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Thermo-mechanically coupled Duffing oscillator: Heating, feedback, and attractor dynamics
1Department Structural Mechanics, Moscow State University of Civil Engineering, Moscow, Russia.
Chaos (Woodbury, N.Y.)
|August 6, 2026
Summary
This study analyzes a Duffing oscillator with temperature-dependent stiffness due to thermodynamic coupling. Thermomechanical coupling significantly alters nonlinear dynamics, creating novel attractor structures distinct from the classical Duffing model.
Area of Science:
- Nonlinear Dynamics
- Thermodynamics
- Mechanical Engineering
Background:
- The classical Duffing oscillator exhibits a prescribed cubic nonlinearity.
- Understanding temperature-dependent nonlinear systems is crucial for advanced engineering applications.
Purpose of the Study:
- To analyze a Duffing oscillator with dynamically modified stiffness via thermodynamic coupling.
- To investigate the temperature-dependent nonlinear response and resulting attractor structures.
Main Methods:
- Employed stroboscopic sampling to analyze system dynamics.
- Utilized a normalized cardinality measure for attractor classification.
- Constructed dynamical-regime maps in thermal-capacity-thermal-cooling parameter space.
Main Results:
- Identified periodic, quasi-periodic, and chaotic responses.
- Revealed systematic shifts in dominant attractor types with varying thermal parameters.
- Demonstrated that thermomechanical coupling substantially modifies nonlinear behavior.
Conclusions:
- Thermomechanical coupling introduces novel attractor structures in the Duffing oscillator.
- The nonlinear response is significantly altered compared to the standard Duffing formulation.
- This work highlights the impact of thermodynamic feedback on mechanical oscillator dynamics.
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