具摩擦-碰撞的复杂边界动力学系统算法研究

Study on complex-boundary dynamic system with friction and impact

结合含摩擦的二维动力学系统的非线性响应解析解,通过引入状态变量转换不同运动状态的求解算法,提出了一种适用复杂边界的具摩擦碰撞的系统响应算法,并利用曲线边界和混合边界进行了精度和稳定性验证.结果表明:与传统算法相比,该算法能以更高的精度和稳定性计算系统的滑移、黏滞、黏/滑转换和碰撞响应,并克服误差累积现象;趋于复杂的边界会导致系统通向稳态响应的时间增大,并改变系统的稳态周期.

With combining the analytical solution of the nonlinear responses of the two-dimension dynamic system with friction,a new algorithm for the complex-boundary dynamic system with friction and impact was proposed through introducing the state variable to transform the solving algorithm of different motion states.Then the precision and stability of the new algorithm were verified by using curved boundary and hybrid boundary.The results clearly show that this algorithm has higher precision and stability for obtaining slip,stick,stick-slip transition,slip-stick transition and impact than the traditional algorithm and has no error accumulation.The increasingly complex boundary will lead to the increase of the time for the system to reach the steady state and change the steady-state period of the system.