|
|
|
| Periodic Solutions Initiation and Evolving of a Symmetrical Double-Potential Well Duffing System with Forced Harmonic Excitation |
| XIAO Shifu, CHEN Hongyong, NIU Hongpan
|
| Institute of Systems Engineering, CAEP, Mianyang 621999, China |
|
|
|
|
Abstract For a Duffing equation with symmetrical double potential well, which is derived from a self-rotating mass-spring pendulum with three-order nonlinear stiffness, the periodic solutions type, initiation mode and evolving behavior adapting to the frequency of excitation are investigated meticulously by Harmonic Balance Method and numerical simulation. Some rewarding results are obtained. This Duffing system has local periodic solutions in the region near its equilibrium point and many global periodic solutions with symmetry, antisymmetry and dissymmetry. The global periodic solutions derive from saddle-node bifurcation. The local periodic solutions and the dissymmetrical global periodic solutions evolve directly into chaos passing through double-periodic bifurcation. The symmetrical global 1-periodic solutions evolve into chaos through passing the double-periodic bifurcation only after losting their symmetry by symmetry-breaking, and the antisymmetric global 3-periodic solutions evolve into quasi-periodic solutions through passing the triple-periodic bifurcation also after lost their symmetry by antisymmetry-breaking.The studies help to raise the understanding of the nonlinear phenomenon and the evolution of solutions of the Duffing equation.
|
|
Received: 13 June 2017
Published: 10 January 2019
|
|
|
|
|
|
| No related articles found! |
|
|
|
|
