Subharmonic resonance analysis of asymmetrical stiffness nonlinear systems with time delay

Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems, where the resulting nonlinearities critically influence subharmonic resonance phenomena, yet comprehensive investigations remain limited. This...

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Vydané v:Applied mathematics and mechanics Ročník 46; číslo 7; s. 1347 - 1364
Hlavní autori: Liu, Xinliang, Fang, Bin, Wan, Shaoke, Li, Xiaohu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2025
Springer Nature B.V
Vydanie:English ed.
Predmet:
Applications of Mathematics
Applied mathematics
Asymmetry
Bifurcation theory
Classical Mechanics
Duffing oscillators
Dynamical systems
Equilibrium
Fluid- and Aerodynamics
Initial conditions
Investigations
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Mechanical engineering
Mechanics
Nonlinear systems
Nonlinearity
Numerical integration
Parameters
Partial Differential Equations
Resonance
Stiffness
System dynamics
Systems stability
Time lag
O322
34C15
bifurcation
subharmonic resonance
34K18
time delay feedback
harmonic balance (HB) method
asymmetrical stiffness
ISSN:0253-4827, 1573-2754
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Abstract Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems, where the resulting nonlinearities critically influence subharmonic resonance phenomena, yet comprehensive investigations remain limited. This study employs the generalized harmonic balance (HB) method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay. To further examine the switching behavior between primary and subharmonic resonances, a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed. The analytical and numerical continuation solutions are validated through direct numerical integration. Subsequently, the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory. Finally, the effects of delay parameters on the existence range of subharmonic responses are discussed in detail, and the influence of initial conditions on system dynamics is explored with basin of attraction plots. This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness, providing valuable theoretical insights into the stability management of such dynamic systems.
AbstractList Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems, where the resulting nonlinearities critically influence subharmonic resonance phenomena, yet comprehensive investigations remain limited. This study employs the generalized harmonic balance (HB) method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay. To further examine the switching behavior between primary and subharmonic resonances, a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed. The analytical and numerical continuation solutions are validated through direct numerical integration. Subsequently, the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory. Finally, the effects of delay parameters on the existence range of subharmonic responses are discussed in detail, and the influence of initial conditions on system dynamics is explored with basin of attraction plots. This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness, providing valuable theoretical insights into the stability management of such dynamic systems.
Author Fang, Bin
Wan, Shaoke
Li, Xiaohu
Liu, Xinliang
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  surname: Wan
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  organization: Key Laboratory of Education Ministry for Modern Design & Rotor-Bearing System, Xi’an Jiaotong University, School of Mechanical Engineering, Xi’an Jiaotong University
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  givenname: Xiaohu
  surname: Li
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  email: li.xiaohu@xjtu.edu.cn
  organization: Key Laboratory of Education Ministry for Modern Design & Rotor-Bearing System, Xi’an Jiaotong University, School of Mechanical Engineering, Xi’an Jiaotong University
