Finite element approach to acoustic transmission-radiation systems and application to horn and silencer design

Kagawa, Y.; Yamabuchi, Tatsuo; Yoshikawa, Tomohiro; Ooie, S.; Kyouno, Noboru; Shindou, T.

doi:10.1016/0022-460x(80)90607-0

Cited by 22 publications

(6 citation statements)

References 4 publications

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“…Equations (1) and (2) may conveniently be written (9) [L] (10) [K' LS ] may also be written where and assembled in this form from the appropriate element submatrices. Each row of Eq.…”

Section: Formation and Minimization Of Residualsmentioning

confidence: 99%

“…Most FEM analyses are based on residual schemes, although in the case with no mean flow a variational statement of the problem is possible. 1 " 3 ' 9 The residual formulations used are generally variants of the Galerkin process although the method of residual least squares has also been proposed as a computationally attractive alternative. 8 ' 12 When no mean flow is present or when the mean flow is irrotational the problem may be formulated in terms of a single dependent variable (pressure or velocity potential).…”

Section: Introductionmentioning

confidence: 99%

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Accuracy and Stability of Finite Element Schemes for the Duct Transmission Problem

1982

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A one-dimensional numerical model is used to investigate the characteristics of finite element computational schemes for linearized acoustical transmission in ducts with flow. Primitive variables and coupled first-order equations are used. The relative performances of Lagrangian and Hermitian elements with Galerkin and residual least squares formulations are assessed. Results of the numerical study are shown to correlate with the characteristics of analytic solutions for the equivalent regular grid difference equations. Galerkin solutions are shown to introduce spurious nonphysical modes which must be eliminated by careful attention to the local resolution requirements of the finite-element mesh. Residual least squares formulations do not introduce spurious numerical modes but result in significant numerical damping. This is particularly severe if Lagrangian elements are used.

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“…Equations (1) and (2) may conveniently be written (9) [L] (10) [K' LS ] may also be written where and assembled in this form from the appropriate element submatrices. Each row of Eq.…”

Section: Formation and Minimization Of Residualsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Accuracy and Stability of Finite Element Schemes for the Duct Transmission Problem

1982

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“…In acoustics, the application of the method is arguably less widespread and examples tend to favour exterior problems. For example, Kagawa et al 19 used the FEM to analyse an interior problem and then applied MM to "join" this solution to a Green's function representation of the exterior acoustic far-field. Astley and Cummings 20 also used MM but they analysed sound radiation from a vibrating ventilation duct wall, using finite elements to discretise the exterior acoustic near field before coupling this to an eigenexpansion of the acoustic far field.…”

Section: Introductionmentioning

confidence: 99%

Modeling sound propagation in acoustic waveguides using a hybrid numerical method

Kirby

2008

The Journal of the Acoustical Society of America

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Sound propagation in an acoustic waveguide is examined using a hybrid numerical technique.Here, the waveguide is assumed to be infinite in length with an arbitrary but uniform crosssection. Placed centrally within the guide is a short component section with an irregular, nonuniform, shape. The hybrid method utilises a wave based modal solution for a uniform section of the guide and, using either a mode matching or point collocation approach, matches this to a standard finite element based solution for the component section. Thus, one needs only to generate a transverse finite element mesh in uniform sections of the waveguide and this significantly reduces the number of degrees of freedom required. Moreover, utilising a wave based solution removes the need to numerically enforce a non-reflecting boundary condition at infinity using a necessarily finite mesh, which is often encountered in studies that use only the standard finite element method. Accordingly, the component transmission loss may readily be computed and predictions are presented here for three examples: an expansion chamber, a converging-diverging duct and a circular cylinder. Good agreement with analytic models is observed, and transmission loss predictions are also presented for multi-mode incident and transmitted sound fields. Kirby, JASA 3

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“…For acoustic filters and mufflers with abrupt area changes, finite element predictions of transmission losses 5 ' 6 are also in good agreement with theory. Kagawa et al 7 recently developed a combination of the finite element (in duet) and analytical methods (Green's theorem in the far field) to analyze sound propagation from a loud speaker. The measured far field sound pressure and directivity characteristics were predicted within a few decibels over a wide frequency range.…”

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confidence: 99%

Acoustics in variable area duct - Finite element and finite difference comparisons to experiment

et al. 1983

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Plane wave sound propagation without flow in a rectangular duct with a converging-diverging area variation is studied experimentally and theoretically. The area variation was of sufficient magnitude to produce large reflections and induce modal scattering. The rms pressure and phase angle on both the flat and curved surface were measured and tabulated. The "steady"-state finite element theory of Astley and Eversman and the transient finite difference theory of White are in good agreement with the data. It is concluded that numerical finite difference and finite element theories appear ideally suited for handling duct propagation problems which encounter large area variations.

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Finite element approach to acoustic transmission-radiation systems and application to horn and silencer design

Cited by 22 publications

References 4 publications

Accuracy and Stability of Finite Element Schemes for the Duct Transmission Problem

Accuracy and Stability of Finite Element Schemes for the Duct Transmission Problem

Modeling sound propagation in acoustic waveguides using a hybrid numerical method

Acoustics in variable area duct - Finite element and finite difference comparisons to experiment

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