Vibration control for structural damage mitigation

Abstract

Substantial developments have taken place in the areas of structural health monitoring, wherein, the objective is not only to detect damage but also to determine its size and location across the structure. Often, the damaged structures do not become obsolete unless the damage is severe. Thus, it is important to mitigate the growth of damage and prevent the possibilities of a structural failure. Vibration is an important source of damage growth. Therefore, it is important to control vibrations such that the damage growth is mitigated. Supposing an effect of damage in the structure is said to be mitigated when the vibration response of the damaged structure with control is the same as the vibration response of the undamaged structure, then one of the requirements is that the closed loop eigenstructure of the damaged structure needs to match with the open loop eigenstructure of the undamaged structure. In this framework, this paper uses a linear algebraic technique to assign the undamaged eigenvalues and eigenvectors for the damaged structure with a stiffness loss using a state feedback controller. Through this technique, it is shown that the vibration control using an actuator load can help to mitigate damage growth by reducing the vibration response magnitudes at the damaged structural degrees of freedom, while these magnitudes at other nodes are allowed to increase due to the actuator loads. Vibration control in this sense for structural damage mitigation is illustrated using discrete and continuous structures.