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Cites_doi 10.1006/jsvi.2001.3974
10.1088/0951-7715/18/5/027
10.1023/A:1008278526811
10.1007/s40435-020-00645-8
10.1299/jamdsm.2023jamdsm0028
10.1002/mma.9336
10.1016/j.apm.2018.01.010
10.1142/S0218127414501260
10.1016/j.physd.2014.02.005
10.1016/j.chaos.2024.115624
10.1007/s11071-023-08605-5
10.7498/aps.65.094502
10.1007/s11071-014-1344-y
10.1007/s11071-016-2750-0
10.1103/PhysRevE.108.064205
10.1016/j.neucom.2013.09.036
10.1016/S0960-0779(03)00269-8
10.1007/978-3-030-14023-6
10.1016/j.ijnonlinmec.2010.09.016
10.1007/s10483-006-0903-1
10.1016/j.chaos.2016.11.008
10.1007/s42417-021-00293-y
10.1016/j.ymssp.2018.10.008
10.1109/TNN.2007.912593
10.1177/1077546311410763
10.1145/321607.321609
10.1016/j.ymssp.2023.110693
10.1002/rnc.3600
10.1016/j.cnsns.2012.01.028
10.1016/j.ymssp.2021.108207
10.1016/j.jsv.2014.11.038
10.1007/s42417-023-01151-9
10.1007/s11071-012-0678-6
10.1016/j.chaos.2007.07.048
10.1016/j.cnsns.2019.02.018
10.1016/j.nonrwa.2012.07.024
10.1016/j.jsv.2006.03.043
10.1016/j.automatica.2016.12.005
10.1016/j.automatica.2017.04.048
10.1007/s11071-014-1485-z
10.1016/j.probengmech.2011.12.003
10.1007/s10483-022-2921-8
10.1007/s10884-014-9420-z
10.1016/j.chaos.2022.113099
10.1016/j.chaos.2016.02.005
10.1016/j.physleta.2004.06.028
10.1016/j.ijnonlinmec.2014.04.012
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Keywords O322
34C15
bifurcation
subharmonic resonance
34K18
time delay feedback
harmonic balance (HB) method
asymmetrical stiffness
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References A C J Luo (3273_CR28) 2016; 85
L Renson (3273_CR51) 2019; 120
Y F Jin (3273_CR7) 2023; 168
Z Dombovari (3273_CR43) 2011; 46
H T Liao (3273_CR27) 2014; 103
C Zhang (3273_CR36) 2022; 120
A C Luo (3273_CR45) 2012
Y H Fan (3273_CR25) 2023; 46
L C Sheng (3273_CR37) 2023; 17
M Krack (3273_CR50) 2019
D M Huang (3273_CR34) 2022; 164
S F Wen (3273_CR30) 2017; 94
X M Zhang (3273_CR5) 2017; 84
A C J Luo (3273_CR6) 2016; 89
Y X Guo (3273_CR13) 2013; 71
H Wu (3273_CR26) 2021; 9
H Y Hu (3273_CR41) 1998; 15
S F Wen (3273_CR31) 2016; 65
C Li (3273_CR3) 2004; 19
W Y Xu (3273_CR15) 2014; 129
B Xu (3273_CR33) 2014; 77
S J Guo (3273_CR8) 2005; 18
J Q Sun (3273_CR29) 2012; 29
J C Ji (3273_CR21) 2006; 297
A A Valido (3273_CR18) 2023; 108
H Y Hu (3273_CR24) 2009; 40
S S Mou (3273_CR14) 2008; 19
H H Miao (3273_CR44) 2023; 202
A H Nayfeh (3273_CR12) 2012; 18
Z Mei (3273_CR1) 2022; 43
J Ji (3273_CR39) 2002; 253
V Pyragas (3273_CR19) 2019; 73
A C Luo (3273_CR47) 2014; 24
X M Zhao (3273_CR17) 2014; 275
R Kumar (3273_CR20) 2023; 111
Y X Xu (3273_CR42) 2006; 27
R Rusinek (3273_CR23) 2014; 65
L A Baltazar-Tadeo (3273_CR38) 2024; 12
Y Yu (3273_CR22) 2018; 57
H L Dai (3273_CR11) 2014; 78
X L Liu (3273_CR40) 2024; 189
Z Hao (3273_CR48) 2015; 340
S Zhang (3273_CR16) 2013; 14
C S Feng (3273_CR32) 2012; 17
B Lani-Wayda (3273_CR2) 2016; 28
A C J Luo (3273_CR46) 2014
H Akima (3273_CR49) 1970; 17
Q Zhang (3273_CR4) 2004; 328
L J Zhang (3273_CR9) 2017; 27
F Mazenc (3273_CR10) 2017; 78
P Ruttanatri (3273_CR35) 2021; 9
References_xml – volume: 253
  start-page: 985
  issue: 5
  year: 2002
  ident: 3273_CR39
  publication-title: Journal of Sound and Vibration
  doi: 10.1006/jsvi.2001.3974
– volume: 18
  start-page: 2391
  issue: 5
  year: 2005
  ident: 3273_CR8
  publication-title: Nonlinearity
  doi: 10.1088/0951-7715/18/5/027
– volume: 15
  start-page: 311
  issue: 4
  year: 1998
  ident: 3273_CR41
  publication-title: Nonlinear Dynamics
  doi: 10.1023/A:1008278526811
– volume: 9
  start-page: 85
  issue: 1
  year: 2021
  ident: 3273_CR35
  publication-title: International Journal of Dynamics and Control
  doi: 10.1007/s40435-020-00645-8
– volume: 17
  start-page: JAMDSM0028
  issue: 2
  year: 2023
  ident: 3273_CR37
  publication-title: Journal of Advanced Mechanical Design Systems and Manufacturing
