Abstract
For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of the corresponding phase portraits are identified and analyzed. Under different parameter conditions, exact homoclinic and heteroclinic solutions, periodic solutions, compacton solutions, as well as peakons and periodic peakons, are all found explicitly. © World Scientific Publishing Company.
| Original language | English |
|---|---|
| Article number | 2450039 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 34 |
| Issue number | 3 |
| Online published | 6 Mar 2024 |
| DOIs | |
| Publication status | Published - 15 Mar 2024 |
Funding
This research was partially supported by the National Natural Science Foundations of China (11871231, 12071162, 11701191) and the National Natural Science Foundations of Fujian Province, 2021J01303.
Research Keywords
- bifurcation
- cantilever beam model
- compacton
- homoclinic and heteroclinic solutions
- Nonlinear vibration
- peakon
- periodic peakon
- periodic solution
- singular nonlinear equation