd.2016.02.002
82.
Kapitaniak
,
T.
, and
Jafari
,
S.
,
2018
, “
Nonlinear Effects in Life Sciences. Editorial
,”
Eur. Phys. J. Spec. Top.
,
227
(
7–9
), pp. 693–696.10.1140/epjst/e2018-800104-6
83.
Tolkacheva
,
E. G.
,
Feeny
,
B.
, and
Zhao
,
X.
,
2019
, “S
pecial Issue: Nonlinear and Computational Dynamics in Biomedical Applications. Guest Editorial
,”
ASME J. Comput. Nonlinear Dyn.
,
14
(
10
), p. 100301.10.1115/1.4044144
84.
Rega
,
G.
,
Settimi
,
V.
, and
Lenci
,
S.
,
2020
, “
Chaos in One-Dimensional Structural Mechanics
,”
Nonlinear Dyn.
,
102
(
2
), pp.
785
834
.10.1007/s11071-020-05849-3
85.
Sauer
,
T.
,
Yorke
,
J. A.
, and
Casdagli
,
M.
,
1991
, “
Embedology
,”
J. Stat. Phys.
,
65
(
3–4
), pp.
579
616
.10.1007/BF01053745
86.
Holmes
,
P.
,
Lumley
,
J. L.
, and
Berkooz
,
G.
,
1996
, “
Turbulence, Coherent Structures
,”
Dynamical Systems and Symmetry
,
Cambridge University Press
,
Cambridge, UK
.
87.
Virgin
,
L. N.
,
2019
,
Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration
,
Cambridge University Press
,
Cambridge, UK
.
88.
Lacarbonara
,
W.
,
Yabuno
,
H.
, and
Yoshizawa
,
M.
,
2011
, “
Experiments in Dynamics and Control. Preface
,”
J. Vib. Control
,
18
(
4
), p 483.
89.
Alaggio
,
R.
, and
Rega
,
G.
,
2000
, “
Characterizing Bifurcations and Classes of Motion in the Transition to Chaos Through 3D-Tori of a Continuous Experimental System in Solid Mechanics
,”
Phys. D
,
137
(
1–2
), pp.
70
93
.10.1016/S0167-2789(99)00169-4
90.
Rega
,
G.
, and
Alaggio
,
R.
,
2009
, “
Experimental Unfolding of the Nonlinear Dynamics of a Cable-Mass Suspended System Around a Divergence-Hopf Bifurcation
,”
J. Sound Vib.
,
322
(
3
), pp.
581
611
.10.1016/j.jsv.2009.01.060
91.
Hikihara
,
T.
, and Kambe, T., eds.,
2012
,
IUTAM Symposium on 50 Years of Chaos: Applied and Theoretical
, Procedia IUTAM, Vol.
5
,
Elsevier
, Amsterdam, The Netherlands.
92.
Guirao
,
J. L. G.
, and
Luo
,
A. C. J.
,
2016
, “
New Trends in Nonlinear Dynamics and Chaoticity
. Preface,”
Nonlinear Dyn.
,
84
, pp. 1–2.10.1007/s11071-016-2656-x
93.
Gardini
,
L.
,
Grebogi
,
C.
, and
Lenci
,
S.
,
2020
, “
Chaos Theory and Applications: A Retrospective on Lessons Learned and Missed or New Opportunities
. Preface,”
Nonlinear Dyn.
,
102
(
2
), pp. 643–644.10.1007/s11071-020-05903-0
94.
Cadot
,
O.
,
Ducceschi
,
M.
,
Humbert
,
T.
,
Miquel
,
B.
,
Mordant
,
N.
,
Josserand
,
C.
, and
Touzé
,
C.
,
2016
, “
Wave Turbulence in Vibrating Plates
,”
Handbook of Applications of Chaos Theory
,
C.
Skiadas
, ed.,
Chapman and Hall/CRC
,
London
, pp.
425
448
.
95.
Düring
,
G.
,
Josserand
,
C.
, and
Rica
,
S.
,
2017
, “
Wave Turbulence Theory of Elastic Plates
,”
Phys. D
,
347
, pp.
42
73
.10.1016/j.physd.2017.01.002
96.
Patil
,
N. S.
, and
Cusumano
,
J. P.
,
2020
, “
The High Forecasting Complexity of Stochastically Perturbed Periodic Orbits Limits the Ability to Distinguish Them From Chaos
,”
Nonlinear Dyn
,.,
102
(
2
), pp.
