Passive damping of bending vibrations of a beam near its resonance frequencies using piezoeffect

Introduction. The paper describes a fundamentally new method of passive damping of vibrations of a structure in the vicinity of its resonant frequencies. The method is based on the use of piezoeffect. For this purpose, piezoelectric elements are added to the structure, which serve as energy converters (mechanical energy into electrical energy and vice versa).

Materials and methods. Piezoelectric elements are polarized piezoceramics with electrodes. Two different types of electrical conditions on the electrodes are used for passive vibration damping: a) the electrodes are short-circuited and b) disconnected electrodes. By changing the electrical conditions on the electrodes, we change the boundary value problem. The spectrum of natural frequencies of the boundary value problem for a structure with short-circuited electrodes differs from the spectrum of natural frequencies of the boundary value problem for the same structure with disconnected electrodes. The idea of the method is as follows: let the vibration frequency of the structure with short-circuited electrodes approach its resonant frequency. Let us disconnect the electrodes, thereby changing the spectrum of natural frequencies of the structure. The vibration frequency, which is the resonant frequency for the structure with short-circuited electrodes, will not be resonant for the structure with disconnected electrodes. As a result of changes in electrical conditions, the amplitudes of the required quantities (deflection, bending moment, shearing force, etc.) will decrease significantly. To evaluate the effectiveness of passive vibration damping, a simple formula is proposed.

Results. For a beam undergoing forced bending vibrations in the vicinity of its resonant frequency, calculations were performed using the proposed method of passive vibration damping, tables of vibration damping efficiency in the vicinity of resonant frequencies were obtained, and graphs are plotted. The possibility of increasing the efficiency of vibration damping by choosing the direction of pre-polarization of the piezoelectric material, the location of the electrodes and their number was investigated.

Conclusions. The results of studies of passive vibration damping near resonant frequencies using the piezoeeffect confirmed the simplicity and reliability of the proposed method.

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