  doi: 10.1299/jamdsm.2023jamdsm0028
– volume: 46
  start-page: 14576
  issue: 13
  year: 2023
  ident: 3273_CR25
  publication-title: Mathematical Methods in the Applied Sciences
  doi: 10.1002/mma.9336
– volume: 57
  start-page: 448
  year: 2018
  ident: 3273_CR22
  publication-title: Applied Mathematical Modelling
  doi: 10.1016/j.apm.2018.01.010
– volume: 103
  start-page: 155
  issue: 3
  year: 2014
  ident: 3273_CR27
  publication-title: Computer Modeling in Engineering & Sciences
– volume-title: ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
  year: 2014
  ident: 3273_CR46
– volume: 24
  start-page: 1450126
  issue: 10
  year: 2014
  ident: 3273_CR47
  publication-title: International Journal of Bifurcation and Chaos
  doi: 10.1142/S0218127414501260
– volume-title: Continuous Dynamical Systems
  year: 2012
  ident: 3273_CR45
– volume: 275
  start-page: 54
  year: 2014
  ident: 3273_CR17
  publication-title: Physica D-Nonlinear Phenomena
  doi: 10.1016/j.physd.2014.02.005
– volume: 189
  start-page: 115624
  year: 2024
  ident: 3273_CR40
  publication-title: Chaos, Solitons & Fractals
  doi: 10.1016/j.chaos.2024.115624
– volume: 111
  start-page: 13889
  issue: 15
  year: 2023
  ident: 3273_CR20
  publication-title: Nonlinear Dynamics
  doi: 10.1007/s11071-023-08605-5
– volume: 65
  start-page: 094502
  issue: 9
  year: 2016
  ident: 3273_CR31
  publication-title: Acta Physica Sinica
  doi: 10.7498/aps.65.094502
– volume: 77
  start-page: 819
  issue: 3
  year: 2014
  ident: 3273_CR33
  publication-title: Nonlinear Dynamics
  doi: 10.1007/s11071-014-1344-y
– volume: 85
  start-page: 1141
  issue: 2
  year: 2016
  ident: 3273_CR28
  publication-title: Nonlinear Dynamics
  doi: 10.1007/s11071-016-2750-0
– volume: 108
  start-page: 064205
  issue: 6
  year: 2023
  ident: 3273_CR18
  publication-title: Physical Review E
  doi: 10.1103/PhysRevE.108.064205
– volume: 129
  start-page: 232
  year: 2014
  ident: 3273_CR15
  publication-title: Neurocomputing
  doi: 10.1016/j.neucom.2013.09.036
– volume: 19
  start-page: 853
  issue: 4
  year: 2004
  ident: 3273_CR3
  publication-title: Chaos, Solitons & Fractals
  doi: 10.1016/S0960-0779(03)00269-8
– volume-title: Harmonic Balance for Nonlinear Vibration Problems
  year: 2019
  ident: 3273_CR50
  doi: 10.1007/978-3-030-14023-6
– volume: 46
  start-page: 330
  issue: 1
  year: 2011
  ident: 3273_CR43
  publication-title: International Journal of Non-Linear Mechanics
  doi: 10.1016/j.ijnonlinmec.2010.09.016
– volume: 27
  start-page: 1171
  year: 2006
  ident: 3273_CR42
  publication-title: Applied Mathematics and Mechanics (English Edition)
  doi: 10.1007/s10483-006-0903-1
– volume: 94
  start-page: 54
  year: 2017
  ident: 3273_CR30
  publication-title: Chaos, Solitons & Fractals
  doi: 10.1016/j.chaos.2016.11.008
– volume: 9
  start-page: 1239
  issue: 6
  year: 2021
  ident: 3273_CR26
  publication-title: Journal of Vibration Engineering & Technologies
  doi: 10.1007/s42417-021-00293-y
– volume: 120
  start-page: 449
  year: 2019
  ident: 3273_CR51
  publication-title: Mechanical Systems and Signal Processing
  doi: 10.1016/j.ymssp.2018.10.008
– volume: 120
  start-page: 5885
  issue: 9–10
  year: 2022
  ident: 3273_CR36
  publication-title: The International Journal of Advanced Manufacturing Technology
– volume: 19
  start-page: 532
  issue: 3
  year: 2008
  ident: 3273_CR14
  publication-title: IEEE Transactions on Neural Networks
  doi: 10.1109/TNN.2007.912593
– volume: 18
  start-page: 1106
  issue: 8
  year: 2012
  ident: 3273_CR12
  publication-title: Journal of Vibration and Control
  doi: 10.1177/1077546311410763
– volume: 17
  start-page: 589
  issue: 4
  year: 1970
  ident: 3273_CR49
  publication-title: Journal of the ACM
  doi: 10.1145/321607.321609
– volume: 202
  start-page: 110693
  year: 2023
  ident: 3273_CR44
  publication-title: Mechanical Systems and Signal Processing
  doi: 10.1016/j.ymssp.2023.110693
– volume: 27
  start-page: 781
