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An optimization approach to establish dynamical equivalence for soft and rigid impact models
Bo Tian1, Shan Yin1, Joseph Páez Chávez2,3
1Exeter Small-Scale Robotics Laboratory, Engineering Department, University of Exeter, Exeter EX4 4QF, United Kingdom.
Chaos (Woodbury, N.Y.)
|July 1, 2024
Summary
This study presents a computational method to create equivalent dynamical responses in impacting systems with soft and rigid constraints. The approach accurately models impacts, offering advantages over existing techniques for physical property identification.
Area of Science:
- Computational dynamics
- Nonlinear systems analysis
- Mechanical engineering
Background:
- Oscillatory impacting systems often involve complex interactions under different constraint types (soft vs. rigid).
- Accurately modeling these impacts is crucial for predicting system behavior and identifying physical properties.
- Existing methods may face challenges with discontinuities and accuracy, especially with soft constraints.
Purpose of the Study:
- To develop a computational approach for establishing equivalent dynamical responses in oscillatory impacting systems.
- To determine stiffness and damping parameters for soft constraints that match the behavior of rigid constraints.
- To provide a more accurate and convenient method for analyzing impacting systems.
Main Methods:
- An adaptive differential evolution algorithm coupled with the Metropolis criterion was employed.
- The algorithm determined soft constraint parameters (stiffness, damping) based on a prescribed coefficient of restitution for the rigid constraint.
- Equivalent dynamical responses were evaluated based on energy dissipation and contact time duration.
Main Results:
- The two models (soft and rigid constraints) showed nearly identical dynamical responses in bifurcation diagrams for large restitution coefficients.
- Discrepancies were observed between the models when using a low restitution coefficient.
- Numerical tests confirmed the proposed method's enhanced effectiveness compared to prior techniques.
Conclusions:
- The developed computational method effectively establishes equivalent dynamical responses for impacting systems with soft and rigid constraints.
- The approach offers improved accuracy and convenience for analyzing impacting systems, particularly in experimental identification of impact surface properties.
- This method mitigates potential inaccuracies associated with handling discontinuities in numerical integration during impact events.
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