Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches

Abstract

Shunted piezoelectric patches are periodically placed along rods to control the longitudinal wave propagation in these rods. The resulting periodic structure is capable of filtering the propagation of waves over specified frequency bands called stop bands. The location and width of the stop bands can be tuned, using the shunting capabilities of the piezoelectric materials, in response to external excitations and to compensate for any structural uncertainty.A mathematical model is developed to predict the response of a rod with periodic shunted piezoelectric patches and to identify its stop band characteristics. The model accounts for the aperiodicity, introduced by proper tuning of the shunted electrical impedance distribution along the rod. Disorder in the periodicity typically extends the stop bands into adjacent propagation zones and, more importantly, produces the localization of the vibration energy near the excitation source. The conditions for achieving localized vibration are established and the localization factors are evaluated for different levels of disorder on the shunting parameters.The numerical predictions demonstrate the effectiveness and potentials of the proposed treatment that requires no control energy and combines the damping characteristics of shunted piezoelectric films, the attenuation potentials of periodic structures, and the localization capabilities of aperiodic structures. The theoretical investigations presented in this paper provide the guidelines for designing tunable periodic structures with high control flexibility where propagating waves can be attenuated and localized.

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

“…In these two electrical boundary cases, the transmission spectra of a finite periodic piezoelectric composite rod consisting of 14 unit cells are also calculated by our MTMM, which are depicted and compared in Figure 5 with the corresponding results by Degraeve et al [20]. In order to compare to the numerical transmission from FEM [20], the ordinate in Figure 5a is specified as 20log 10 ˇˇ1 {rpc`e 2 {αqAT G12 sˇˇ(, where the parameters of PZT-5H are utilized. In Figure 5b, the ordinate is the transmission R computed from T G22 by using Equation (25), for the sake of comparing with the experiment measurements [20].…”

“…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.…”

“…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.…”

“…One kind is formed by periodically bonding shunted piezoelectric patches on the host rod, and the other is shaped through periodically arranging the piezoelectric constituent rods [9]. The attenuation of longitudinal vibrations/waves in rods with periodic shunted piezoelectric patches have been studied by Thorp et al [10], Chen et al [11] and Lossouarn et al [12,13] using the transfer matrix method (TMM). Here, we focus on the longitudinal vibrations/waves in periodically arranged piezoelectric rods.…”

Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network

“…In order to obtain a set of equations equivalent to Eqs. (8), consisting of n single mode piezoelectric shunting systems [10; 11], a coordinate transformation is introduced…”