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Nonlinear phenomena in 1D acoustic metamaterials

Abstract : The subject of this PhD thesis is the propagation of nonlinear waves in 1D acoustic metamaterials. More specifically we aim to study the interplay between nonlinearity, loss and dispersion. Our studies combine analytical calculations, numerical simulations and experimental results. In particular we focus our analysis on two main phenomena: the second harmonic generation and the formation of solitary waves. Two different acoustic metamaterials are studied: (i) A waveguide loaded with a periodic distribution of side holes (featuring negative effective bulk modulus) and (ii) a waveguide periodically loaded with clamped elastic plates (featuring negative effective mass density). Relying on the electroacoustic analogy and the transmission line approach, we derive a discrete lattice model for each system. The corresponding long wavelength, continuum approximation of the lattice models, leads to a nonlinear, dispersive and dissipative wave equation. From the latter, by utilising a perturbation method, we obtain analytical results regarding the second harmonic generation. Furthermore with the use of a multiple scale analysis we find various envelope (bright, gap, black and gray) soliton solutions supported by the acoustic metamaterial. The analytical predictions are corroborated by direct numerical simulations. We finally perform experiments on an acoustic waveguide loaded with a periodic distribution of side holes and measure the second harmonic generation in close agreement with our theoretical predictions.
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Submitted on : Wednesday, December 2, 2020 - 1:04:03 AM
Last modification on : Wednesday, December 2, 2020 - 3:37:59 AM
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  • HAL Id : tel-03035015, version 1


Jiangyi Zhang. Nonlinear phenomena in 1D acoustic metamaterials. Acoustics [physics.class-ph]. Université du Maine, 2019. English. ⟨NNT : 2019LEMA1014⟩. ⟨tel-03035015⟩



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