Enhanced inertia from lossy effective fluids using multi-scale sonic crystals

n this work, a recent theoretically predicted phenomenon of enhanced permittivity with electromagnetic waves using lossy materials is investigated for the analogous case of mass density and acoustic waves, which represents inertial enhancement. Starting from fundamental relationships for the homogenized quasi-static effective density of a fluid host with fluid inclusions, theoretical expressions are developed for the conditions on the real and imaginary parts of the constitutive fluids to have inertial enhancement, which are verified with numerical simulations. Realizable structures are designed to demonstrate this phenomenon using multi-scale sonic crystals, which are fabricated using a 3D printer and tested in an acoustic impedance tube, yielding good agreement with the theoretical predictions and demonstrating enhanced inertia.This work was supported by the U.S. Office of Naval Research (Award N000141210216).Guild, M.; García Chocano, VM.; Kan, W.; Sánchez-Dehesa Moreno-Cid, J. (2014). Enhanced inertia from lossy effective fluids using multi-scale sonic crystals. AIP Advances. 4(12). https://doi.org/10.1063/1.4901880412Dowling, J. P. (1992). Sonic band structure in fluids with periodic density variations. The Journal of the Acoustical Society of America, 91(5), 2539-2543. doi:10.1121/1.402990Sigalas, M. M., & Economou, E. N. (1992). Elastic and acoustic wave band structure. Journal of Sound and Vibration, 158(2), 377-382. doi:10.1016/0022-460x(92)90059-7Kushwaha, M. S., Halevi, P., Dobrzynski, L., & Djafari-Rouhani, B. (1993). Acoustic band structure of periodic elastic composites. Physical Review Letters, 71(13), 2022-2025. doi:10.1103/physrevlett.71.2022Sánchez-Pérez, J. V., Caballero, D., Mártinez-Sala, R., Rubio, C., Sánchez-Dehesa, J., Meseguer, F., … Gálvez, F. (1998). Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders. Physical Review Letters, 80(24), 5325-5328. doi:10.1103/physrevlett.80.5325Krokhin, A. A., Arriaga, J., & Gumen, L. N. (2003). Speed of Sound in Periodic Elastic Composites. Physical Review Letters, 91(26). doi:10.1103/physrevlett.91.264302Torrent, D., Håkansson, A., Cervera, F., & Sánchez-Dehesa, J. (2006). Homogenization of Two-Dimensional Clusters of Rigid Rods in Air. Physical Review Letters, 96(20). doi:10.1103/physrevlett.96.204302Torrent, D., & Sánchez-Dehesa, J. (2008). Anisotropic mass density by two-dimensional acoustic metamaterials. New Journal of Physics, 10(2), 023004. doi:10.1088/1367-2630/10/2/023004Zigoneanu, L., Popa, B.-I., Starr, A. F., & Cummer, S. A. (2011). Design and measurements of a broadband two-dimensional acoustic metamaterial with anisotropic effective mass density. Journal of Applied Physics, 109(5), 054906. doi:10.1063/1.3552990Torrent, D., & Sánchez-Dehesa, J. (2008). Acoustic cloaking in two dimensions: a feasible approach. New Journal of Physics, 10(6), 063015. doi:10.1088/1367-2630/10/6/063015Sanchis, L., García-Chocano, V. M., Llopis-Pontiveros, R., Climente, A., Martínez-Pastor, J., Cervera, F., & Sánchez-Dehesa, J. (2013). Three-Dimensional Axisymmetric Cloak Based on the Cancellation of Acoustic Scattering from a Sphere. Physical Review Letters, 110(12). doi:10.1103/physrevlett.110.124301Guild, M. D., Alù, A., & Haberman, M. R. (2014). Cloaking of an acoustic sensor using scattering cancellation. Applied Physics Letters, 105(2), 023510. doi:10.1063/1.4890614García-Chocano, V. M., Cabrera, S., & Sánchez-Dehesa, J. (2012). Broadband sound absorption by lattices of microperforated cylindrical shells. Applied Physics Letters, 101(18), 184101. doi:10.1063/1.4764560Christensen, J., Romero-García, V., Picó, R., Cebrecos, A., de Abajo, F. J. G., Mortensen, N. A., … Sánchez-Morcillo, V. J. (2014). Extraordinary absorption of sound in porous lamella-crystals. Scientific Reports, 4(1). doi:10.1038/srep04674Frenzel, T., David Brehm, J., Bückmann, T., Schittny, R., Kadic, M., & Wegener, M. (2013). Three-dimensional labyrinthine acoustic metamaterials. Applied Physics Letters, 103(6), 061907. doi:10.1063/1.4817934Climente, A., Torrent, D., & Sánchez-Dehesa, J. (2012). Omnidirectional broadband acoustic absorber based on metamaterials. Applied Physics Letters, 100(14), 144103. doi:10.1063/1.3701611Naify, C. J., Chang, C.-M., McKnight, G., & Nutt, S. (2010). Transmission loss and dynamic response of membrane-type locally resonant acoustic metamaterials. Journal of Applied Physics, 108(11), 114905. doi:10.1063/1.3514082Yang, Z., Dai, H. M., Chan, N. H., Ma, G. C., & Sheng, P. (2010). Acoustic metamaterial panels for sound attenuation in the 50–1000 Hz regime. Applied Physics Letters, 96(4), 041906. doi:10.1063/1.3299007Hussein, M. I., & Frazier, M. J. (2013). Metadamping: An emergent phenomenon in dissipative metamaterials. Journal of Sound and Vibration, 332(20), 4767-4774. doi:10.1016/j.jsv.2013.04.041Reyes-Ayona, E., Torrent, D., & Sánchez-Dehesa, J. (2012). Homogenization theory for periodic distributions of elastic cylinders embedded in a viscous fluid. The Journal of the Acoustical Society of America, 132(4), 2896-2908. doi:10.1121/1.4744933Carbonell, J., Cervera, F., Sánchez-Dehesa, J., Arriaga, J., Gumen, L., & Krokhin, A. (2010). Homogenization of two-dimensional anisotropic dissipative photonic crystal. Applied Physics Letters, 97(23), 231122. doi:10.1063/1.3526381Carbonell, J., Sánchez-Dehesa, J., Arriaga, J., Gumen, L., & Krokhin, A. (2011). Electromagnetic absorption in anisotropic photonic crystal of alumina cylinders. Metamaterials, 5(2-3), 74-80. doi:10.1016/j.metmat.2011.03.001Godin, Y. A. (2013). Effective complex permittivity tensor of a periodic array of cylinders. Journal of Mathematical Physics, 54(5), 053505. doi:10.1063/1.4803490Torrent, D., Sánchez-Dehesa, J., & Cervera, F. (2007). Evidence of two-dimensional magic clusters in the scattering of sound. Physical Review B, 75(24). doi:10.1103/physrevb.75.241404Martin, P. A., Maurel, A., & Parnell, W. J. (2010). Estimating the dynamic effective mass density of random composites. The Journal of the Acoustical Society of America, 128(2), 571-577. doi:10.1121/1.3458849Erokhin, S. G., Lisyansky, A. A., Merzlikin, A. M., Vinogradov, A. P., & Granovsky, A. B. (2008). Photonic crystals built on contrast in attenuation. Physical Review B, 77(23). doi:10.1103/physrevb.77.233102Song, B. H., & Bolton, J. S. (2000). A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials. The Journal of the Acoustical Society of America, 107(3), 1131-1152. doi:10.1121/1.42840