Optimal vibration control of an isotropic beam through boundary conditions

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