In this paper, we consider absolute stability for an axially moving Kirchhoff beam under nonlinear boundary feedback controls. The nonlinear boundary control which satisfies a slope-restricted condition is a negative feedback of the transverse velocity at the right eyelet of the moving beam. First, the well-posedness of the resulting closed-loop system is established by means of the Faedo–Galerkin approximation combined with some priori estimates. By invoking the integral-type multiplier method, the exponential stability of the closed-loop is developed. The numerical simulations by the finite element method are presented to demonstrate the effectiveness of the proposed controller.

在本文中，我们考虑了在非线性边界反馈控制下轴向移动的基尔霍夫光束的绝对稳定性。满足斜率限制条件的非线性边界控制是运动梁右眼处横向速度的负反馈。首先，通过Faedo-Galerkin逼近结合一些先验估计来建立所得闭环系统的适定性。通过调用积分型乘法器方法，开发了闭环的指数稳定性。通过有限元方法进行了数值模拟，以证明所提出控制器的有效性。