Adrien Pelat

On the use of leaky modes in open waveguides for the sound propagation modeling in street canyons

An urban, U-shaped, street canyon being considered as an open waveguide in which the sound may propagate, one is interested in a multimodal approach to describe the sound propagation within. The key point in such a multimodal formalism is the choice of the basis of local transversal modes on which the acoustic field is decomposed. For a classical waveguide, with a simple and bounded cross-section, a complete orthogonal basis can be analytically obtained. The case of an open waveguide is more difficult, since no such a basis can be exhibited. However, an open resonator, as displays, for example, the U-shaped cross-section of a street, presents resonant modes with complex eigenfrequencies, owing to radiative losses. This work first presents how to numerically obtain these modes. Results of the transverse problem are also compared with solutions obtained by the finite element method with perfectly mathed layers. Then, examples are treated to show how these leaky modes can be used as a basis for the modal decomposition of the sound field in a street canyon.

A coupled modal-finite element method for the wave propagation modeling in irregular open waveguides.

In modeling the wave propagation within a street canyon, particular attention must be paid to the description of both the multiple reflections of the wave on the building facades and the radiation in the free space above the street. The street canyon being considered as an open waveguide with a discontinuously varying cross-section, a coupled modal-finite element formulation is proposed to solve the three-dimensional wave equation within. The originally open configuration-the street canyon open in the sky above-is artificially turned into a close waveguiding structure by using perfectly matched layers that truncate the infinite sky without introducing numerical reflection. Then the eigenmodes of the resulting waveguide are determined by a finite element method computation in the cross-section. The eigensolutions can finally be used in a multimodal formulation of the wave propagation along the canyon, given its geometry and the end conditions at its extremities: initial field condition at the entrance and radiation condition at the output.

Sound propagation in a street canyon: A study by modal decomposition

An urban, U‐shaped, street canyon being considered as an open waveguide in which the sound may propagate, one is interested in a multimodal approach to describe the sound propagation within. The key point in such a multimodal formulation is the choice of the basis of local transversal modes on which the acoustic field is projected. For a classical waveguide, with a simple and bounded cross‐section, a complete orthogonal basis can be analytically obtained. The case of an open waveguide is more difficult, since no such a basis can be exhibited. However, an open resonator, as displays for example the U‐shaped cross‐section of a street, presents resonant modes with complex eigen frequencies, owing to radiative losses. This work first presents how to numerically obtain these modes and, then, how they can be used as a basis for the modal decomposition of the sound field in a street canyon. Results are compared with experimental measurements on a scale model.

Reflexion of flexural waves at the end of a tapered beam of quadratic profile covered with a thin viscoelastic layer

Flexural waves propagating in a beam can be efficiently absorbed if one extremity is tapered with a power law profile and covered by a very thin viscoelastic layer (V. Krylov, JSV 274 (2004), 605-619). Such a terminaison induces an effect known as ?the acoustic black hole effect? (ABH), which is resulting from properties of propagation of flexural wave in beams having non homogeneous thicknesses: if the thickness decreases locally, flexural waves slow down and the amplitude of the displacement field increases, leading to efficient energy dissipation if an absorbing layer is placed where the thickness is minimum (V. Georgiev et al., JSV 330 (2011), 2497-2508). Absorption of the ABH terminaison is estimated thanks to the direct measurement of the reflexion coefficient, using a wave decomposition technique. Experimental modal Analysis of a ABH beam can be performed using a high resolution technique which permits to estimate the modal density. Analysis of these experimental results is performed thanks to a mo...