697
712
.10.1007/s11071-020-05920-z
97.
Dudkowski
,
D.
,
Wojewoda
,
J.
,
Czołczyński
,
K.
, and
Kapitaniak
,
T.
,
2020
, “
Is It Really Chaos? The Complexity of Transient Dynamics of Double Pendula
,”
Nonlinear Dyn.
,
102
(
2
), pp.
759
770
.10.1007/s11071-020-05697-1
98.
Hussein
,
M. I.
,
Leamy
,
M. J.
, and
Ruzzene
,
M.
,
2013
, “
Special Issue on Dynamics of Phononic Materials and Structures. Editorial
,”
ASME J. Vib. Acoust
,
135
(
4
), p.
040201
.10.1115/1.4024399
99.
Hussein
,
M. I.
,
Leamy
,
M. J.
, and
Ruzzene
,
M.
,
2014
, “
Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook
,”
ASME Appl. Mech. Rev.
,
66
(
4
), p.
040802
.10.1115/1.4026911
100.
Belykh
,
I.
,
di Bernardo
,
M.
,
Kurths
,
J.
, and
Porfiri
,
M.
,
2014
, “
Evolving Dynamical Networks. Editorial
,”
Phys. D
,
267
, pp.
1
6
.10.1016/j.physd.2013.10.008
101.
Serban
,
R.
,
Wang
,
Y.
,
Choi
,
K. K.
, and
Jayakumar
,
P.
,
2019
, “Special Issue:
Sensitivity Analysis and Uncertainty Quantification. Guest Editorial
,”
ASME J. Comput. Nonlinear Dyn
,
14
(
2
), p.
020301
.10.1115/1.4042262
102.
Hamzi
,
B.
,
Lamb
,
J.
,
Livi
,
L.
, and
Li
,
Q.
, eds.,
2020
, “
Machine Learning and Dynamical Systems
. Article Collection,”
Phys. D
.
103.
Touzé
,
C.
,
Vizzaccaro
,
A.
, and
Thomas
,
O.
,
2021
, “
Model Order Reduction Methods for Geometrically Nonlinear Structures: A Review of Nonlinear Techniques
,”
Nonlinear Dyn.
,
105
(
2
), pp.
1141
1190
.10.1007/s11071-021-06693-9
104.
Mignolet
,
M. P.
,
Przekop
,
A.
,
Rizzi
,
S. A.
, and
Spottswood
,
S. M.
,
2013
, “
A Review of Indirect/Non-Intrusive Reduced Order Modeling of Nonlinear Geometric Structures
,”
J. Sound Vib.
,
332
(
10
), pp.
2437
2460
.10.1016/j.jsv.2012.10.017
105.
Shen
,
Y.
,
Vizzaccaro
,
A.
,
Kesmia
,
N.
,
Yu
,
T.
,
Salles
,
L.
,
Thomas
,
O.
, and
Touzé
,
C.
,
2021
, “
Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures
,”
Vibration
,
4
(
1
), pp.
175
204
.10.3390/vibration4010014
106.
Touzé
,
C.
,
2014
, “
Normal Form Theory and Nonlinear Normal Modes: Theoretical Settings and Applications
,”
Modal Analysis of Nonlinear Mechanical Systems
,
G.
Kerschen
, ed., (CISM Courses and Lectures, Vol.
555
),
Springer
,
New York
, pp.
75
160
.
107.
Neild
,
S. A.
,
Champneys
,
A. R.
,
Wagg
,
D. J.
,
Hill
,
T. L.
, and
Cammarano
,
A.
,
2015
, “
The Use of Normal Forms for Analysing Nonlinear Mechanical Vibrations
,”
Phil. Trans. R. Soc. A
,
373
(
2051
), p.
20140404
.10.1098/rsta.2014.0404
108.
Liu
,
X.
, and
Wagg
,
D. J.
,
2019
, “
Simultaneous Normal Form Transformation and Model-Order Reduction for Systems of Coupled Nonlinear Oscillators
,”
Proc. R. Soc. A
,
475
(
2228
), p.
20190042
.10.1098/rspa.2019.0042
109.
Vizzaccaro
,
A.
,
Salles
,
L.
, and
Touzé
,
C.
