一类几何非线性干摩擦振子的分岔研究

BIFURCATION OF A CLASS OF GEOMETRICALLY NONLINEAR DRY-FRICTION OSCILLATORS

考虑了一个几何非线性干摩擦振子.介绍了如何利用事件驱动方法模拟该类具有不连续矢量场的Filippov系统,所介绍的算法是基于Filippov方法的扩展,从而可以精确地检测出滑动运动区域的入口和出口.用了两种不同的Poincaré截面,表示了随参数变化,不同类型含滑动过程的周期运动之间的转化过程,研究了不同类型的滑动分岔和周期倍化分岔,并发现了在倍化过程中多滑动段的存在.

The dynamic behaviors of a geometrically nonlinear oscillator with dry friction were studied by the event-driv⁃en method.Firstly,the geometrically nonlinear dry-friction oscillation system was modeled as a Filippov system.Then,the algorithm based on the event-driven method was introduced to solve the Filippov system with discrete vector field,which could accurately detect the entry and exit of the sliding motion area.Two different kinds of Poincare cross section were used to reveal the transformation process between different types of periodic motions with sliding process as parame⁃ters change.Finally,different types of sliding bifurcation and periodic doubling bifurcation were studied,and the exis⁃tence of multiple sliding segments in the doubling process was found.