Complete band gaps and deaf bands of triangular and honeycomb water-steel phononic crystals

Abstract

International audiencePhononic crystals with triangular and honeycomb lattices are investigated experimentally and theoretically. They are composed of arrays of steel cylinders immersed in water. The measured transmission spectra reveal the existence of complete band gaps but also of deaf bands. Band gaps and deaf bands are identified by comparing band structure computations, obtained by a periodic-boundary finite element method, with transmission simulations, obtained using the finite difference time domain method. The appearance of flat bands and the polarization of the associated eigenmodes is also discussed. Triangular and honeycomb phononic crystals with equal cylinder diameter and smallest spacing are compared. As previously obtained with air-solid phononic crystals, it is found that the first complete band gap opens for the honeycomb lattice but not for the triangular lattice, thanks to symmetry reduction

Evanescent waves and deaf bands in sonic crystals

“…In the usual case that a plane wave is normally incident on the phononic crystal, a mode that is antisymmetric with respect to the propagation direction will be deaf. 23 The analogous effect has been also observed in photonic materials. 24,25 In this work we show that deaf bands are ranges of frequencies in which the evanescent modes with the correct symmetry are excited, being the attenuation related to the imaginary part of the Bloch vector.…”

Experimental and Theoretical Investigation of Lowering the Band Gaps of Phononic Crystal Beams through Fluid-Solid Coupling

“…In addition, the sub-matrix for each material in Equation (10) are again derived based on Equations (6)- (9). The degrees of freedom (DOFs) in the middle point connecting to the two beam segments can be eliminated by relating u m to u l and u r (i.e., u m = − S T22a + S T11p −1 (S T21a u l + S T21a u r ) Thus, Equation (10) can be further reduced as…”

“…Due to their ability to forbid propagation of acoustic or elastic waves through band gaps induced by Bragg scattering or local resonance, PCs have received significant attention in the applications of wave manipulation, vibration suppression, wave guiding, and so on [4][5][6]. Although fluid-solid PCs have been one of the research focuses in the past years, in most literature fluid only serves as a constituent or a medium through which acoustic waves propagate [7][8][9][10][11]. Conventionally, accelerometers (e.g., [8,12] for flexural waves) or ultrasonic immersion transmission technique (e.g., [9,11] for longitudinal waves) are used to detect the transmission spectra of phononic crystals.The fluid-structure interaction (FSI) on tuning the band-gap or transmission properties of the PCs are seldom addressed.…”

“…Although fluid-solid PCs have been one of the research focuses in the past years, in most literature fluid only serves as a constituent or a medium through which acoustic waves propagate [7][8][9][10][11]. Conventionally, accelerometers (e.g., [8,12] for flexural waves) or ultrasonic immersion transmission technique (e.g., [9,11] for longitudinal waves) are used to detect the transmission spectra of phononic crystals.The fluid-structure interaction (FSI) on tuning the band-gap or transmission properties of the PCs are seldom addressed. As a promising method for the PCs to adapt to different operation conditions, tuning band gaps through solid-fluid coupling is currently receiving attention.…”

Active wave-guiding of piezoelectric phononic crystals

“…12,13 Under the assumption of the piezoelectric polling in the z direction, one can mainly focus on out-of-plane displacement modes because in-plane modes are not affected by the piezoelectric coupling state. 12 The dispersion curves of the PC with piezoelectrically coupled and decoupled inclusions (will be referred to as the coupled and decoupled PC) calculated by the finite element 18 exist in the coupled PC while both deaf and propagating modes exist in the decoupled PC. Since such deaf modes cannot be excited by incident plane waves, no wave can actually propagate through the coupled PC while the decoupled PC allows an incident plane wave to pass through.…”