Ultrasonic transmission through plates perforated with compound hole arrays

Abstract

Numerical results obtained under the rigid-solid assumption are presented for compound arrays as a function of both parallel-to-plate wave-vector and frequency. Transmission minima arising from the interference between hole resonances interact with Wood anomalies. In addition, preliminary results on underwater ultrasound transmission measurements through a plate perforated with a rectangular hole array employing single point and synthetic aperture technique are presented.In the last years, extraordinary optical transmission through a metallic film perforated with subwavelength apertures [1] has received attention, not only due to the rich physics behind the phenomenon but also because of its potential application in optics [2]. Recently, due to the wave nature of sound, the ideas initially developed for electromagnetic waves have been extended to the field of acoustics and ultrasonics. Sound transmission through arrays of subwavelength apertures has been investigated both theoretically and experimentally. First studies focused in the physics of resonant transmission [3]-[6], extraordinary sound screening [7], [8] and Lamb wave-hole resonance interaction [9], [10]. Fig. 1. Diagram of the perforated plate unit-cell and the incident wave. The perforated plate is characterized by a period a, a hole diameter d, and a plate thickness h. The incident wave having a wave-vector k 0 has a parallel to the plate component given by k .Besides the physical phenomena, the implications of these results could have an impact in the design and operation of phononic plate-based sensors [11]. Thus, different arrangements of holes could provide alternative ways to influence the transmission spectra of perforated plates. Due to its simplicity, rigid-solid assumption [12], [13] is used to calculate the sound transmission through a compound hole array [14].The basic geometry of a simple hole array in a plate unitcell is depicted in Fig. 1 together with the orientation of the incident wave. The proportions of the basic hole array of Fig. 1 are d/a = 0.4 and h/a = 0.5. This primary array is combined with a secondary array having half of the period and hole size so that d /h = 0.4 while d/h = 0.8. This difference in the diameter to thickness ratio is clearly reflected in the individual hole transmission spectra at normal incidence as shown in Fig. 2(a). Not only the resonance frequencies are different, but also the maximum normalized sound transmitted power τ/πr 2 . When arranged periodically ( Fig. 2(b)), the differences in the transmitted sound power τ between both arrays are drastically accentuated. Only one full transmission peak can be observed for the primary array (dark blue curve) besides the one at λ → ∞ which always exists. However, two full transmission peaks are clearly distinguishable for the secondary array (light blue curve). The reason to explain this behavior can be found in the position of the minima, which corresponds to Wood anomalies given by(1) Thus, at normal incidence (k = 0) for the primary array (dark blue curve) w...