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Published on: September 11, 2019
Transient tumbling chaos and damping identification for parametric pendulum.
Bryan Horton1, Marian Wiercigroch, Xu Xu
1Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Kings College, Aberdeen AB24 3UE, UK.
Summary
This study introduces a new method for calculating damping in parametric pendula, accurately modeling chaotic motions. The technique combines viscous and Coulomb damping for improved system dynamics representation.
Area of Science:
- Mechanical Engineering
- Nonlinear Dynamics
- Vibrational Analysis
Background:
- Parametric pendula exhibit complex behaviors, including transient tumbling chaotic motions.
- Accurate modeling of damping is crucial for understanding and predicting these dynamics.
- Existing methods may not fully capture the combined effects of different damping types.
Purpose of the Study:
- To develop a simple, effective, and generally applicable technique for determining damping in parametric pendula.
- To create a model that accurately represents system dynamics, including chaotic motions.
- To validate the proposed damping identification procedure against experimental data.
Main Methods:
- Assumed system dynamics are modeled by a combination of viscous and Coulomb damping.
- Developed a parameter identification procedure based on the combined damping model.
- Compared numerical and experimental time histories of free oscillations using the identified parameters.
Main Results:
- The proposed model accurately describes the qualitative features of experimentally observed transient tumbling chaotic motions.
- Numerical results closely corroborate experimental transient chaotic trajectories.
- The identified parameters from the new method show good agreement with the classic logarithmic decrement technique.
Conclusions:
- The developed technique provides a robust method for determining damping in parametric pendula.
- The model's ability to represent chaotic dynamics validates its effectiveness.
- The close agreement between theoretical and experimental results underscores the method's reliability.
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