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Streszczenie:
The analytical formulas describing the acoustic field inside the hemi-cylindrical room with the quarter-spherical dome were obtained. The considered enclosure can represent an interior of a sacral or historical object, as well as a room of modern architectural design. It was assumed that a point source generates an acoustic field, and a sound energy can be absorbed by materials on the floor and on an inner surface of the dome. The two appropriate solutions were proposed. One of them describes the sound field inside the hemi-cylindrical part of the room, and the second one presents the sound field inside the dome. Then, these solutions were coupled with the use of the continuity conditions. The formulas and the methodology to calculate the eigenfrequencies of the considered room were also presented. The results given by the obtained formulas agree with those provided by the finite element method (FEM). Moreover, the numerical simulations proved that the use of the presented formulas to calculate the sound pressure amplitude can be more numerically efficient than the FEM and can provide more accurate results. This means that the obtained formulas can be used instead of the FEM to improve the analysis of the sound field inside the considered room. The presented formulas can be used to predict the acoustical behavior of the considered room and consequently to design the room with appropriate acoustic conditions. As an example, the distributions of the acoustic pressure amplitude were predicted by using the obtained formulas.

Słowa kluczowe:
modal analysis, propagation and radiation, structural acoustics

Streszczenie:
Enclosures with a mixed rectangular-cylindrical geometry are common in sacred, historic and modern buildings. Therefore, obtaining efficient analytical formulas for describing the sound radiation inside such structures is of practical importance. These formulas can be implemented in open-source software and can aid in the analysis of acoustic fields. In this study, the problem of sound radiation by a point source located inside a rectangular enclosure with a sound-absorbing quarter-cylindrical ceiling was analytically solved. The formulas presented in this paper can also be used to obtain the eigenfrequencies and eigenfunctions. To obtain the analytical solution, two connected subregions, namely rectangular space, and quarter-cylinder, were considered, and the continuity conditions were imposed on the region’s coupling interface. The acoustic field was described using the solution for a rigid-walled room and the additional components containing the Fourier and Dini series. These components allow the solution to satisfy the impedance boundary condition and the continuity conditions. The formulas and their computer implementation were validated using the finite element method (FEM). A good agreement was achieved between results given by both methods. The numerical analysis demonstrated that the use of the formulas is less time-consuming than using FEM when the frequency is greater than 150 Hz. Moreover, compared to FEM, the analytical solution can be applied to higher frequencies for which the use of FEM requires hardware with high computing capability.

Słowa kluczowe:
Room acoustics,Irregular enclosure,Efficient analytical solution,Acoustic pressure field,Acoustic intensity vector field,Complex eigenfrequencies