Simultaneous control of the S and A Lamb modes by graded phononic crystal plates

Abstract

A cylindrical optical black hole using graded index photonic crystalsWe propose a theory of gradient index devices in plates that allow the simultaneous control of both S 0 and A 0 Lamb modes. This is in contrast to the existing approaches that are mainly limited to the manipulation of only the lowest A 0 modes. These devices are based on phononic crystal plates, which are studied in the low frequency (homogenization) limit. We demonstrate a direct relationship between the dispersion relation of these two modes in phononic crystal plates that, together with the thickness dependence of the dispersion relation of the A 0 mode, allows their simultaneous control. As a matter of illustration, a flat gradient index lens and a circular Luneburg lens are designed by means of the simultaneous variation of the inclusions' radii and the thickness of the plate. Numerical simulations show that the performance of these devices is good for the two modes in a broadband frequency region and that this approach can be used to design more advanced refractive devices for the total control of guided vibrational modes. Potential applications for the detection of small vibrations and energy harvesting devices are finally discussed. V C 2015 AIP Publishing LLC. [http://dx.

Tunable waveguide and cavity in a phononic crystal plate by controlling whispering-gallery modes in hollow pillars

“…Phononic crystals (PCs) [1][2][3][4], or acoustic band gap materials, constituted of a periodic arrangement of inclusions embedded in a matrix are receiving increasing attention for elastic/acoustic wave control and have found several fields of applications such as waveguiding [5,6], filtering [7], acoustic lensing [8][9][10][11], and fluid sensing [12]. Besides the two-dimensional (2D) infinite crystal and the control of bulk elastic waves, the interest of the phononic community has turned to the control of waves confined on the surface of a half-infinite PC [13,14] or propagating in finite PC plates.…”

Cavity modes Investigation in phononic crystal

“…Currently, and by their extraordinary properties, the phononic crystals and arouse considerably the interest of the researchers (Capdeville et al, 2015), (Wang et al, 2017). These structures are made by periodic repetition of inclusions in a network (Bergamini et al, 2014), (Jin et al, 2015). The latter presents a periodicity of acoustic impedance to confine the acoustic waves and lead to new applications (Reinhardt et al, 2010), (Gedge and Hill, 2012), (Trigo et al, 2002).…”

Comparison of Lamb wave focusing performance using wave dispersion-compensated actuation and plano-concave lenses

“…This method is referred to as focusing and allows users to generate high-amplitude signals at the "hot spot," thus improving the signal-to-noise ratio in pitch-catch and pulse-echo methods used for damage quantification. Lamb wave mode focusing can be achieved using gradient-index phononic crystals [2][3][4][5][6][7] or locally resonant metamaterials, [8][9][10] phased-array beamforming, [11][12][13][14] dispersion-compensated actuation, 15 and plano-concave slice lenses. 16 Wu et al numerically demonstrated focusing of the A0 mode of Lamb waves in a gradient-index phononic crystal.…”

“…2 Jin et al proposed using gradient-index phononic plates for simultaneous control of both the A0 and S0 modes in a broadband frequency range. 3 Yan et al 4 proposed using surface bonded elastic metamaterials made of planar arrays of lead discs with varying thicknesses to focus the A0 mode of Lamb waves. Other methods based on Lamb wave mode conversion phenomena can be applied to Lamb wave focusing techniques, but the converted waves obtained have a low amplitude.…”