,
2021
, “
Comparison of Nonlinear Mappings for Reduced-Order Modelling of Vibrating Structures: Normal Form Theory and Quadratic Manifold Method With Modal Derivatives
,”
Nonlinear Dyn.
,
103
(
4
), pp.
3335
3370
.10.1007/s11071-020-05813-1
110.
Guo
,
T. D.
, and
Rega
,
G.
,
2022
, “
Reduced-Order Modelling of Nonlinear Structures. Part 1: A Perturbation-Driven Low-Order Elimination Technique Using Passive Patterns
,”
Nonlinear Dyn.
(Submitted).
111.
Guo
,
T. D.
, and
Rega
,
G.
,
2022
, “
Reduced-Order Modelling of Nonlinear Structures. Part 2: Equivalence of Different Techniques, and Refined Order/Degree of Truncated Models
,”
Nonlinear Dyn.
(Submitted).
112.
Haro
,
A.
,
Canadell
,
M.
,
Figueras
,
J. L.
,
Luque
,
A.
, and
Mondelo
,
J. M.
,
2016
,
The Parameterization Method for Invariant Manifolds. From Rigorous Results to Effective Computations
,
Springer International Publishing
, Switzerland.
113.
Haller
,
G.
, and
Ponsioen
,
S.
,
2017
, “
Exact Model Reduction by a Slow–Fast Decomposition of Nonlinear Mechanical Systems
,”
Nonlinear Dyn.
,
90
(
1
), pp.
617
647
.10.1007/s11071-017-3685-9
114.
Ponsioen
,
S.
,
Jain
,
S.
, and
Haller
,
G.
,
2020
, “
Model Reduction to Spectral Submanifolds and Forced Response Calculation in High-Dimensional Mechanical Systems
,”
J. Sound Vib.
,
488
, p.
115640
.10.1016/j.jsv.2020.115640
115.
Pisarchik
,
A. N.
, and
Feudel
,
U.
,
2014
, “
Control of Multistability
,”
Phys. Rep.
,
540
(
4
), pp.
167
218
.10.1016/j.physrep.2014.02.007
116.
Zhang
,
Z.
,
Li
,
Y.
,
Yu
,
X.
,
Li
,
X.
,
Wu
,
H.
,
Wu
,
H.
,
Jiang
,
S.
, and
Chai
,
G.
,
2019
, “
Bistable Morphing Composite Structures: A Review
,”
Thin-Walled Struct.
,
142
, pp.
74
97
.10.1016/j.tws.2019.04.040
117.
Chillara
,
V. S. C.
, and
Dapino
,
M. J.
,
2020
, “
Review of Morphing Laminated Composites
,”
ASME Appl. Mech. Rev.
,
72
(
1
), p.
010801
.10.1115/1.4044269
118.
Settimi
,
V.
,
Rega
,
G.
, and
Saetta
,
E.
,
2018
, “
Avoiding/Inducing Dynamic Buckling in a Thermomechanically Coupled Plate: A Local and Global Analysis of Slow/Fast Response
,”
Proc. R. Soc. A
,
474
(
2213
), p.
20180206
.10.1098/rspa.2018.0206
119.
Rega
,
G.
, and
Settimi
,
V.
,
2021
, “
Global Dynamics Perspective on Macro- to Nano-Mechanics
,”
Nonlinear Dyn.
,
103
(
2
), pp.
1259
1303
.10.1007/s11071-020-06198-x
120.
Rega
,
G.
, and
Lenci
,
S.
,
2015
, “
A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control and Design Engineering
,”
ASME Appl. Mech. Rev.
,
67
(
5
), p.
050802
.10.1115/1.4031705
121.
Silva
,
F. M. A.
,
Gonçalves
,
P. B.
, and
del Prado
,
Z. J. G. N.
,
2012
, “
Influence of Physical and Geometrical System Parameters Uncertainties on the Nonlinear Oscillations of Cylindrical Shells
,”
J. Braz. Soc. Mech. Sci. Eng.
,
34
(
spe2
), pp.
622
632
.10.1590/S1678-58782012000600011
122.
Silva
,
F. M. A.
, and
Gonçalves
,
P. B.
,
2015
, “
The Influence of Uncertainties and Random Noise on the Dynamical Integrity of a System Liable to Unstable Buckling
,”
Nonlinear Dyn.
