Direct discrete complex image method for sound field evaluation above a non-locally reacting layer

Abstract

Thin layers of porous media are widely adopted in sound absorption and noise control applications due to their compact arrangement. Particularly, porous media with low flow resistivity exhibit complex, non-local reaction behavior. Therefore, sound field prediction above these media is computationally challenging. This is due to singularities and branch points in the expression for the reflection coefficient. This paper introduces a framework based on the direct discrete complex image method to analyze the sound field above a rigid-backed, non-locally reacting porous sample. In contrast to traditional complex image applications, the proposed framework avoids the extraction of the quasi-static term and the poles from the reflection coefficient. Instead, the reflection coefficient—including its singularities—is directly approximated in terms of a series of complex exponentials, whose coefficients are determined with the matrix pencil method. This study analyzes the sound field above two test samples made of melamine and rockwool. The sound field computation is efficient and accurate in the near- and in the far-field. Moreover, predicted specific impedances agree well with experimental in situ impedance measurements. The proposed framework serves for more applications including object detection in multilayered porous grounds or sound propagation prediction in layered atmosphere.

Probabilistic Estimation of the Oblique Incidence Sound Absorption Coefficient - A Numerical Concept Study

“…We adopt a Bayesian approach, which has initially been proposed for the direct identification of a porous panel absorber's frequency-dependent surface admittance [6]. In this study however, this Bayesian approach is extended to identify the frequency-dependent sound propagation characteristics and the associated uncertainty in these parameters.…”

“…However, this approach requires an individual numerical integration for the sound pressure and for the particle velocity for each source-receiver combination, which makes it impractical for the present inverse problem. Therefore, we use the direct discrete complex image method (dD-CIM) [7] to efficiently evaluate an accurate approximation of the theoretical sound field. The dDCIM's efficiency is based on a single step solution of the sound field for an arbitrary number of source-receiver combinations, since the coefficients of the complex images are independent of the positions of source and receiver [7].…”

“…For modeling the sound field, we assume a harmonic time dependence of exp (+iωt), where i 2 = −1, is the imaginary unit, ω = 2πf , is the angular frequency at the frequency f and t is the time. Hence, the recorded sound pressure p (r, r S ) is directly proportional to the specific half-space Green's function [7]…”

“…The sound field is mathematically challenging to evaluate, due to the integrand in the Green's function [3,7,9]. For this reason, the identification of the sound propagation characteristics requires an iterative approach [3].…”

“…[3][4][5]. However, there are numerous sources of uncertainty associated with such impedance measurements [6]. This paper aims at quantifying the uncertainty in an estimate of the oblique incidence sound absorption coefficient.…”