A Numerical Approach to Calculate the Radiation Efficiency of Baffled Planar Structures Using the Far Field

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A numerical method is developed for estimating the acoustic power of any baffled planar structure, which is vibrating with arbitrary surface velocity profile. It is well known that this parameter may be calculated with good accuracy using near field data, in terms of an impedance matrix, which is generated by the discretization of the vibrating surface into a number of elementary radiators. Thus, the sound pressure field on the structure surface can be determined by a combination of the matrix and the volume velocity vector. Then, the sound power can be estimated through integration of the acoustic intensity over a closed surface. On the other hand, few works exist in which the calculation is done in the far field from near field data by the use of radiation matrices, possibly because the numerical integration becomes complicated and expensive due to large variations of directivity of the source. In this work a different approach is used, based in the so-called Propagating Matrix, which is useful for calculating the sound pressure of an arbitrary number of points into free space, and it can be employed to estimate the sound power by integrating over a finite number of pressure points over a hemispherical surface surrounding the vibrating structure. Through numerical analysis, the advantages/disadvantages of the current method are investigated, when compared with numerical methods based on near field data. A flexible rectangular baffled panel is considered, where the normal velocity profile is previously calculated using a commercial finite element software. However, the method can easily be extended to any arbitrary shape. Good results are obtained in the low frequency range showing high computational performance of the method. Moreover, strategies are proposed to improve the performance of the method in terms of both computational cost and speed.

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