,
81
(
1–2
), pp.
707
724
.10.1007/s11071-015-2021-5
123.
Benedetti
,
K. C. B.
, and
Gonçalves
,
P. B.
,
2022
, “
Nonlinear Response of an Imperfect Microcantilever Static and Dynamically Actuated Considering Uncertainties and Noise
,”
Nonlinear Dyn.
,
107
(
2
), pp.
1725
1754
.10.1007/s11071-021-06600-2
124.
Benedetti
,
K. C. B.
,
Gonçalves
,
P. B.
,
Lenci
,
S.
, and
Rega
,
G.
,
2022
, “
Global Analysis of Stochastic Nonlinear Dynamical Systems. Part 1: Adaptative Phase-Space Discretization Strategy
,” (in preparation).
125.
Benedetti
,
K. C. B.
,
Gonçalves
,
P. B.
,
Lenci
,
S.
, and
Rega
,
G.
,
2022
, “
Global Analysis of Stochastic Nonlinear Dynamical Systems. Part 2: Influence of Uncertainties and Noise on Basins/Attractors Topology and Integrity
,” (in preparation).
126.
Agarwal
,
V.
,
Yorke
,
J. A.
, and
Balachandran
,
B.
,
2020
, “
Noise-Induced Chaotic-Attractor Escape Route
,”
Nonlinear Dyn.
,
102
(
2
), pp.
863
876
.10.1007/s11071-020-05873-3
127.
Dudkowski
,
D.
,
Jafari
,
S.
,
Kapitaniak
,
T.
,
Kuznetsov
,
N. V.
,
Leonov
,
G. A.
, and
Prasad
,
A.
,
2016
, “
Hidden Attractors in Dynamical Systems
,”
Phys. Rep.
,
637
, pp.
1
50
.10.1016/j.physrep.2016.05.002
128.
Dudkowski
,
D.
,
Prasad
,
A.
, and
Kapitaniak
,
T.
,
2017
, “
Perpetual Points: New Tool for Localization of Coexisting Attractors in Dynamical Systems
,”
Int. J. Bif. Chaos
,
27
(
04
), p.
1750063
.10.1142/S0218127417500638
129.
Jain
,
S.
, and
Haller
,
G.
,
2022
, “
How to Compute Invariant Manifolds and Their Reduced Dynamics in High- Dimensional Finite-Element Models?
,”
Nonlinear Dyn.
,
107
(
2
), pp.
1417
1450
.10.1007/s11071-021-06957-4
130.
Jain
,
S.
,
Thurnher
,
T.
,
Li
,
M.
, and
Haller
,
G.
,
2022
, “
SSMTool 2.2: Computation of Invariant Manifolds in High-Dimensional Mechanics Problems
,”
Zenodo, accessed Mar. 28, 2022, https://zenodo.org/record/6338831#.Yj7P8KjSKUk
131.
Dankowicz
,
H.
, and
Schilder
,
F.
,
2013
,
Recipes for Continuation
,
Society for Industrial and Applied Mathematics
,
Philadelphia
, PA.
132.
Hegedűs
,
F.
,
Lauterborn
,
W.
,
Parlitz
,
U.
, and
Mettin
,
R.
,
2018
, “
Non-Feedback Technique to Directly Control Multistability in Nonlinear Oscillators by Dual-Frequency Driving
,”
Nonlinear Dyn.
,
94
(
1
), pp.
273
293
.10.1007/s11071-018-4358-z
133.
Hegedűs
,
F.
,
Krähling
,
P.
,
Lauterborn
,
W.
,
Mettin
,
R.
, and
Parlitz
,
U.
,
2020
, “
High-Performance GPU Computations in Nonlinear Dynamics: An Efficient Tool for New Discoveries
,”
Meccanica
,
55
(
12
), pp.
2493
2504
.10.1007/s11012-020-01146-w
134.
Eason
,
R.
, and
Dick
,
A. J.
,
2014
, “
A Parallelized Multi-Degrees-of-Freedom Cell Map Method
,”
Nonlinear Dyn.
,
77
(
3
), pp.
467
479
.10.1007/s11071-014-1310-8
135.
Xiong
,
F. R.
,
Qin
,
Z. C.
,
Ding
,
Q.
,
Hernández
,
C.
,
Fernandez
,
J.
,
Schütze
,
O.
