ИСТИНА

In many applications of axially moving materials, such as paper making processes, printing presses and belt drives, there is a demand for driving or running the system at fast speed and at the same time, avoiding damages and vibrations. In this context in this paper the translation movement of a thermoelastic web (panel) performing transverse vibrations caused by initial disturbance is considered. It is supposed that the web moving with a constant translation velocity is described by the model of a thermoelastic panel (beam) with simply supported edges of the examined span. The problem of the optimal suppression of transverse vibrations of a multispan panel (web) supported at discrete points is formulated with consideration of forces applied to the web. In order to solve the optimization problem, we use modern methods developed in the control theory of dis-tributed parameter systems described by partial differential equations. With the assump-tion of initial disturbances of the transverse displacements and velocities of the web, an efficient disturbance suppression algorithm is proposed. It is based on obtaining and using necessary optimality conditions and emerging dynamic partial differential equations. The equations describe both the vibration processes of the moving thermoelastic web (direct problems) and certain processes with adjoint variables introduced (adjoint problems). It is shown, that the direct and the adjoint problems can be solved using the Galerkin method. An example illustrating the main steps of solving the problem of optimal suppression of vibrations is presented. https://virtual.wccm-eccomas2020.org/