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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Bibliographic Details
Published in:Applied mathematics and mechanics Vol. 46; no. 7; pp. 1347 - 1364
Main Authors: Liu, Xinliang, Fang, Bin, Wan, Shaoke, Li, Xiaohu
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2025
Springer Nature B.V
Edition:English ed.
Subjects:
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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Summary: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.
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ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-025-3273-8