An analytical approach to vibration control is presented, and verified experimentally, for cases where it is undesirable to add actuators with significant mass and stiffness to the structure. A linear coupling control (LCC) strategy is implemented by coupling a second order linear system to an oscillatory plant to create an energy exchange between the two component systems. One of the advantages of this approach is that the control strategy is ultimately capable of controlling unforced and periodically forced vibrations in the plant.
The paper covers the application of the LCC control strategy to a cantilevered beam actuated by piezoceramic actuators. A novel model for the piezoactuated beam is derived for any representative mode, resulting in a set of linearized equations. Also, the model provides flexibility in actuator location and dimensions.
The controller is modelled as a single-degree-of-freedom linear oscillator which is coupled to the plant via linear terms. The result is a small actuating force, or weak coupling between plant and controller which lends itself well to piezoceramic actuation. This system is solved as a linear eigenvalue problem which provides a computationally efficient means of finding the response.
The solution is also verified by means of a finite element (FE) simulation which is carried out for both free and forced vibration. Apart from confirming the theoretical model and closed-form solution, the FE method provides another flexible means in predicting the response of the LCC strategy, the control strategy and the theoretical studies have been verified experimentally.