Acoustic Radiation of Axisymmetric Thin Bodies by Integral Variational Method

Abstract:

In this paper, a variational formulation by integral equations for the study of acoustic radiation by thin axisymmetric bodies is developed. This new approach derives from the three-dimensional variational formulation. It is based on the Fourier decomposition with respect to the angle of revolution. The three-dimensional problem is reduced to the resolution of several two-dimensional problems. Thus, by construction, the obtained axisymmetric variational equation is prepared to the numerical calculations because it avoids the regularisation of the double normal derivative of modal Green’s function. As for the Fourier coefficients of the singular part of Green’s function and its normal derivative, they are evaluated precisely by the same recurrence relation expressed in terms of the complete elliptic integrals. In addition, the axisymmetric free term derived from the 3-D solid angle, is given by a new expression. Numerical results clearly demonstrate the accuracy of this approach to predict the acoustic fields particularly on corners.

• Periodical: Advanced Materials Research (Volumes 488-489)
• Pages: 1437-1445
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.488-489.1437
• Online since: March 2012
• Authors: M. Beldi, L. Zarrouk
• Keywords: 2D Axisymmetric, Integral Variational Method, Singular Integral, Sound Radiation

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