, and
Sun
,
J. Q.
,
2015
, “
Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems
,”
ASME J. Appl. Mech.
,
82
(
11
), p.
111010
.10.1115/1.4031149
136.
Xiong
,
F. R.
,
Han
,
Q.
,
Hong
,
L.
, and
Sun
,
J. Q.
,
2018
, “
Global Analysis of Nonlinear Dynamical Systems
,”
Global Nonlinear Dynamics for Engineering Design and System Safety
(CISM Courses and Lectures, Vol.
588
),
S.
Lenci
and
G.
Rega
, eds.,
Springer Nature
, Cham, Switzerland, pp.
287
318
.
137.
Belardinelli
,
P.
, and
Lenci
,
S.
,
2016
, “
An Efficient Parallel Implementation of Cell Mapping Methods for Mdof Systems
,”
Nonlinear Dyn.
,
86
(
4
), pp.
2279
2290
.10.1007/s11071-016-2849-3
138.
Belardinelli
,
P.
,
Lenci
,
S.
, and
Rega
,
G.
,
2018
, “
Seamless Variation of Isometric and Anisometric Dynamical Integrity Measures in Basins' Erosion
,”
Commun. Nonlinear Sci. Numer. Simul.
,
56
, pp.
499
507
.10.1016/j.cnsns.2017.08.030
139.
Habib
,
G.
,
2021
, “
Dynamical Integrity Assessment of Stable Equilibria: A New Rapid Iterative Procedure
,”
Nonlinear Dyn.
,
106
(
3
), pp.
2073
2096
.10.1007/s11071-021-06936-9
140.
Menck
,
P. J.
,
Heitzig
,
J.
,
Marwan
,
N.
, and
Kurths
,
J.
,
2013
, “
How Basin Stability Complements the Linear-Stability Paradigm
,”
Nat. Phys.
,
9
(
2
), pp.
89
92
.10.1038/nphys2516
141.
Brzeski
,
P.
,
Lazarek
,
M.
,
Kapitaniak
,
T.
,
Kurths
,
J.
, and
Perlikowski
,
P.
,
2016
, “
Basin Stability Approach for Quantifying Responses of Multistable Systems With Parameters Mismatch
,”
Meccanica
,
51
(
11
), pp.
2713
2726
.10.1007/s11012-016-0534-8
142.
Brzeski
,
P.
, and
Perlikowski
,
P.
,
2019
, “
Sample-Based Methods of Analysis for Multistable Dynamical Systems
,”
Arch. Comput. Meth. Eng.
,
26
(
5
), pp.
1515
1545
.10.1007/s11831-018-9280-5
143.
Stender
,
M.
, and
Hoffmann
,
N.
,
2022
, “
bSTAB: An Open-Source Software for Computing the Basin Stability of Multi-Stable Dynamical Systems
,”
Nonlinear Dyn.
,
107
(
2
), pp.
1451
1468
.10.1007/s11071-021-06786-5
144.
Serdukova
,
L.
,
Zheng
,
Y.
,
Duan
,
J.
, and
Kurths
,
J.
,
2016
, “
Stochastic Basins of Attraction for Metastable States
,”
Chaos
,
26
(
7
), p.
073117
.10.1063/1.4959146
145.
Lindner
,
M.
, and
Hellmann
,
F.
,
2019
, “
Stochastic Basins of Attraction and Generalized Committor Functions
,”
Phys. Rev. E
,
100
(
2
), p.
022124
.10.1103/PhysRevE.100.022124
146.
Goswami
,
D.
,
Thackray
,
E.
, and
Paley
,
D. A.
,
2018
, “
Constrained Ulam Dynamic Mode Decomposition: Approximation of the Perron-Frobenius Operator for Deterministic and Stochastic Systems
,”
IEEE Control Syst. Lett.
,
2
(
4
), pp.
809
814
.10.1109/LCSYS.2018.2849552
147.
Dellnitz
,
M.
,
Klus
,
S.
, and
Ziessler
,
A.
,
2017
, “
A Set-Oriented Numerical Approach for Dynamical Systems With Parameter Uncertainty
,”
SIAM J. Appl. Dyn. Syst.
,
16
(
1
), pp.
120
138
.10.1137/16M1072735
148.
Vakakis
,
A. F.
,
2018
, “
Passive Nonlinear Targeted Energy Transfer
,”
Phil. Trans. R. Soc. A
,
376
(
2127
), p.
