Journal Press India®

Solutions of the Acoustic Problem in the 3D Form of the Helmholtz Equation Using DRBEM

Vol 4 , Issue 1 , January - March 2016 | Pages: 272-277 | Research Paper  

https://doi.org/10.51976/ijari.411639

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Author Details ( * ) denotes Corresponding author

1. * Hassan Ghassemi, Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran (gasemi@aut.ac.ir)
2. Ahmad Reza Kohansal, Shipbuilding Eng. Group, School of Engineering, Persian Gulf University, Bushehr, Iran

This paper presents to the solutions of the acoustic problem using dual reciprocity boundary element method (DRBEM). The acoustic propagates inside the silencer and its sound can be formulated by the three dimensional (3D) Helmholtz equation. The form of the equation is which can be solved by the integral form on the boundary. The conventional boundary element method (BEM) is not suitable for solving the acoustic problems of silencers with higher Mach number subsonic flow, due to the presence of domain integral. The dual reciprocity method (DRM) is a method that converts the domain integral into the boundary integral. Mathematical formulations discretisation form and evaluation of the integrals are described and discussed. Algorithm of the method is also presented.

Keywords

Acoustic Problem; 3D Helmholtz Equation; Dual Reciprocity Method.


  1. Miao, X. H., Wang X. R, Jia, D. Qian D. J., and Pang F. Z., Substructure dual reciprocity boundary element method for prediction of acoustic attenuation performance of silencers with potential flow, APCOM & ISCM, 2013,

  2. Nardini, D. and Brebbia, C.A., New Approach to Vibration Analysis Using Boundary Elements, in Boundary Element Methods in Engineering, Computational Mechanics Publications 1982, Southampton and Springer-Verlag, Berlin.

  3. Ramachandran, P.A., Boundary Element Methods in Transport Phenomena, Computational Mechanics Publication, Southampton, Boston, 1994.

  4. Zakerdoost, H., Ghassemi, H., Dual reciprocity boundary element method for steady state convection-diffusion-radiation problems, International Journal of Partial Differential Equations and Applications. 2(4), 2014, 68-71.

  5. Lee L, Wu T W, Zhang P. A dual-reciprocity method for acoustic radiation in a subsonic non-uniform flow, Engineering Analysis with Boundary Elements, 13, 1994, 365-370.

  6. Dokumaci E., An integral equation formulation for boundary element analysis of acoustic radiation problems in viscous fluids, Journal of Sound and Vibration, 147(2), 1991, 335-348.

  7. Karra C, Ben Tahar M. An integral equation formulation for boundary element analysis of propagation in viscothermal fluids. Journal of the Acoustical Society of America, 102(3), 1997, 1311-1318.

  8. Zhen-Lin Ji Xue-ren Wang, Application of dual reciprocity boundary element method to predict acoustic attenuation characteristics of marine engine, exhaust silencers, Journal Marine Science Application, 7, 2008, 102-110.

  9. Chen CS, Rashed YF. Evolution of thin plate spline based particular solutions for Helmholtz-type equation for the DRM. Mechanical and Research Communication, 25(2), 1998,195–201.

  10. Perrey-Debaine. Analysis of convergence and accuracy of the DRBEM for axisymmetric Helmholtz-type equation, Engineering Analysis with Boundary Elements, 23, 1999, 703–711.

  11. Ghassemi, H., Kohansal, A.R.,. Numerical evaluation of various levels of singular integrals, arising in BEM and its application in hydrofoil analysis. Applied Mathematics and Computation 213, 2009, 277–289.

  12. Gao, X.W. Evaluation of regular and singular domain integrals with boundary-only discetization—theory and Fortran code, Journal of Computational and Applied Mathematics, 175, 2005, 265–290.

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