Broadband Vibration Attenuation Using Hybrid Periodic Rods

Abstract

This paper presents both theoretically and experimentally a new kind of a broadband vibration isolator. It is a table-like system formed by four parallel hybrid periodic rods connected between two plates. The rods consist of an assembly of periodic cells, each cell being composed of a short rod and piezoelectric inserts. By actively controlling the piezoelectric elements, it is shown that the periodic rods can efficiently attenuate the propagation of vibration from the upper plate to the lower one within critical frequency bands and consequently minimize the effects of transmission of undesirable vibration and sound radiation. In such a system, longitudinal waves can propagate from the vibration source in the upper plate to the lower one along the rods only within specific frequency bands called the "Pass Bands" and wave propagation is efficiently attenuated within other frequency bands called the "Stop Bands". The spectral width of these bands can be tuned according to the nature of the external excitation. The theory governing the operation of this class of vibration isolator is presented and their tunable filtering characteristics are demonstrated experimentally as functions of their design parameters. This concept can be employed in many applications to control the wave propagation and the force transmission of longitudinal vibrations both in the spectral and spatial domains in an attempt to stop/attenuate the propagation of undesirable disturbances.

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

“…The proposed MTMM combines the Love rod theory [27,28], [29] (pp. 139-142), [30], the method of reverberation-ray matrix (MRRM) [5] and the transfer matrix method (TMM) [14][15][16][17][18][19]21,22,25] to analyze the dispersion curves by considering the Floquet-Bloch theorem [31,32] and to calculate the transmission spectra. The Love rod theory is adopted to model the longitudinal wave motions in the piezoelectric, elastic and electrode constituent rods of the unit cell.…”

“…After Baz [9] proposed the seminal concept about active control of periodic structures, Singh et al [14] illustrated the effectiveness of the periodic rod with piezoelectric actuators by analyzing the frequency bands and responses with the TMM. Asiri et al [15] and Asiri [16,17] predicted the attenuation of longitudinal waves in periodic binary piezoelectric-elastic composite rods using the combination of spectral element method and TMM, and validated their analysis by experiment. Using the same TMM, Li et al [18] and Wang et al [19] analyzed the localization of frequency bands in randomly disordered periodic binary piezoelectric-elastic rods without and with initial stress, respectively.…”

“…The influence of the elastic rod inserts on the band structures is not clear enough. (3) Two electrical control manners in general have been proposed, i.e., setting the external voltage through the feedback control gain [14][15][16][17] and tuning the external electric capacity [18][19][20][21][22][23][24][25][26], since the electric-open and electric-short conditions correspond to zero and infinity electric capacities, respectively. The connection and difference of the influences of the applied feedback control and of the applied electric capacity on the frequency bands are not known.…”

“…Among these smart periodic rods, the periodic piezoelectric rods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] have particularly been paid more attention, because the piezoelectric materials are widely used and the electric field is comparatively easier to control. Thus far, two kinds of rod-type piezoelectric phononic crystals have been presented to actively control longitudinal-wave bands via electromechanical coupling.…”

“…Therefore, rod-type phononic crystals containing smart material components have been presented in order to control the longitudinal waves in an active mode. Their frequency bands can be adjusted by tuning the temperature [6,7], magnetic [8] or electric [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] field to suit the external excitations.…”