20170132
.10.1098/rsta.2017.0132
149.
Wagg
,
D.
,
2021
, “
A Review of the Mechanical Inerter: Historical Context, Physical Realisations and Nonlinear Applications
,”
Nonlinear Dyn.
,
104
(
1
), pp.
13
34
.10.1007/s11071-021-06303-8
150.
Wiercigroch
,
M.
,
Najdecka
,
A.
, and
Vazirii
,
V.
,
2011
, “
Nonlinear Dynamics of Pendulums System for Energy Harvesting
,”
Vibration Problems ICOVP 2009
, Vol.
139
,
J.
Náprstek
, eds.,
Springer Proceedings in Physics
, pp.
35
42
.
151.
Yurchenko
,
D.
, and
Alevras
,
P.
,
2018
, “
Parametric Pendulum Based Wave Energy Converter
,”
Mech. Syst. Signal Proc.
,
99
, pp.
504
515
.10.1016/j.ymssp.2017.06.026
152.
Dotti
,
F. E.
, and
Virla
,
J. N.
,
2021
, “
Nonlinear Dynamics of the Parametric Pendulum With a View on Wave Energy Harvesting Applications
,”
ASME J. Comput. Nonlinear Dyn.
,
16
(
6
), p.
061007
.10.1115/1.4050699
153.
Caetano
,
V. J.
, and
Savi
,
M. A.
,
2022
, “
Star-Shaped Piezoelectric Mechanical Energy Harvesters for Multidirectional Sources
,”
Int. J. Mech. Sci.
,
215
, p.
106962
.10.1016/j.ijmecsci.2021.106962
154.
Mendes
,
B. A. P.
,
Ribeiro
,
E. A. R.
, and
Mazzilli
,
C. E. N.
,
2020
, “
Piezoelectric Vibration Controller in a Parametrically-Excited System With Modal Localisation
,”
Meccanica
,
55
(
12
), pp.
2555
2569
.10.1007/s11012-020-01195-1
155.
Blanchard
,
A.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2020
, “
Vortex-Induced Vibration of a Linearly Sprung Cylinder With an Internal Rotational Nonlinear Energy Sink in Turbulent Flow
,”
Nonlinear Dyn.
,
99
(
1
), pp.
593
609
.10.1007/s11071-019-04775-3
156.
Rezaei
,
M.
,
Talebitooti
,
R.
, and
Liao
,
W. H.
,
2021
, “
Exploiting Bi-Stable Magneto-Piezoelastic Absorber for Simultaneous Energy Harvesting and Vibration Mitigation
,”
Int. J. Mech. Sci.
,
207
, p.
106618
.10.1016/j.ijmecsci.2021.106618
157.
Su
,
X.
,
Kang
,
H.
, and
Guo
,
T.
,
2022
, “
Modelling and Energy Transfer in the Coupled Nonlinear Response of a 1:1 Internally Resonant Cable System With a Tuned Mass Damper
,”
Mech. Syst. Sign. Proc.
,
162
, p.
108058
.10.1016/j.ymssp.2021.108058
158.
Verstraete
,
M. L.
,
Roccia
,
B. A.
,
Mook
,
D. T.
, and
Preidikman
,
S.
,
2019
, “
A Co-Simulation Methodology to Simulate the Nonlinear Aeroelastic Behavior of a Folding-Wing Concept in Different Flight Configurations
,”
Nonlinear Dyn.
,
98
(
2
), pp.
907
927
.10.1007/s11071-019-05234-9
159.
Guo
,
X.
,
Wang
,
S.
,
Qu
,
Y.
, and
Cao
,
D.
,
2021
, “
Nonlinear Dynamics of Z-Shaped Morphing Wings in Subsonic Flow
,”
Aerosp. Sci. Technol.
,
119
, p.
107145
.10.1016/j.ast.2021.107145
160.
Fonseca
,
L. M.
,
Rodrigues
,
G. V.
, and
Savi
,
M. A.
,
2022
, “
An Overview of the Mechanical Description of Origami-Inspired Systems and Structures
,” Int. J. Mech. Sci. (Submitted).
161.
Kovacic
,
I.
,
Zukovic
,
M.
, and
Radomirovic
,
D.
