Controle de vibrações em vigas usando o efeito de buracos negros acústicos e atuadores piezelétricos

Abstract

The reduction of cost in the construction of a structure is desired by designers. However, in this way, structures become lighter and less rigid, and consequently more vulnerable to unwanted vibrations. For this reason, the implementation of vibration control methods is necessary when considering flexible structures in mechanical projects. In view of that, this work proposes the use of two types of vibration control in a beam, passive and active, to obtain an efficient design. Passive control does not require the use of energy for control, instead devices and/or techniques that absorb, isolate or dissipate vibration energy are added to the system. For this control, it is proposed to use the effect of Acoustic Black Holes (BNAs), since this effect predicts the insertion of prescribed holes in the structure, causing the vibration to be restricted inside the hole(s), and only a small part is transmitted to the rest of the structure. On the other hand, active control requires a set of sensors and actuators coupled to or inserted into the structure. So, to produce an active control, one must choose a suitable actuator and implement a controller for it. The actuator that will be used in this work is a piezoelectric material, and the chosen controller is the Linear Quadratic Regulator (LQR). The piezoelectric actuator is employed to generate an oscillatory movement contrary to the existing movement in the structure, so that vibrations be controlled. In order to solve the control problem, the movement of the structure is initially modeled, which in continuum mechanics problems, is usually obtained by solving a system of partial differential equations. Since the analytical resolution of these equations can be complicated, the Finite Element Method is used to discretize the structure domain. Therefore, taking into account the mentioned aspects, the objective of this work is to simulate the dynamics and vibration control in beam-type structures, using the ABHs technique and to use an LQR controller to operate a piezoelectric actuator. Another purpose is to analyze the vibration amplitudes, through the Fourier Transform, in order to verify the decrease in the vibration amplitude generated by the insertion of holes. The results of these simulations will be presented and discussed.