Control of vibrations in beams using prescribed holes and piezoelectric actuators

Abstract

The implementation of vibration control methods is increasingly necessary when it comes to the use of flexible structures in mechanical projects. The appearance of vibrations in structures, through movement, always deserves the attention of the designers, as they can be unwanted when they affect the structure’s useful life or damage its surroundings. With that, this work offers the use of two types of control in a beam fixed on one side. The first technique applied was prescribed holes, which is a type of passive control where material is removed from the structure so that it has holes. The vibration, when it enters this hole, is trapped inside, not reflecting the wave to the rest of the beam. The second applied technique was the implementation of a Linear Quadratic Regulator (LQR) to operate a piezoelectric actuator. The formulation and modeling of the structure was made based on the Finite Element Method (FEM), being used for the discretization of the structure domain. The vibrations were analyzed through modal analysis. Vibration amplitude comparisons were made for the first and second modes, considering one, two and three prescribed holes in the beam. Computer simulations were carried out to show the efficiency of the proposed control techniques. The results of these simulations are presented and discussed.