Contents: 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001

2008, 18

E. A. Navarro, J. Segura, R. Sanchis, A. Soriano

Solving 2D acoustic ducts and membranes by using FDTD method

language: English

received 28.08.2008, published 27.11.2008

Download article (PDF, 250 kb, ZIP), use browser command "Save Target As..."
To read this document you need Adobe Acrobat © Reader software, which is simple to use and available at no cost. Use version 4.0 or higher. You can download software from Adobe site (http://www.adobe.com/).

ABSTRACT

The paper describes an application of the FDTD (Finite Difference Time Domain) method, combined with the discrete Fourier transform (DFT) for solving Eigenvalue problems in acoustical waveguides and membranes of arbitrary cross-section. The governing acoustic equations are discretised in a two-dimensional domain, in which boundary conditions are defined over pressure or velocity. At cut-off, the cross-section of a waveguide acts as a two dimensional resonator. Therefore, the spectral response gives the cut-off frequencies of the waveguide or the resonant frequencies of the membrane. Once each frequency is known, the application of the discrete Fourier transform also provides the spatial distribution of the pressure-velocity modes in the cross-section of the waveguide or membrane.

Keywords: finite differences in time domain, Euler equations, waveguide, membrane.

13 pages, 4 figures

Сitation: E. A. Navarro, J. Segura, R. Sanchis, A. Soriano. Solving 2D acoustic ducts and membranes by using FDTD method. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2008, 18.

REFERENCES

1. N. H. Fletcher and T. D. Rossing. The physics of Musical Instruments. Springer-Verlag, New York 1991.
2. M. Guerich and M. A. Hamdi. A numerical method for vibro-acoustic problems with incompatible finite element meshes using B-spline functions. J. Acoust. Soc. Am., vol. 105, no. 3, pp. 1682–1694, March 1999.
3. F. Fontana and D. Rocchesso. Physical Modeling of Membranes for Percussion Instruments. ACUSTICA-acta acustica, vol. 84, pp. 529–542, 1998.
4. J. Bretos, C. Santamaria and J. Alonso-Moral. Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis. J. Acoust. Soc. Am., vol. 105, no. 3, pp. 1942–1950, March 1999.
5. A-C. Hladky-Hennion and R. Bossut. Time analysis of immersed waveguides using the finite element method. J. Acoust. Soc. Am., vol. 104, no. 1, pp. 64–71, Jul. 1998.
6. T. Angkaew, M Masanori and N. Kumagai. Finite element analysis of waveguide modes: a novel approach that eliminates spurious modes. IEEE Trans. Microw. Theory Techniques, vol. MTT 35, (2), pp. 117–123, 1987.
7. K. S. Yee. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antenna Propagat., vol. AP 14, (5), pp. 302–307, 1966.
8. A. Taflove and M.E. Brodwin. Numerical solution of steady state electromagnetic scattering problems using the time dependent Maxwell's equations. IEEE Trans. Microw. Theory Techniques, vol. MTT 23, (8), pp. 623–630, 1975.
9. R. Holland, L. Simpson and K. Kunz. Finite difference analysis of EMC coupling to lossy dielectric structures. IEEE Trans. Electromagnetic Compat., vol. EMC 22, pp. 203–209, 1980.
10. K. Umashankar and A. Taflove. A novel method to analyze electromagnetic scattering of complex objects. IEEE Trans. Electromagnetic Compat., vol. EMC 24, pp. 397–405, 1982.
11. Kurt L. Shlager and John B. Schneider. A selective survey of the Finite-Difference Time-Domain Literature. IEEE Antennas and Propagation Magazine, vol. 37, no.4, August 1995, pp.39–56.
12. R. Madariaga. Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am., vol. 66, pp. 639–666, 1976.
13. J. Virieux. SH-wave propagation in heterogeneous media: Velocity-stress finite difference method. Geophysics, vol. 49, pp. 1933–1942, 1984.
14. Q-H. Liu, E. Schoen, F. Daube, C. Randall, H-L. Liu and P. Lee. A three-dimensional finite difference simulation of sonic logging. J. Acoust. Soc. Am., vol.100, no.1, pp. 72–79, 1996.
15. Y-H. Chen, W. C. Chew and Q-H. Liu. A three-dimensional finite difference code for the modeling of sonic logging tools. J. Acoust. Soc. Am., vol. 103, no. 2, pp. 702–712, 1998.
16. S. Wang. Finite-difference time-domain approach to underwater acoustic scattering problems. J. Acoust. Soc. Am., vol. 99, no. 4, pt. 1, pp. 1924–1931, Apr.1996.
17. F.D. Hastings, J.B. Schneider and S.L. Broschat. A finite-difference time-domain solution to scattering from a rough pressure-release surface. J. Acoust. Soc. Am., vol. 102, no. 6, pp. 3394–3400, 1997.
18. D. Botteldooren. Finite-difference time-domain simulation of low-frequency room acoustic problems. J. Acoust. Soc. Am., vol. 98, pp. 3302–3308, 1995.
19. J. LoVetri, D. Mardare and G. Soulodre. Modeling of the seat dip effect using the finite-difference time-domain method. J. Acoust. Soc. Am., vol. 100, pp. 2204–2212, 1996.
20. J. De Poorter and D. Botteldooren. Acoustical finite-difference time-domain simulations of subwavelength geometries. J. Acoust. Soc. Am., vol. 104, no. 3, pp. 1171-1177, 1998.
21. D. Botteldooren. Acoustical finite-difference time-domain simulation in quasi-Cartesian grids. J. Acoust. Soc. Am., vol. 95, no. 5, pp. 2313–2319, 1994.
22. D. Botteldooren. Vorticity and entropy boundary conditions for acoustical finite-difference time-domain simulations. J. Acoust. Soc. Am., vol. 102, pp. 170–178, 1997.
23. D. Botteldooren. Numerical model for moderately nonlinear sound propagation in three-dimensional structures. J. Acoust. Soc. Am., vol. 100, pp. 1357–1367, 1996.
24. I. M. Hallaj, R. O. Cleveland. FDTD simulation of finite-amplitude pressure and temperature fields for biomedical ultrasound. J. Acoust. Soc. Am., vol. 105, no. 5, pp. L7-L12, 1999.
25. X. Zhang and K. K. Mei. Time domain finite difference approach to the calculation of the frequency dependent characteristics of microstrip discontinuities. IEEE Trans., 1988, MTT 36, (12), pp. 1775 1787
26. E. O. Brigham. The fast Fourier transform and its applications. Prentice Hall, 1988.
27. E. A. Navarro, N. T. Sangary and J. Litva. Some Considerations on the accuracy of the non-uniform FDTD method and its application to waveguide analysis when combined with the Perfect Matched Layer. IEEE Trans. Microwave Theory Tech., vol. 44, no. 7, pp. 1115–1124, July 1996.


