Sound field reconstruction of structural source based on element radiation superposition method

Abstract

In order to improve the sound field reconstruction accuracy of distributed structural source, a new near-field acoustic holography is established based on the element radiation superposition method (ERSM). In the proposed method, the surface of structural source is divided into several regular pistons. The sound field of structural source is considered as the superposition of sound field of pistons. Firstly, we compare the sound field calculated by ERSM with that by Rayleigh's integral. It is proved that ERSM is quite accurate in sound field prediction. Based on ERSM, a vibration acoustic transfer (VAT) function is derived. The VAT function has computable analytical expression and embodies the transfer relationship between the structural source surface and the radiated sound field. The VAT function can precisely characterize the acoustic propagation of continuous distributed coherent sources. Subsequently, we employ the VAT function to replace the Green's function, and apply the VAT function to sound field reconstruction. Different with the equivalent source method (ESM) which is widely used in sound field reconstruction, ERSM directly divides the piston-sources on the surface of structural source rather than constructing the equivalent point-sources on a plane behind the structural source. Furthermore, we introduce a weight matrix into ERSM and iteratively calculate the vibration velocity for a more accurate result, and we call the proposed method as iterative weighted ERSM (IWERSM). In this paper, the simulations and experiment of sound field reconstruction of a rectangular plate are performed. In the proposed method, the rectangular plate is divided into several rectangular pistons. The reconstruction results of ERSM and IWERSM are compared with that of ESM and iterative weighted ESM (IWESM) respectively. The reconstruction accuracies at different distances between the plate and array (test distances) are analyzed. The simulation results show the accuracy of ERSM and IWERSM are better than that of ESM and IWESM respectively. With the increase of test distance, the phenomenon is more obvious, and IWERSM even shows a good reconstruction accuracy while the test distance is more than half a wavelength. The experiment results also validate that ERSM and IWERSM have better reconstruction accuracy than ESM and IWESM respectively at the same test distance. In a word, the simulations and experiments demonstrate that the proposed method can improve the sound field reconstruction accuracy of regular structural source and expand the valid test distance of near-field acoustic holography.

Extension of sound field reconstruction based on element radiation superposition method in a sparsity framework

“…Figure 1 shows a rectangular planar piston mounted in corresponding infinite rigid baffle. The pressure produced by rectangular planar piston can be expressed as [16,17,25] p (R, θ , φ ) = −2jρckvL x L y e jkR πR sinc (kL x cos θ cos φ )…”

“…Previous results well show that the ERSM maintains high calculation accuracy from the transition distance to the far field of the piston. [17] In this study, the piston length is set to L x < 0.12λ min (λ min is the minimum wavelength of the applied frequency band), and all the distance-parameters satisfy the applicable scope of Eq. ( 6).…”

“…Recently, a new NAH technique based on the element radiation superposition method (ERSM) was proposed for spatially extended sources. The theoretical justification of ERSM was given first by Wang et al [16] Then, ERSM applied to NAH was first suggested by Shi et al [17] In ERSM, the actual source surface is divided into regular-shaped pistons (surface sources), and the total sound field is regarded as the superposition of the responses radiated by the pistons. The ERSM is directly derived from the Helmholtz integral equation, and a Fraunhofer approximation is used to construct the transfer matrix.…”

“…Besides, as an approximation of the IBEM, the ERSM avoids the complex numerical integration, and it is immune to the singularity and nonuniqueness difficulties. Shi et al [17] not only proved that the ERSM provides high accuracy in sound field prediction of rectangular plate within nearfield, but also compared the ERSM with ESM in the sound field reconstruction of rectangular plate by using regular sampling. To satisfy the application conditions of the far field approximation, the sizes of pistons are assumed to be as small as possible.…”