Abstract
Piezoelectric shunting arrays are employed to control the elastic wave propagation in L‐shape beams. Unlike straight beams where longitudinal and flexural waves usually propagate independently, these waves are coupled in an L‐shape beam. Based on transfer matrix method and Bloch theorem, dispersion curves and vibration transmissibility are evaluated and analyzed. A locally resonant gap is produced on the flexural and longitudinal waves, respectively, whose locations are nonoverlapped if the shunt damping is void. However, the longitudinal wave band gap can be completely overlaid by the flexural one when a proper shunting resistance is involved. With the decreasing of shunting inductance, the locations of longitudinal and flexural wave gaps both go up to higher frequencies which agree with the variation of resonant frequencies, but they are less affected by shunting resistance. As the resistance increases, the width of the band gaps grows, whereas the attainable maximum attenuation within the band gaps shows a significant decrease. Also, finite element simulations are performed to validate the numerical predictions, which demonstrate that the resulting transmissibility of displacements agree well with the band gaps.
Highlights
Flexible structures are extensively applied in large aerospace products, which represents a trend as well as great challenge work for industrial and academic communities
In the past two decades, elastic wave propagation in periodic composite materials or structures, named phononic crystals (PCs), has received great attention [6,7,8,9]. e primary property of PCs is band-gap behavior, i.e., the propagation of elastic waves whose frequencies lie in the band gap will be forbidden. e seminal work of Liu et al sparked passionate research interest in locally resonant (LR) PCs [8]. ey examined three-dimensional PCs consisting of cubic arrays of coated lead spheres immersed in an epoxy matrix and proposed a new type of band-gap formation mechanism, i.e., locally resonant band gap
One locally resonant gap is induced in longitudinal and flexural waves, respectively. e band gap of longitudinal wave is a pure attenuation zone (PAZ) ranging from 1528 Hz to 1558 Hz, in which the propagation constant is a pure real number. e maximum attenuation occurs at the lower bounding frequency of the band gap, which is a typical feature observed in conventional locally resonant crystals
Summary
Flexible structures are extensively applied in large aerospace products, which represents a trend as well as great challenge work for industrial and academic communities. Erefore, much effort has been exerted on vibration mitigation of flexible beams. This vibration or elastic wave propagation in the beam-type structures attracts significant attention, especially when the vibrationless environment is desired, such as payload of high resolution satellites and platform for high accuracy experiments. In the past two decades, elastic wave propagation in periodic composite materials or structures, named phononic crystals (PCs), has received great attention [6,7,8,9]. Ey examined three-dimensional PCs consisting of cubic arrays of coated lead spheres immersed in an epoxy matrix and proposed a new type of band-gap formation mechanism, i.e., locally resonant band gap. Acoustic metamaterials are generally regarded as materials with artificial microstructures that possess unusual physical properties such as band gaps, negative refraction, acoustic cloaking, etc
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