,
2020
, “
On a Localization Phenomenon in Two Types of Bio-Inspired Hierarchically Organized Oscillatory Systems
,”
Nonlinear Dyn.
,
99
(
1
), pp.
679
706
.10.1007/s11071-019-05337-3
162.
Georgiades
,
F.
,
2021
, “
Augmented Perpetual Manifolds and Perpetual Mechanical Systems-Part I: Definitions, Theorem and Corollary for Triggering Perpetual Manifolds, Application in Reduced Order Modeling and Particle-Wave Motion of Flexible Mechanical Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
16
(
7
), p.
071005
.10.1115/1.4050554
163.
Settimi
,
V.
, and
Rega
,
G.
,
2016
, “
Exploiting Global Dynamics of a Noncontact Atomic Force Microcantilever to Enhance Its Dynamical Robustness Via Numerical Control
,”
Int. J. Bifurcation Chaos
,
26
(
07
), p.
1630018
.10.1142/S0218127416300184
164.
Ren
,
X.
,
Das
,
R.
,
Tran
,
P.
,
Ngo
,
T. D.
, and
Xie
,
Y. M.
,
2018
, “
Auxetic Metamaterials and Structures: A Review
,”
Smart Mater. Struct.
,
27
(
2
), p.
023001
.10.1088/1361-665X/aaa61c
165.
Surjadi
,
J. U.
,
Gao
,
L.
,
Du
,
H.
,
Li
,
X.
,
Xiong
,
X.
,
Fang
,
N. X.
, and
Lu
,
Y.
,
2019
, “
Mechanical Metamaterials and Their Engineering Applications
,”
Adv. Eng. Mater.
,
21
(
3
), p.
1800864
.10.1002/adem.201800864
166.
Valdevit
,
L.
,
Bertoldi
,
K.
,
Guest
,
J.
, and
Spadaccini
,
C.
,
2018
, “
Architected Materials: Synthesis, Characterization, Modeling, and Optimal Design, Focus Issue
,”
J. Mater. Res.
,
33
(
3
), pp.
241
246
.10.1557/jmr.2018.18
167.
Wu
,
L.
,
Wang
,
Y.
,
Chuang
,
K.
,
Wu
,
F.
,
Wang
,
Q.
,
Lin
,
W.
, and
Jiang
,
H.
,
2021
, “
A Brief Review of Dynamic Mechanical Metamaterials for Mechanical Energy Manipulation
,”
Mater. Today
,
44
, pp.
168
193
.10.1016/j.mattod.2020.10.006
168.
Wang
,
Y. F.
,
Wang
,
Y. Z.
,
Wu
,
B.
,
Chen
,
W.
, and
Wang
,
Y. S.
,
2020
, “
Tunable and Active Phononic Crystals and Metamaterials
,”
ASME Appl. Mech. Rev.
,
72
(
4
), p.
040801
.10.1115/1.4046222
169.
Romeo
,
F.
, and
Rega
,
G.
,
2015
, “
Periodic and Localized Solutions in Chains of Oscillators With Softening or Hardening Cubic Nonlinearity
,”
Meccanica
,
50
(
3
), pp.
721
730
.10.1007/s11012-014-9977-y
170.
Higashiyama
,
N.
,
Doi
,
Y.
, and
Nakatani
,
A.
,
2017
, “
Nonlinear Dynamics of a Model of Acoustic Metamaterials
,”
Nonlinear Theory Appl.
,
8
(
2
), pp.
129
145
.10.1587/nolta.8.129
171.
Micheletti
,
A.
,
Ruscica
,
G.
, and
Fraternali
,
F.
,
2019
, “
On the Compact Wave Dynamics of Tensegrity Beams in Multiple Dimensions
,”
Nonlinear Dyn.
,
98
(
4
), pp.
2737
2753
.10.1007/s11071-019-04986-8
172.
Fang
,
X.
,
Wen
,
J.
,
Yin
,
J.
, and
Yu
,
D.
,
2016
, “
Wave Propagation in Nonlinear Metamaterial Multi-Atomic Chains Based on Homotopy Method
,”
AIP Adv.
,
6
(
12
), p.
121706
.10.1063/1.4971761
173.
Settimi
,
V.
,
Lepidi
,
M.
, and
Bacigalupo
,
A.
,
2021
, “
Nonlinear Dispersion Properties of One-Dimensional Mechanical Metamaterials With Inertia Amplification
,”
Int. J. Mech. Sci.
