一类推广的干摩擦问题周期解的存在性

The Existence of Periodic Solutions of a Kind of Popularized Dry Friction Problem

为了得到干摩擦问题存在周期解的判断方法,利用微分包含理论对系统+k^2x+μSngp(t)+T(t)a.e.进行了讨论.在周期外力p(t)周期等于固有周期2π/R的情形下得到了周期解存在的充要条件,在周期外力p(t)周期不等于固有周期整数倍2nπ/R的情形下得到了周期解存在的充分条件.

In order to explore a method to judge the existence of periodic solution for dry friction problem, the theory of differential indusion is used to discuss this problem based on the system x＋k^2x＋μSngx p（t）＋ρτ（t） a.e.. the sufficient and necessary condition for the existence of periodic solution is obtained when the period of outside force p（t） is equal to 2π/R, and the sufficient condition for the same problem is also obtained when the period of p（t） is unequal to 2nπ/R.