Passive Damping of Longitudinal Vibrations of a Beam in the Vicinity of Natural Frequencies Using the Piezoelectric Effect

Abstract

To significantly reduce the amplitude of longitudinal vibrations of the beam in the vicinity of its natural frequencies, a fundamentally new method of damping vibrations is used. For this purpose, the beam surfaces are covered with layers of polarized piezoceramics with a strong piezoelectric effect. We will use two types of electrical conditions on the electrodes of the piezoelectric layers: short-circuited electrodes and disconnected electrodes. On short-circuited electrodes, the electric potential is zero. As a result of the piezoelectric effect, an electric charge appears on the disconnected electrodes when the beam is deformed. The electroelastic state of a beam with different electrical conditions is described by different boundary value problems. A new approach to damping vibrations in the vicinity of natural frequencies is based on the following rule for controlling the dynamic characteristics of a structure: when the beam vibration frequency approaches its natural vibration frequency, we change the electrical conditions on the electrodes of the piezoelectric layers, thereby changing the spectrum of its natural frequencies. Let, for example, the vibration frequency of a beam with short-circuited electrodes approach its natural frequency. In this case, the amplitudes of the sought quantities grow without limit. The natural frequency spectrum of a beam with disconnected electrodes will differ from the spectrum of a beam with short-circuited electrodes. As a result, the amplitudes of the sought quantities will decrease. It is shown that the efficiency of vibration damping can be significantly increased by choosing the direction of the preliminary polarization of the piezoelectric material and the location of its electrodes. Numerical examples are given that demonstrate the effectiveness of the proposed method. The advantage of the method lies in its simplicity and the low cost of the piezoelectric material, which serves as a non-inertial damper.