Optimization approach to suppression of vibrations: For axially moving webs in a fluid flow

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.