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Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators
1Nuclear Advanced Manufacturing Research Centre, University of Sheffield, Rotherham S60 5WG, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|September 20, 2019
Summary
This study introduces a direct normal form decomposition to simplify coupled nonlinear oscillators. The method effectively reduces system order while accurately capturing nonlinear dynamics and internal resonances.
Area of Science:
- Nonlinear dynamics
- Mechanical vibrations
- Applied mathematics
Background:
- Coupled nonlinear oscillators are common in mechanical systems.
- Analyzing these systems often involves complex mathematical models.
- Order reduction and resonance analysis are critical for understanding system behavior.
Purpose of the Study:
- To present a direct normal form decomposition method for coupled nonlinear oscillators.
- To demonstrate order reduction during normal form transformations.
- To address challenges in analyzing systems with varying nonlinearity orders and internal resonances.
Main Methods:
- Developed a direct normal form decomposition technique.
- Applied the method to a 2 degrees-of-freedom (d.f.) system with quadratic/cubic nonlinearities.
- Extended the expansion to ε^2-order for accurate dynamic behavior capture.
- Analyzed a thin plate model with ε^1-order nonlinearities and internal resonance.
- Utilized continuation software for numerical verification.
Main Results:
- Successfully reduced the order of a 2 d.f. system from 2 to 1 d.f.
- Accurately captured nonlinear dynamic behavior by extending the normal form expansion.
- Demonstrated order reduction and normal form derivation for a system with internal resonance.
- Validated results against numerical computations.
Conclusions:
- The direct normal form decomposition is effective for simplifying complex nonlinear oscillator systems.
- The method facilitates order reduction and accurate modeling of nonlinear dynamics.
- It provides a robust approach for analyzing systems with internal resonances and varying nonlinearity strengths.
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