Materials Research Centre, Indian Institute of Science, Bangalore 560012, India.
Chaos. 2013 Mar;23(1):013116. doi: 10.1063/1.4790845.
We develop a unified model to explain the dynamics of driven one dimensional ribbon for materials with strain and magnetic order parameters. We show that the model equations in their most general form explain several results on driven magnetostrictive metallic glass ribbons such as the period doubling route to chaos as a function of a dc magnetic field in the presence of a sinusoidal field, the quasiperiodic route to chaos as a function of the sinusoidal field for a fixed dc field, and induced and suppressed chaos in the presence of an additional low amplitude near resonant sinusoidal field. We also investigate the influence of a low amplitude near resonant field on the period doubling route. The model equations also exhibit symmetry restoring crisis with an exponent close to unity. The model can be adopted to explain certain results on magnetoelastic beam and martensitic ribbon under sinusoidal driving conditions. In the latter case, we find interesting dynamics of a periodic one orbit switching between two equivalent wells as a function of an ac magnetic field that eventually makes a direct transition to chaos under resonant driving condition. The model is also applicable to magnetomartensites and materials with two order parameters.
我们开发了一个统一的模型来解释具有应变和磁序参量的一维带状材料的驱动力学。我们表明，在存在正弦场的情况下，作为直流磁场的函数，模型方程在其最一般的形式中解释了一些关于驱动磁致伸缩金属玻璃带的结果，例如倍周期通向混沌的路径，作为固定直流场的正弦场的函数的准周期通向混沌的路径，以及在存在附加的低幅度近共振正弦场时诱导和抑制混沌。我们还研究了低幅度近共振场对倍周期途径的影响。模型方程也表现出具有接近单位的指数的对称恢复危机。该模型可以用来解释在正弦驱动条件下的磁弹性梁和马氏体带的某些结果。在后一种情况下，我们发现作为交流磁场的函数的两个等效势阱之间的周期性单轨道切换的有趣动力学，最终在共振驱动条件下直接过渡到混沌。该模型也适用于磁马氏体和具有两个序参量的材料。