  issue: 5
  year: 2017
  ident: 3273_CR9
  publication-title: International Journal of Robust and Nonlinear Control
  doi: 10.1002/rnc.3600
– volume: 17
  start-page: 3763
  issue: 10
  year: 2012
  ident: 3273_CR32
  publication-title: Communications in Nonlinear Science and Numerical Simulation
  doi: 10.1016/j.cnsns.2012.01.028
– volume: 164
  start-page: 108207
  year: 2022
  ident: 3273_CR34
  publication-title: Mechanical Systems and Signal Processing
  doi: 10.1016/j.ymssp.2021.108207
– volume: 340
  start-page: 61
  year: 2015
  ident: 3273_CR48
  publication-title: Journal of Sound and Vibration
  doi: 10.1016/j.jsv.2014.11.038
– volume: 12
  start-page: 4765
  issue: 3
  year: 2024
  ident: 3273_CR38
  publication-title: Journal of Vibration Engineering & Technologies
  doi: 10.1007/s42417-023-01151-9
– volume: 71
  start-page: 515
  issue: 3
  year: 2013
  ident: 3273_CR13
  publication-title: Nonlinear Dynamics
  doi: 10.1007/s11071-012-0678-6
– volume: 40
  start-page: 13
  issue: 1
  year: 2009
  ident: 3273_CR24
  publication-title: Chaos, Solitons & Fractals
  doi: 10.1016/j.chaos.2007.07.048
– volume: 73
  start-page: 338
  year: 2019
  ident: 3273_CR19
  publication-title: Communications in Nonlinear Science and Numerical Simulation
  doi: 10.1016/j.cnsns.2019.02.018
– volume: 14
  start-page: 661
  issue: 1
  year: 2013
  ident: 3273_CR16
  publication-title: Nonlinear Analysis-Real World Applications
  doi: 10.1016/j.nonrwa.2012.07.024
– volume: 297
  start-page: 183
  issue: 1–2
  year: 2006
  ident: 3273_CR21
  publication-title: Journal of Sound and Vibration
  doi: 10.1016/j.jsv.2006.03.043
– volume: 78
  start-page: 1
  year: 2017
  ident: 3273_CR10
  publication-title: Automatica
  doi: 10.1016/j.automatica.2016.12.005
– volume: 84
  start-page: 221
  year: 2017
  ident: 3273_CR5
  publication-title: Automatica
  doi: 10.1016/j.automatica.2017.04.048
– volume: 78
  start-page: 907
  issue: 2
  year: 2014
  ident: 3273_CR11
  publication-title: Nonlinear Dynamics
  doi: 10.1007/s11071-014-1485-z
– volume: 29
  start-page: 1
  year: 2012
  ident: 3273_CR29
  publication-title: Probabilistic Engineering Mechanics
  doi: 10.1016/j.probengmech.2011.12.003
– volume: 43
  start-page: 1747
  year: 2022
  ident: 3273_CR1
  publication-title: Applied Mathematics and Mechanics (English Edition)
  doi: 10.1007/s10483-022-2921-8
– volume: 28
  start-page: 627
  year: 2016
  ident: 3273_CR2
  publication-title: Journal of Dynamics and Differential Equations
  doi: 10.1007/s10884-014-9420-z
– volume: 168
  start-page: 113099
  year: 2023
  ident: 3273_CR7
  publication-title: Chaos, Solitons & Fractals
  doi: 10.1016/j.chaos.2022.113099
– volume: 89
  start-page: 405
  year: 2016
  ident: 3273_CR6
  publication-title: Chaos, Solitons & Fractals
  doi: 10.1016/j.chaos.2016.02.005
– volume: 328
  start-page: 163
  issue: 2–3
  year: 2004
  ident: 3273_CR4
  publication-title: Physics Letters A
  doi: 10.1016/j.physleta.2004.06.028
– volume: 65
  start-page: 98
  year: 2014
  ident: 3273_CR23
  publication-title: International Journal of Non-Linear Mechanics
  doi: 10.1016/j.ijnonlinmec.2014.04.012
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Snippet Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,...
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SubjectTerms Applications of Mathematics
Applied mathematics
Asymmetry
Bifurcation theory
Classical Mechanics
Duffing oscillators
Dynamical systems
Equilibrium
Fluid- and Aerodynamics
Initial conditions
Investigations
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Mechanical engineering
Mechanics
Nonlinear systems
Nonlinearity
Numerical integration
Parameters
Partial Differential Equations
Resonance
Stiffness
System dynamics
Systems stability
Time lag
Title Subharmonic resonance analysis of asymmetrical stiffness nonlinear systems with time delay
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