Nonlinear dynamics of coupled transverse-rotational waves in granular chains

The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semiinfinite systems. It is shown that the sum-frequency and difference-frequency components of the coupled transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave. Nonlinear resonances are not present in the chain with no substrate where these frequency components have low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to the wave numbers asynchronism. The results confirm the possibility of a highly efficient energy transfer between the waves of different frequencies, which could find applications in the design of acoustic devices for energy transfer and energy rectification

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

Acoustic insertion loss due to two dimensional periodic arrays of circular cylinders parallel to a nearby surface

The acoustical performances of regular arrays of cylindrical elements, with their axes aligned and parallel to a ground plane, have been investigated through predictions and laboratory experiments. Semi-analytical predictions based on multiple scattering theory and numerical simulations based on a boundary element formulation have been made. Measurements have been made in an anechoic chamber using arrays of (a) cylindrical acoustically-rigid scatterers (PVC pipes) and (b) thin elastic shells. Insertion loss (IL) spectra due to the arrays have been measured without and with ground planes for several receiver heights. Data and predictions have been compared. The minima in the excess attenuation spectrum i.e., attenuation maxima due to the ground alone resulting from destructive interference between direct and ground-reflected sound waves, tend to have an adverse influence on the band gaps (BG) related to a periodic array in the free field when these two effects coincide. On the other hand, the presence of rigid ground may result in an IL for an array near the ground similar to or, in the case of the first BG, greater than that resulting from a double array, equivalent to the original array plus its ground plane mirror image, in the free field.Comment: J. Acoust. Soc. Am. 130 (6), December 201

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

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

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

Scattering by coupled resonating elements in 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

Trends in the Transformation of Modern Law under the Influence of a New Stage of Scientific and Technological Progress

The article examines the trends of transformation of modern law under the influence of a technological breakthrough as a new stage of scientific and technological progress. The general trends of globalization and differentiation of law are highlighted, and the consequences of these trends, expressed in the growth of the number of complex branches of law that combine public and private interests, are considered. For the purpose of systematization, three main forms of globalization in law are identified: universalization, internationalization and integration. The analysis of the evolution of the legal system in the historical dimension allows to distinguish three stages of differentiation of modern law. At the first stage of the differentiation of law in the XX century, it was mainly expressed in the fragmentation of traditional branches of law. The second stage of the differentiation of law at the turn of the XX and XXI centuries is characterized by the intensive formation of complex mixed branches of law that join the institutions of public and private law for certain purposes of legal regulation. At the third, modern stage at the junction of the first and second decades of the XXI century. under the influence of scientific and technological progress, there is not only a further diversification and integration of traditional  and  new  complex  branches of law, but also a group of functional and instrumental branches of law. Th se branches of auxiliary law (due to its functional significance) determine the socio-legal technologies of regulation, implementation and development of law (for example, collision law, mediation law, digital law).The author puts forward the concept and reveals the system of branches of law of the new generation as the highest form of evolution of complex branches of law, justifies their special nature and significance in the system of law. The author also systematizes the branches of law of the new generation, taking into account the degree of their development in legal doctrine and law practice.Special attention is paid to digital law and bio-law, which most clearly indicate the impact of scientific and technological progress on law, as well as exposing the problem of the need for closer interaction of the principles and norms of law and ethics