Multi-resonant scatterers in sonic crystals: Locally multi-resonant acoustic metamaterial

An acoustic metamaterial made of a two-dimensional (2D) periodic array of multi-resonant acoustic scatterers is analyzed both experimentally and theoretically. The building blocks consist of a combination of elastic beams of low-density polyethylene foam (LDPF) with cavities of known area. Elastic resonances of the beams and acoustic resonances of the cavities can be excited by sound producing several attenuation peaks in the low frequency range. Due to this behavior the periodic array with long wavelength multi-resonant structural units can be classified as a locally multi-resonant acoustic metamaterial (LMRAM) with strong dispersion of its effective properties. The results presented in this paper could be used to design effective tunable acoustic filters for the low frequency range. (C) 2012 Elsevier Ltd. All rights reserved.This work was supported by MCI Secretaria de Estado de Investigacion (Spanish government) and FEDER funds, under Grants MAT2009-09438 and MTM2009-14483-C02-02. V.R.G. is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV (CEI-01-11)". A.K. and O.U. are grateful for the support of EPSRC (UK) through research Grant EP/E063136/1.Romero García, V.; Krynkin, A.; García-Raffi, LM.; Umnova, O.; Sánchez Pérez, JV. (2013). Multi-resonant scatterers in sonic crystals: Locally multi-resonant acoustic metamaterial. Journal of Sound and Vibration. 332(1):184-198. doi:10.1016/j.jsv.2012.08.003S184198332

Omnidirectional acoustic absorber with a porous core and a metamaterial matching layer

An omnidirectional sound absorber based on the acoustic analogy of the electromagnetic metamaterial “black hole” has been developed and tested. The resulting structure is composed of a hollow cylindrical porous absorbing core and a graded index matching layer which employs multiple rods of varying size and spacing to gradually adjust the impedance of the air to that of the porous absorbing core. A semi-analytical model is developed, and the practical challenges and their implications with respect to performance are considered. A full size device is built and tested in an anechoic chamber and the semi-analytical model used in the design process is validated. Finally, the theory is extended to allow for losses in the metamaterial matching layer, and it is shown that improved performance may be achieved with a dual purpose layer which acts as an absorber whilst also providing the required impedance matching condition

Genetic Algorithm in the Optimization of the Acoustic Attenuation System

[EN] It is well known that Genetic Algorithms (GA) is an optimization method which can be used in problems where the traditional optimization techniques are difficult to be applied. Sonic Crystals (SC) are periodic structures that present ranges of sound frequencies related with the periodicity of the structure, where the sound propagation is forbidden. This means that in the acoustic spectrum there are ranges of frequencies with high acoustic attenuation. This attenuation can be improved producing vacancies in the structure. In this paper we use a parallel implementation of a GA to optimize those structures, by means of the creation of vacancies in a starting SC, in order to obtain the best acoustic attenuation in a predetermined range of frequencies. The cost function used in GA is based on the Multiple Scattering Theory (MST), which is a self consistent method for calculating acoustic pressure in SCs. As a final result we achieve a quasi ordered structures that presents a high acoustic attenuation in a predetermined range of frequencies, independent of the periodicity of the SC.The authors acknowledge financial support provided by the Spanish MEC (Project No. MAT2006-03097) and by the Generalitat Valenciana (Spain) under Grant No. GV/2007/191. This work also has been partially supported by MEC (Spanish government) and FEDER funds: projects DPI2005-07835, DPI2004- 8383-C03-02 and GVA-026.Romero García, V.; Fuster García, E.; Sánchez Pérez, JV.; García Raffi, LM.; Blasco, X.; Herrero Durá, JM.; Sanchís Saez, J. (2007). Genetic Algorithm in the Optimization of the Acoustic Attenuation System. Lecture Notes in Computer Science. 4507:614-621. https://doi.org/10.1007/978-3-540-73007-1_74S6146214507Martínez-Sala, R., Sancho, J., Sánchez Pérez, J.V., Llinares, J., Meseguer, F.: Sound attenuation by sculpture. Nature (London) 387, 241 (1995)Hushwaha, M.S., Halevi, P., Martínez, G., Dobrynski, L., Djafari-Rouhani, B.: Theory of acoustic band structure of periodic elastic composites. Phys. Rev. B 49(4), 2313–2322 (1994)Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Xhan, C.T., Sheng, P.: Locally resonatn sonic materials. Science 289, 1734 (2000)Hu, X., Chan, C.T., Zi, J.: Two dimensional sonic crystals with Helmholtz resonators. Phys. Rev. E 71, 055601 (2005)Umnova, O., Attenborough, K., Linton, C.M.: Effects of porous covering on sound attenuation by poriodi arrays of cylinders. J. Acoust. Soc. Am. 119, 278 (2006)Caballero, D., Sánchez-Dehesa, J., Martínez-Sala, R., Rubio, C., Sánchez Pérez, J.V.S., Sanchis, L., Meseguer, F.: Suzuki phase in two-dimensional sonic crystals. Phys. Rev. B 64, 064303 (2001)Hakansson, A., Sánchez-Dehesa, J., Sanchis, L.: Acoustic lens design by genetic algorithms. Phys. Rev. B 70, 214302 (2004)Romero-García, V., Fuster, E., García-Raffi, L.M., Sánchez-Pérez, E.A., Sopena, M., Llinares, J., Sánchez-Pérez, J.V.: Band gap creation using quasiordered strutures based on sonic crystals. Appl. Phys. Lett. 88, 174104-1 174104-3 (2006)Chen, Y.Y., Ye, Z.: Theoretical analysis of acoustic stop bands in two-dimensional periodic scattering arrays. Phys. Rev. E 64, 036616 (2001)Economou, E.N., Sigalas, M.M.: Classical wave propagation in periodic structures: Cermet versus network topology. Phys. Rev. B 48(18), 13434 (1993)Sigalas, M.M., Economou, E.N., Kafesaki, M.: Spectral gaps for electromagnietic and scalar waves: Possible explanation for certain differences. Phys. Rev. B 50(5), 3393 (1994)Goldberg, D.E.: Genetic Algorithms in search, optimization and machine learning. Addison-Wesley, London (1989)Bäck, T.: Evolutionaty Algorithms in theory and practice. Oxford University Press, New York (1996)Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proc. Second International Conference on Genetic Algorithms (1987)Mühlenbein, H., Schlierkamp-Voosen, D.: Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization. Evolutionary Computation 1(1) (1993)Cantú-Paz, E.: A summary of resaearch on parallel genetic algorithms. Technical Report 95007, Illinois Genetic Algorithms Laboratory. IlliGAL (1995

