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一根轴向运动弦的横向振动稳定性是通过随时间变化的,使用对边界的横向运动或者外部的边界力的控制来实现的。平移弦的全部机械能量是一个亚普诺夫函数,边界控制法则被设计用于分散弦的整个振动能量在左侧或者右侧的边界。一种最佳的反馈可通过降低受边界条件影响的能量获得,是边界控制的张力与入射波的传播速率的比值。同样,所需的最大时间用来稳定系统中的最初的扰动造成的全部振动能量,就是波在弦的跨度范围内在撞击边界之前传播所需要的时间。通过能量准则的衰减比率和半群理论的使用,边界控制下的轴向运动弦的渐近线和指数稳定性被分析验证。模拟被用于证实平移弦稳定性的理论预测和最优边界控制。
The lateral vibration stability of an axially moving string is achieved by controlling over time the lateral movement of the boundary or the external boundary force as a function of time. The total mechanical energy of a transposed string is a function of a Probolov and the law of boundary control is designed to disperse the entire vibrational energy of a chord at the left or right side of the boundary. An optimal feedback can be obtained by reducing the energy affected by the boundary conditions, which is the ratio of the boundary-controlled tension to the incident wave propagation rate. Again, the maximum amount of time required to stabilize the total amount of vibrational energy caused by the initial disturbance in the system is the time it takes for the wave to propagate before striking the boundary within the span of the string. The asymptotic and exponential stability of the axially moving chord under boundary control is verified by the attenuation criterion of energy criterion and the use of semigroup theory. Simulation was used to confirm the theoretical prediction of translational string stability and optimal boundary control.