×

Nonlinear approach to approximate acoustic boundary admittance in cavities. (English) Zbl 1140.76457

Summary: An algorithm is derived to solve a problem of inverse acoustics. It considers the damped acoustic boundary value problem, i.e. the Helmholtz equation and admittance boundary condition, in order to approximate the boundary admittance of interior domains. The algorithm is implemented by using a finite element method and tested for two-dimensional cavities with arbitrary shapes. The admittance condition is reconstructed based on sound pressure measurements. The solution of the arising nonlinear system of equations is obtained by applying the Newton method following a presetting method for finding reasonable initial boundary admittance values. A residual norm accounts for the objective function. Its first- and second-order sensitivities are determined analytically by using a modal decomposition in order to avoid direct inversion of the system matrix. The experiment is simulated by taking sound pressure data of the forward solution as inputs for the inverse problem. Test examples show that very few measurement points are necessary to reproduce piecewise constant boundary admittance values very accurately. Then, the admittance boundary condition is applied to reproduce the sound pressure distribution in the cavity. Again, it becomes obvious that only a few measurement points are required to reconstruct the sound pressure field.

MSC:

76Q05 Hydro- and aero-acoustics
76M10 Finite element methods applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/j.mechrescom.2006.03.006 · Zbl 1192.76045 · doi:10.1016/j.mechrescom.2006.03.006
[2] DOI: 10.1121/1.404263 · doi:10.1121/1.404263
[3] DOI: 10.1007/s00158-001-0166-y · doi:10.1007/s00158-001-0166-y
[4] Bronstein I. N., Handbook of Mathematics (1999)
[5] DOI: 10.1088/0266-5611/19/3/302 · Zbl 1033.76053 · doi:10.1088/0266-5611/19/3/302
[6] DOI: 10.2514/2.2432 · doi:10.2514/2.2432
[7] DOI: 10.1007/b98828 · Zbl 0908.65091 · doi:10.1007/b98828
[8] DOI: 10.1121/1.417112 · doi:10.1121/1.417112
[9] DOI: 10.1121/1.426842 · doi:10.1121/1.426842
[10] Koopmann G. H., Designing Quiet Structures: A Sound Power Minimization Approach (1997)
[11] DOI: 10.1007/BF03041465 · Zbl 1099.74538 · doi:10.1007/BF03041465
[12] DOI: 10.1142/S0218396X02001401 · Zbl 1360.76168 · doi:10.1142/S0218396X02001401
[13] DOI: 10.1016/S0955-7997(99)00024-7 · Zbl 0962.76089 · doi:10.1016/S0955-7997(99)00024-7
[14] DOI: 10.1121/1.392911 · doi:10.1121/1.392911
[15] Mechel F. P., Formulas of Acoustics (2002)
[16] DOI: 10.1142/S0218396X05002608 · Zbl 1137.76427 · doi:10.1142/S0218396X05002608
[17] DOI: 10.1121/1.1529668 · doi:10.1121/1.1529668
[18] DOI: 10.1016/j.apacoust.2004.11.004 · doi:10.1016/j.apacoust.2004.11.004
[19] DOI: 10.1121/1.1841511 · doi:10.1121/1.1841511
[20] DOI: 10.1121/1.394536 · doi:10.1121/1.394536
[21] DOI: 10.1121/1.419691 · doi:10.1121/1.419691
[22] Williams E. G., Fourier Acoustics. Sound Radiation and Nearfield Acoustical Holography (1999)
[23] DOI: 10.1121/1.423719 · doi:10.1121/1.423719
[24] DOI: 10.1121/1.1487845 · doi:10.1121/1.1487845
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.