论文标题
具有外力干燥摩擦的动力系统的数学公式
Mathematical formulation of a dynamical system with dry friction subjected to external forces
论文作者
论文摘要
我们考虑具有摩擦的一维系统的响应。 S.W. Shaw（《声音与振动杂志》，1986年）引入了静态和动态相的不同系数的设置（也称为棍子和滑动相）。他构造了逐步解决方案，对应于谐波强迫。在本文中，我们表明，变异不平等的理论提供了一种优雅而合成的方法来获得解决方案的存在和独特性，从而避免了逐步的构造。然后，我们将理论应用于具有真实数据的真实结构，并表明该模型非常准确。在我们的情况下，由于温度，强迫运动来自扩张。
We consider the response of a one-dimensional system with friction. S.W. Shaw (Journal of Sound and Vibration, 1986) introduced the set up of different coefficients for the static and dynamic phases (also called stick and slip phases). He constructs a step by step solution, corresponding to an harmonic forcing. In this paper, we show that the theory of variational inequalities provides an elegant and synthetic approach to obtain the existence and uniqueness of the solution, avoiding the step by step construction. We then apply the theory to a real structure with real data and show that the model is quite accurate. In our case, the forcing motion comes from dilatation, due to temperature.
