Abstract

A web (continuum) traveling in a flow of ideal fluid between two fixed supports with a constant velocity and performing transverse vibrations is considered by modeling the web as an isotropic type elastic panel. The fluid flow is considered as a potential flow. The web transverse vibration process is analyzed taking into account both material elasticity and the fluid-structure interaction between the traveling material and the surrounding flowing fluid. It is supposed that the actuator system is used for suppression of occurring transverse vibrations. An optimization approach based on the modern control theory and calculus of variations is proposed for determining the optimal suppressive actions at a given time interval. The quality of suppression vibration process is evaluated by means of the functional depending on displacements and velocities at the terminal time. The example (carried out in an analytical way) illustrating all basic stages of finding of optimal vibration suppression is presented.

摘要

通过将腹板建模为各向同性弹性面板，考虑在理想流体流中以恒定速度在两个固定支撑之间移动并执行横向振动的腹板（连续体）。流体流动被认为是潜在流动。腹板横向振动过程的分析同时考虑了材料弹性和行进材料与周围流动流体之间的流固耦合。假定致动器系统用于抑制发生的横向振动。提出了一种基于现代控制理论和变分法的优化方法，用于确定给定时间间隔内的最佳抑制动作。抑制振动过程的质量通过依赖于终端时间的位移和速度的泛函来评估。示例（以分析方式进行）说明了寻找最佳振动抑制的所有基本阶段。