Optimal vibration control of an isotropic beam through boundary conditions

Abstract

An isotropic structure modelled as a Timoshenko beam is considered for the optimal vibration control problem. The beam model to be controlled is described by a distributed parameter system with the selection of Timoshenko?s shear correction factor. Control of the vibrations is achieved through a function placed on the boundary conditions. The performance index which seeks to be minimized indicates that the goal is to minimize the magnitude of performance measure without consuming control effort in large quantities. It is shown how to derive the optimal control function using Pontryagin?s principle that turns the control problem into solving optimality system of PDE with terminal values. Wellposedness of the optimal solution on the control set is presented and controllability of the problem is analyzed. Numerical simulations are given in terms of computer codes produced in MATLAB? in the forms of graphical and tables in order to show the applicability and effectiveness of the control acting on the boundary conditions.