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Simulation of a single mode wave generation in cylindrical systems applying numerical methods

100%

Gorazd Ł. , Snakowska A.

Vibrations in Physical Systems

2019

tom Vol. 30, nr 1

art. no. 2019118

The paper presents simulations of a selected single mode generation in systems containing duct-like elements applying the finite element method (FEM). Simulations were carried out for values of the Helmholtz number exceeding the plane-wave propagation, i.e. for a multimode wave. The presented results constitute the first step to analyse propagation of the multimode wave through more complicated systems such as mufflers, even in a form of a cascade. Propagation of the incident wave in the form of a single mode greatly simplifies solutions of many problems, to mention only derivation of the transmission or the scattering matrices. The results obtained can be applied to analyse the effectiveness of attenuation of acoustic silencers or elements of heating, ventilation and air conditioning systems (HVAC) at the design stage. Results of simulations are compared with already published experimental data obtained in a measurement set-up containing the self-designed single mode synthesizer.

Error Analysis of Sound Source Directivity Interpolation Based on Spherical Harmonics

80%

Szwajcowski A. , Krause D. , Snakowska A.

Archives of Acoustics

2021

tom Vol. 46, No. 1

95--104

Precise measurement of the sound source directivity not only requires special equipment, but also is time-consuming. Alternatively, one can reduce the number of measurement points and apply spatial interpolation to retrieve a high-resolution approximation of directivity function. This paper discusses the interpolation error for different algorithms with emphasis on the one based on spherical harmonics. The analysis is performed on raw directivity data for two loudspeaker systems. The directivity was measured using sampling schemes of different densities and point distributions (equiangular and equiareal). Then, the results were interpolated and compared with these obtained on the standard 5° regular grid. The application of the spherical harmonic approximation to sparse measurement data yields a mean error of less than 1 dB with the number of measurement points being reduced by 89%. The impact of the sparse grid type on the retrieval error is also discussed. The presented results facilitate optimal sampling grid choice for low-resolution directivity measurements.

Evaluation of the transmission and the scattering matrix applicability to the mufflers analysis

80%

Snakowska A. , Gorazd Ł. , Jurkiewicz J.

Vibrations in Physical Systems

2019

tom Vol. 30, nr 1

art. no. 2019102

The analysis of the acoustical systems can be carried out based on a number of different formalisms, of which applied frequently are the transfer matrix formalism, in which the chosen state variables are the sound pressure p and the sound velocity v, and the scattering matrix formalism adopting the sound pressures p+ and p− and the sound velocities v+ and v− of waves propagating through an element in both directions. Even though, they are mathematically equivalent, i.e. there exists the unequivocal transformation from one to another there are some advantages and disadvantages in applying one or the other to analyse mufflers or other acoustic system, especially when the propagation of a multimode wave is assumed and numerical calculations are indispensable. In the paper the transformation between the formalisms has been derived and applied to analyse the phenomena at a junction between the tail pipe and the chamber and also in mufflers composed of one or two chambers. The more flexible for numerical calculations seems the scattering matrix formalism, especially when the number of propagating modes differs on both sides of a junction. On the other hand the transmission matrix formalism is suitable for analysing systems constituting a cascade. The sources of the advantages and disadvantages of both formalisms are explained. The results obtained can be helpful in the effective design of silencers with specific properties.