Vincent Pagneux

A study of wave propagation in varying cross-section waveguides by modal decomposition. Part I. Theory and validation

The propagation of acoustic waves in waveguides with variable cross section is considered using multimodal decomposition. The approach adopted is to construct two infinite first‐order differential equations for the components of the pressure and the velocity projected over the normal modes. From these an infinite matricial Riccati equation is derived for the impedance matrix. These equations are ordinary differential equations that can be integrated after truncation at a sufficient number of modes and take into account the coupling between modes. The stiffness of the pressure‐velocity equations induced by the presence of evanescent modes is avoided by first calculating the impedance matrix along the guide. The method is checked using different examples where the solutions of the plane‐wave approximation or the finite element method are known. Results show the method provides simple and accurate means to obtain the acoustic field with correct boundary conditions in a nonuniform guide with no restriction on...

Sound attenuation in lined bends

In the present paper we are concerned with sound propagation and attenuation in two- or three-dimensional lined bends. First it is shown that the effect of locally reacting absorbing materials at the walls of a waveguide can easily be taken into account in the multimodal formulation proposed in earlier papers by the authors, and, for bends, algebraic solutions are carried out for the acoustic field and scattering properties. Then a study of the sound attenuation in lined bends is given using the multimodal formulation and the properties of such waveguides are shown and discussed, in particular, the presence of a plateau of attenuation at high frequencies and a whispering gallery effect that occurs in bends.

Influence of grazing flow and dissipation effects on the acoustic boundary conditions at a lined wall

The problem of sound propagation near a lined wall taking into account mean shear flow effects and viscous and thermal dissipation is investigated. The method of composite expansion is used to separate the inviscid part, in the core of the flow, from the boundary layer part, near the wall. Two diffusion equations for the shear stress and the heat flux are obtained in the boundary layer. The matching of the solutions of these equations with the inviscid part leads to a modified specific acoustic admittance in the core flow. Depending on the ratio of the acoustic and stationary boundary layer thicknesses, the kinematic wall condition changes gradually from continuity of normal acoustic displacement to continuity of normal acoustic mass velocity. This wall condition can be applied in dissipative silencers and in aircraft engine-duct systems.

Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry

The measurement of an objects shape using projected fringe patterns needs a relation between the measured phase and the objects height. Among various methods, the Fourier transform profilometry proposed by Takeda and Mutoh [Appl. Opt.22, 3977-3982 (1983)] is widely used in the literature. Rajoub et al. have shown that the reference relation given by Takeda is erroneous [J. Opt. A. Pure Appl. Opt.9, 66-75 (2007)]. This paper follows from Rajoubs study. Our results for the phase agree with Rajoubs results for both parallel- and crossed-optical-axes geometries and for either collimated or noncollimated projection. Our two main results are: (i) we show experimental evidence of the error in Takedas formula and (ii) we explain the error in Takedas derivation and we show that Rajoubs argument concerning Takedas error is not correct.

A study of wave propagation in varying cross-section waveguides by modal decomposition. Part II. Results

The full derivation of the equations governing the generalized impedance matrix Z, the pressure, and the velocity were presented in Part I of this series [Pagneux et al., J. Acoust. Soc. Am. 100, 2034–2048 (1996)]. Here only the results of that paper, i.e., the final set of equations which needed to be solved are repeated. Other factors influencing the solution are the boundary conditions at the end of the waveguide: Source and radiation conditions are also presented. Finally, the details of the numerical implementation are also relevant, and will be discussed in some detail.

Perfect and broadband acoustic absorption by critically coupled sub-wavelength resonators

Perfect absorption is an interdisciplinary topic with a large number of applications, the challenge of which consists of broadening its inherently narrow frequency-band performance. We experimentally and analytically report perfect and broadband absorption for audible sound, by the mechanism of critical coupling, with a sub-wavelength multi-resonant scatterer (SMRS) made of a plate-resonator/closed waveguide structure. In order to introduce the role of the key parameters, we first present the case of a single resonant scatterer (SRS) made of a Helmholtz resonator/closed waveguide structure. In both cases the controlled balance between the energy leakage of the several resonances and the inherent losses of the system leads to perfect absorption peaks. In the case of the SMRS we show that systems with large inherent losses can be critically coupled using resonances with large leakage. In particular, we show that in the SMRS system, with a thickness of λ/12 and diameter of λ/7, several perfect absorption peaks overlap to produce absorption bigger than 93% for frequencies that extend over a factor of 2 in audible frequencies. The reported concepts and methodology provide guidelines for the design of broadband perfect absorbers which could contribute to solve the major issue of noise reduction.

Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption

Using the concepts of slow sound and of critical coupling, an ultra-thin acoustic metamaterial panel for perfect and omnidirectional absorption is theoretically and experimentally conceived in this work. The system is made of a rigid panel with a periodic distribution of thin closed slits, the upper wall of which is loaded by Helmholtz Resonators (HRs). The presence of resonators produces a slow sound propagation shifting the resonance frequency of the slit to the deep sub-wavelength regime (

Lamb wave propagation in elastic waveguides with variable thickness

\lambda/88

Measurement of Liner Impedance with Flow by an Inverse Method

). By controlling the geometry of the slit and the HRs, the intrinsic visco-thermal losses can be tuned in order to exactly compensate the energy leakage of the system and fulfill the critical coupling condition to create the perfect absorption of sound in a large range of incidence angles due to the deep subwavelength behavior.

Revisiting the edge resonance for Lamb waves in a semi-infinite plate

The problem of Lamb wave propagation in waveguides with varying height is treated by a multimodal approach. The technique is based on a rearrangement of the equations of elasticity that provides a new system of coupled mode equations preserving energy conservation. These coupled mode equations avoid the usual problem at the cut-offs with zero wavenumber. Thereafter, we define an impedance matrix that is governed by a Riccati equation yielding a stable numerical computation of the solution. Incidentally, the versatility of the multimodal method is exemplified by treating analytically the case of slowly varying guide and by showing how to get easily the Green tensor in any geometry. The method is applied for a waveguide whose height is described by a Gaussian function and the energy conservation in verified numerically. We determine the Green tensor in this geometry.