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We report experiments on high-amplitude sound wave propagation in an acoustic metamaterial composed of an air-filled waveguide periodically side-loaded by holes. In addition to the linear viscothermal and radiation losses, high amplitude sound waves at the locations of the side holes introduce nonlinear losses. The latter result in an amplitude-dependent reflection, transmission, and absorption, which we experimentally characterize. First, we evidence that nonlinear losses change the nature of the device from a reflective to an absorbing one, showing the possibility to use the system as a nonlinear absorber. Second, we study the second-harmonic generation and its beating phenomenon both experimentally and analytically. We find that when considering the propagation of both the fundamental and the second harmonic, nonlinear losses cannot be neglected. Our results reveal the role of nonlinear losses in the proposed device and also provide a quite accurate analytical model to capture the effect of such losses. © 2021 Author(s).

We study analytically and numerically second-harmonic generation in a one-dimensional weakly lossy nonlinear acoustic metamaterial composed of an air-filled waveguide periodically loaded by side holes. Based on the transmission line approach, we derive a lossy nonlinear dispersive lattice model which, in the continuum limit, leads to a nonlinear, dispersive and dissipative wave equation. The latter is studied by means of a perturbation method, which leads to analytical expressions for the first and second harmonics, in very good agreement with numerical results. © S. Hirzel Verlag EAA.

We study dark solitons, namely density dips with a phase jump across the density minimum, in a one-dimensional, weakly lossy nonlinear acoustic metamaterial, composed of a waveguide featuring a periodic array of side holes. Relying on the electroacoustic analogy and the transmission line approach, we derive a lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. The latter, using the method of multiple scales, is reduced to a defocusing nonlinear Schrödinger equation, which leads to dark soliton solutions. The dissipative dynamics of these structures is studied via soliton perturbation theory. We investigate the role-and interplay between-nonlinearity, dispersion and dissipation on the soliton formation and dynamics. Our analytical predictions are corroborated by direct numerical simulations. © 2018 by the authors.

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive, and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement. © 2017 American Physical Society.

We experimentally report perfect acoustic absorption through the interplay of the inherent losses and transparent modes with high $Q$ factor. These modes are generated in a two-port, one-dimensional waveguide which is side-loaded by isolated resonators of moderate $Q$ factor. In symmetric structures, we show that in the presence of small inherent losses, these modes lead to coherent perfect absorption associated with one-sided absorption slightly larger than 0.5. In asymmetric structures, near perfect one-sided absorption is possible (96 \%) with a deep sub-wavelength sample ($\lambda/28$). The control of strong absorption by the proper tuning of few resonators with weak losses will open new possibilities in various wave-control devices.

The physical properties of a periodic distribution of absorbent resonators is used in this work to design a tunable wideband bandstop acoustic filter. Analytical and numerical simulations as well as experimental validations show that the control of the resonances and the absorption of the scatterers along with their periodic arrangement in air introduces high technological possibilities to control noise. Sound manipulation is perhaps the most obvious application of the structures presented in this work. We apply this methodology to develop a device as an alternative to the conventional acoustic barriers with several properties from the acoustical point of view but also with additional aesthetic and constructive characteristics.

Evanescent modes in complete sonic crystals (SC) and SC with point defects are reported both theoretically and experimentally in this paper. Plane wave expansion (PWE) and, in general, $\omega(k)$ methods have been used to calculate band structures showing gaps that have been interpreted as ranges of frequencies where no real $k$ exists. In this work, we extend PWE to solve the complex $k(\omega)$ problem applied to SC, introducing the supercell approximation for studying one vacancy. Explicit matrix formulation of the equations is given. This $k(\omega)$ method enables the calculation of complex band structures, as well as enabling an analysis of the propagating modes related with real values of the function $k(\omega)$, and the evanescent modes related with imaginary values of $k(\omega)$. This paper shows theoretical results and experimental evidences of the evanescent behavior of modes inside the SC band gap. Experimental data and numerical results using the finite elements method are in very good agreement with the predictions obtained using the $k(\omega)$ method., Comment: 15 pages, 3 figures

International audience; Broadband and perfect sound absorption by subwavelength panels for transmission problems is re- ported. The asymmetric panels are composed of a periodic array of open waveguides loaded by Helmholtz resonators (HRs) with slightly different dimensions along the structure depth. In each waveguide, the deepest resonator generates a low cut-off frequency, reducing drastically the transmis- sion. The geometry of the preceding HR is designed to possess a slightly higher resonance frequency and is tuned to match the structure impedance with the surrounding one, thanks to the critical coupling condition. Therefore, reflection vanishes and the structure becomes critically coupled to the incident wave, resulting in perfect sound absorption. This process is repeated by adding HRs, whose resonance frequency is slightly higher than the preceding one, to each waveguide. The last added HR fixes the high cut-off frequency of the perfect absorption band in such a way that slow sound condi- tion is achieved within each open waveguide over a broadband frequency range. We experimentally, theoretically and numerically report perfect sound absorption for two panels: (1) at 300 Hz for a transparent panel of total thickness 2.8 cm, i.e., 40 times smaller than the wavelength, (2) from 350 to 1000 Hz for a transparent panel composed of 9 resonators with a total thickness of 12 cm, i.e., 10 times smaller than the wavelength and covering almost two octaves.