,
201
, p.
106461
.10.1016/j.ijmecsci.2021.106461
174.
Deng
,
B.
,
Li
,
J.
,
Tournat
,
V.
,
Purohit
,
P. K.
, and
Bertoldi
,
K.
,
2021
, “
Dynamics of Mechanical Metamaterials: A Framework to Connect Phonons, Nonlinear Periodic Waves and Solitons
,”
J. Mech. Phys. Solids
,
147
, p.
104233
.10.1016/j.jmps.2020.104233
175.
Raissi
,
M.
,
Perdikaris
,
P.
, and
Karniadakis
,
G. E.
,
2018
, “
Multistep Neural Networks for Data-Driven Discovery of Nonlinear Dynamical Systems
,”
arXiv:1801.01236v1
.10.48550/arXiv.1801.01236
176.
Noël
,
J. P.
, ed.,
2020
,
“Special Issue Data-Driven Modelling of Nonlinear Dynamic Systems,” Vibration
.
177.
Fonzi
,
N.
,
Brunton
,
S. L.
, and
Fasel
,
U.
,
2020
, “
Data-Driven Nonlinear Aeroelastic Models of Morphing Wings for Control
,”
Proc. R. Soc. A
,
476
(
2239
), p.
20200079
.10.1098/rspa.2020.0079
178.
Wan
,
Z. Y.
,
Vlachas
,
P.
,
Koumoutsakos
,
P.
, and
Sapsis
,
T.
,
2018
, “
Data-Assisted Reduced Order Modeling of Extreme Events in Complex Dynamical Systems
,”
PLoS One
,
13
(
5
), p.
e0197704
.10.1371/journal.pone.0197704
179.
Yasuda
,
H.
,
Yamaguchi
,
K.
,
Miyazawa
,
Y.
,
Wiebe
,
R.
,
Raney
,
J. R.
, and
Yang
,
J.
,
2020
, “
Data-Driven Prediction and Analysis of Chaotic Origami Dynamics
,”
Comm. Phys.
,
3
, p. 168.10.1038/s42005-020-00431-0
180.
Li
,
S.
, and
Yang
,
Y.
,
2021
, “
Data-Driven Identification of Nonlinear Normal Modes Via Physics-Integrated Deep Learning
,”
Nonlinear Dyn.
,
106
(
4
), pp.
3231
3246
.10.1007/s11071-021-06931-0
181.
Cenedese
,
M.
,
Axås
,
J.
,
Yang
,
H.
,
Eriten
,
M.
, and
Haller
,
G.
,
2021
, “
Data-Driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems
,”
arXiv:2110.01929
.10.48550/arXiv.2110.01929
182.
Cenedese
,
M.
,
Axås
,
J.
,
Bäuerlein
,
B.
,
Avila
,
K.
, and
Haller
,
G.
,
2022
, “
Data-Driven Modeling and Prediction of Nonlinearizable Dynamics Via Spectral Submanifolds
,” Nat. Commun., 13, p.
872
.
183.
Li
,
J.
,
Wang
,
Y.
,
Jin
,
X.
,
Huang
,
Z.
, and
Elishakoff
,
I.
,
2021
, “
Data-Driven Method for Dimension Reduction of Nonlinear Randomly Vibrating Systems
,”
Nonlinear Dyn.
,
105
(
2
), pp.
1297
1311
.10.1007/s11071-021-06601-1
184.
Farid
,
M.
,
2022
, “
Data-Driven Method for Real-Time Prediction and Uncertainty Quantification of Fatigue Failure Under Stochastic Loading Using Artificial Neural Networks and Gaussian Process Regression
,”
Int. J. Fatigue
,
155
, p.
106415
.10.1016/j.ijfatigue.2021.106415
185.
Farid
,
M.
, and
Solav
,
D.
,
2021
, “
Data-Driven Sensor Placement Optimization for Accurate and Early Prediction of Stochastic Complex Systems
,” (Submitted).
186.
Li
,
Z.
,
Jiang
,
J.
,
Hong
,
L.
, and
Sun
,
J. Q.
,
2019
, “
On the Data-Driven Generalized Cell Mapping Method
,”
Int. J. Bifurcation Chaos
,
29
(
14
), p.
1950204
.10.1142/S0218127419502043
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