Analysis of the wave propagation properties of a periodic array of rigid cylinders perpendicular to a finite impedance surface

The effect of the presence of a finite impedance surface on the wave propagation properties of a two-dimensional periodic array of rigid cylinders with their axes perpendicular to the surface is both numerically and experimentally analyzed in this work. In this realistic situation both the incident and the scattered waves interact with these two elements, the surface and the array. The interaction between the excess attenuation effect, due to the destructive interference produced by the superposition of the incident wave and the reflected one by the surface, and the bandgap, due to the periodicity of the array, is fundamental for the design of devices to control the transmission of waves based on periodic arrays. The most obvious application is perhaps the design of Sonic Crystals Noise Barriers. Two different finite impedance surfaces have been analyzed in the work in order to observe the dependence of the wave propagation properties on the impedance of the surface

Response of multiple rigid porous layers to high levels of continuous acoustic excitation

A model has been developed for the response of a rigid-porous hard-backed medium containing an arbitrary number of layers to high amplitude sound. Nonlinearity is introduced by means of a velocity-dependent flow resistivity in Johnson's equivalent fluid model for the complex tortuosity of each layer. Numerical solution of the resulting system of algebraic equations allows prediction of the dependence of surface impedance and reflection coefficient on the incident pressure amplitude. Measurements have been made of the surface impedance of various triple layers, made from different diameters of spherical lead shot and double layers consisting of gravel with different mean particle size, subject to high-intensity continuous sound. Good agreement between the model predictions and data for these multiple-granular layers is demonstrated. Moreover it is shown both theoretically and experimentally that the layer configuration giving optimum performance at low sound intensities may not continue to do so as the incident sound level is increased and the response becomes increasingly nonlinear. It is shown also that the nonlinear behavior depends strongly on layering and that, in some cases, the behavior is changed simply by changing the top layer thickness

Deduction of tortuosity and poosity from acoustic reflection and transmission on thick sample of rigid-porous materials

An acoustic method for obtaining the tortuosity, and porosity of thick samples of rigid porous materials consisting of large (>1 mm) grains or fibres is proposed. The method uses pulses with central frequencies close to 12 kHz and an approximate bandwidth of between 3 and 20 kHz. In this frequency range, inertial rather than viscous or scattering effects dominate sound propagation in large pores. This allows application of the high frequency limit of the “equivalent fluid” model. Both reflected and transmitted signals are used in the measurements. Tortuosity is deduced from the high frequency limit of the phase speed (obtained from transmission data) and porosity is obtained from the high frequency limit of the reflection coefficient once the tortuosity is known. The method is shown to give good results in the cases where significant scattering does not occur until frequencies much higher than the upper limit of the pulse bandwidth. Apart from its applicability to samples with several centimetres thickness, the method needs only one set of measurements with the sample to deduce both tortuosity and porosity. In principle the method can be used also to estimate characteristic lengths. However, the errors are found to be larger and the results less consistent than for tortuosity

Behavior of rigid – porous layers at high levels of continuous acoustic excitation: Theory and experiment

A model for the propagation of high amplitude continuous sound through hard-backed rigid-porous layers has been developed which allows for Forchheimer's correction to Darcy's law. The nonlinearity associated with this is shown to be particularly important in the range of frequencies around layer resonance. The model is based on the introduction of particle velocity dependent flow resistivity into the equivalent fluid model expression for complex tortuosity. Thermal effects are accounted for by means of a linear complex compressibility function. The model has been used to derive analytical expressions for surface impedance and reflection coefficient as a function of incident pressure amplitude. Depending on the material parameters, sample thickness, and frequency range the model predicts either growth or decrease of reflection coefficient with sound amplitude. Good agreement between model predictions and data for three rigid-porous materials is demonstrated

Scattering by coupled resonating elementsin air

Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of these scatterers in air has been investigated analytically and through laboratory experiments. The composite scatterer forms a system of coupled resonators and gives rise to multiple low-frequency resonances. The corresponding analytical model employs polar angle dependent boundary conditions on the surface of the N-slit cylinder. The solution inside the slits assumes plane waves. It is shown also that in the low-frequency range the N-slit rigid cylinder can be replaced by an equivalent fluid layer. Further approximations suggest a simple square root dependence of the resonant frequencies on the number of slits and this is confirmed by data. The observed resonant phenomena are associated with Helmholtz-like behaviour of the resonator for which the radius and width of the openings are much smaller than the wavelength. The problem of scattering by a finite periodic array of such coupled resonators in air is solved using multiple scattering techniques. The resulting model predicts band-gap effects resulting from the resonances of the individual composite scatterers below the first Bragg frequency. Predictions and data confirm that use of coupled resonators results in substantial insertion loss peaks related to the resonances within the concentric configuration. In addition, for both scattering problems experimental data, predictions of the analytical approach and predictions of the equivalent fluid layer approximations are compared in the low-frequency interval