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Chaos analyses of visco-hyperelastic cylindrical shells based on improved Melnikov method
Ran Wang1,2, Ming E Yin1, Zhentao Zhao3
1School of Mathematics, Liaoning Normal University, Dalian 116029, China.
Chaos (Woodbury, N.Y.)
|March 14, 2025
Summary
This study models large-amplitude oscillations in soft cylindrical shells using a Zener rheological model. An improved Melnikov method analyzes chaos thresholds in visco-hyperelastic shells under harmonic excitation.
Area of Science:
- Solid Mechanics
- Nonlinear Dynamics
- Materials Science
Background:
- Soft-material structures exhibit large deformation and infinite degrees of freedom, necessitating advanced modeling.
- Understanding the dynamic behavior of these structures is crucial for theoretical and applied research.
Purpose of the Study:
- To investigate the large-amplitude oscillation of cylindrical shells under harmonic excitation.
- To develop and validate a method for analyzing the nonlinear dynamics of visco-hyperelastic shells.
- To determine the chaos threshold of the system.
Main Methods:
- Utilizing the Euler-Lagrange equation to derive nonlinear ordinary differential equations for radially symmetric motion.
- Employing the Zener rheological model within the Rivlin-Saunders hyperelastic framework.
- Developing an improved Melnikov method based on the small perturbation of the Maxwell unit for dynamic analysis.
- Performing numerical verification of the proposed analytical method.
Main Results:
- Governing equations for the nonlinear system were established, incorporating material viscosity.
- Bifurcation behaviors and natural frequencies were analyzed for zero- and infinite-viscosity models.
- The improved Melnikov method effectively analyzed the dynamic behavior of visco-hyperelastic shells.
- The chaos threshold of the system was successfully determined.
Conclusions:
- The study provides a robust framework for analyzing the nonlinear dynamics of soft-material cylindrical shells.
- The developed improved Melnikov method is a valuable tool for predicting chaos in visco-hyperelastic systems.
- Findings contribute to the theoretical understanding and practical application of soft-material structures.
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