Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou’s circuit: experimental investigation on beams

Abstract

A periodic array of resistive inductive (RL) shunted piezoelectric (PZT) patches is applied to achieve tunable low-frequency locally resonant (LR) band gaps in a flexible isotropic beam. Each pair of surface-bonded PZT patches is linked to an independent RL circuit. All the circuits are the same and are tuned synchronously. A transfer matrix methodology is used to calculate the frequency range and attenuation properties of the LR band gap. Two main differences are found between the LR band gaps induced by shunting circuits and traditional oscillators. Antoniou's circuits are used to produce large ideal inductances necessary for low eigenfrequencies. The theoretical results are experimentally validated by measuring the harmonic response of the beam. Significant attenuation in the low-frequency LR band gap is observed.

Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network

“…Here is thus added an electrical space dimension, which does not appear with an array of passive resonant shunts that are independently tuned to a single natural frequency [6,7,9,10]. Furthermore, the global capacitance of a unit cell C ε is approximately proportional to A p , the surface area of a piezoelectric patch.…”

“…A classical solution presented in most papers focusing on piezoelectric shunts is to add resistors in series with the inductors [1,4,6,7,8,10,28]. Another less common solution consist in connecting resistors in parallel with the inductors [17,18,19,20].…”

“…Considering onedimensional media, longitudinal wave propagation was firstly analyzed [6,7] and the strategy was then applied to bending waves control [8,9,10]. The classical passive resonant shunts can even be replaced by more broadband active solutions, as amplified resonant shunts [11] or negative capacitance shunts [12,13].…”

Sound transmission loss of metamaterial thin plates with periodic subwavelength arrays of shunted piezoelectric patches

“…Different types of local resonators have been proposed in the design of acoustic metamaterials, such as coated spheres (the coating is elastically soft material while the sphere is high density solid) [1], Helmholtz resonators [3], tensioned elastic membrane carrying mass blocks [7,8,10,14], soft rubber rings encircled with heavy metal rings [5], cantilevered beam-like structures [18,19], resonant piezoelectric shunts [20][21][22][23][24][25][26][27][28][29][30], etc. Compared with other mechanical resonators (or dynamic vibration absorbers), the advantages of piezoelectric resonators include (i) the additional mass introduced by a piezoelectric resonator is always very small, which is of great importance in practical applications; (ii) the performance of a piezoelectric resonator can be tuned very easily and efficiently by only adjusting the properties of shunting circuit, without modifying the structural parameters.…”

“…The resulting periodic structure showed longitudinal wave stop bands which can also be tuned by adjusting the properties of shunting circuit. Subsequently, this concept was later implemented in flexural beams [23][24][25] and plates [21,22,26]. The study of free wave propagation in periodically shunted structures has been extensively carried out and result in many interesting findings.…”