Influence of lattice symmetry on ultrasound transmission through plates with subwavelength aperture arrays

Abstract

We study the transmission of sound waves through aluminum plates perforated with square and triangular hole arrays. We demonstrate both theoretically and experimentally that lattice symmetry affects the position of the Wood anomalies and the width of the transmission peaks. The angle and frequency dependence of sound transmission through perforated plates are thoroughly discussed. Finally, we observe unexpected anisotropic behavior in the long-wavelength Lamb-mode bands of perforated plates. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3196330͔Artificial metamaterial structures can exhibit extraordinary properties that are not found in naturally occurring systems. For example, photonic 1 and phononic 2 crystals can block the propagation of light and sound within frequency band gap regions. Other astonishing properties such as negative refraction have been recently demonstrated. 3 In this context, much attention has been paid to metallic membranes perforated with subwavelength periodic hole arrays, 4-6 for which extraordinary optical transmission ͑EOT͒ has been observed, in contrast to the poor transmission of individual apertures. 7 The last decade has witnessed many efforts intended to clarify the physical origin and the interpretation of EOT, as well as to explore applications to sensing and optical processing. 8,9 The comparison between optics and acoustics has undergone successive revision after it was first discussed in the nineteenth century. [10][11][12] Recently, some of the ideas developed for electromagnetic waves have been transferred to acoustics, [13][14][15][16] emphasizing the similarities between subwavelength transmission in both cases. [13][14][15] However, intrinsic differences separate the two kinds of waves. For example, and in contrast to optics, acoustic waves do not present a cutoff wavelength for the existence of guided modes. 10,11,16,17 Also, sound can be extraordinarily shielded near the onset of diffraction. 18 Furthermore, intrinsic acoustic modes ͑Lamb and Scholte-Stoneley waves͒ are conspicuous in thin plates, quite different from optics. 19 Finally, we have recently shown 18 that perforated plates are highly transparent to sound for both periodic and random distributions of holes.In this letter, we study sound transmission through periodically perforated plates with square and triangular distributions of holes, using both theory and experiment. The plates are immersed in water. The periodic structures considered here consist of square and triangular periodic arrangements of circular holes, drilled on 200-mm-wide, 350-mmlong aluminum plates. The holes have a diameter d = 3 mm. Both square and triangular lattices have a period a = 5 mm.Three different plate thicknesses are investigated: t =2, 3, and 5 mm. In order to perform ultrasonic transmission measurements, we use the well-known ultrasonic immersion technique. 18 The angle of incidence is varied by rotating the plate sample from 0°to 60°in steps of 1°. Moreover, we calculate transmission intensities by rigorously solv...

Sound transmission through plates perforated with two periodic subwavelength hole arrays

“…Estrada et al [16] reported that periodically perforated aluminium plates immersed in water can achieve lower ultrasonic transmission values than homogeneous plates. The influence of the filling fraction of holes and the lattice geometry in the transmission properties has also been studied [17,18]. It has been also demonstrated [19] that the complex interplay between Fabry-Perot resonances inside the holes, lattice resonances in periodic arrays, and elastic Lamb modes governs the transmission properties of perforated plates.…”

On the Role of the Geometrical Parameters in the Ultrasonic Transmission Through Plates with Subwavelength Holes Arrays

“…For a square array, the hole filling fraction, ff, is given by between results obtained for both square and triangular lattices reveals that the transmission dips corresponding to Wood anomalies appear at lower frequencies in the square lattices [19]. As the filling factor of the square lattice is lower than triangular one, the transmission peaks of the square lattice geometries are narrower than the triangular ones.…”

“…The role of the geometrical parameters of the hole array is important in the ultrasonic transmission through perforated plates and has been subject of several studies [18][19][20][21][22]. The purpose of this paper is to describe and summarize theoretically the set of geometrical parameters that affect the ultrasonic transmission through subwavelength holes arrays.…”

Ultrasonic transmission through periodically perforated plates

“…In fact, Lamb waves are guided waves that propagate through plates and, as demonstrated in [67,68], they are definitely linked with perforated plates. Recent results on high transmission have been also observed by He et al [69] for a corrugated brass plate immersed in water without the need of any opening.…”

“…Indeed, it has been found that the geometrical anisotropy of the arrays leads to anisotropy of the modes phase-velocity [68] even if the solid is isotropic (aluminum in this case).…”