Finite element system of elastic structure

Abstract

The article deals with the problems of controllability, observability and stabilizability of an elastic-structural system treated by the finite element method. The results obtained here agree with that obtained in distributed parameter-system model, nevertheless, they are more convenient than those in carrying out the computation with a computer, at the same time the method appears much easier that the conventional one. In section one, the system's controllability and observability are studied and some conditions which are easier to be justified by computer are given. In section two, the problem of stabilizing an elastic object by the use of linear feedback is fully discussed. As the attained results there show that, so far as an elastic-structural system is concerned, it is possible to assign arbitrary frequencies of vibration only by the use of displacement feedback, however, it is impossible to stabilize the system while the system is completely controllable. While the velocity feedback can stabilize the system, but its ability is limited. The case of rigid body motion involved in the system equation has also been discussed. In section three, the control of a straight beam is treated by the finite element method. The whole system of a beam can be decomposed into four irrelevant subsystems of tension-compression, torsion, bending in two directions, their controllability and observability are also analyzed respectively. The controllability and observability of segment-shaped beam are discussed in the end.