 

Enrique A. Navarro was born in Sueca, Spain, in 1965. He received the Licenciado and the Ph.D. degrees in physics from the University of Valencia, Valencia, Spain, in 1988 and 1992, respectively. From 1988 to 1989 he was with Grupo de Mecánica del Vuelo S.A. (GMV S.A.), Madrid, Spain. He joined the Department of Applied Physics at the University of Valencia in 1989 where he is presently a Professor. In 1994 and 1995 he was with the Communications Research Laboratory, McMaster University, Canada. His current research interests include all aspects of numerical methods in electromagnetics, antennas and propagation. Dr. Navarro was the recipient of a 1993 NATO Fellowship.

e-mail: enrique.navarro(at)uv.es

 
 

Jaume Segura was born in Algemesí (Valencia), Spain, in 1973. He received the Licenciado degree in physics from the University of Valencia, Valencia, Spain, in 1998. In 2003 he received his PhD degree in Applied Physics at the University of Valencia.
From 2003 up to now, he has been with Institut de Robotica at the University of Valencia, working at the LISITT (Integrated Laboratory for the application of Intelligent Transportation Systems). Between others his current research interests include environmental and architectural acoustics and the application of numerical methods in acoustics.

e-mail: jaume.segura(at)uv.es

 
 

Raül Sanchis Francés was born in Banyeres de Mariola (Alacant), Spain, on February 6, 1976. He received the Llicenciat degree in physics and Diploma d’Estudis Avançats degree in Electronic Engineering from the University of Valencia, Spain, in 1999 and 2001, respectively, and is currently working toward the Ph.D. degree in computer science at the same institution. From 2000 to 2003 he was a Research Assistant in the Microwave Heating Department of Radiación y Microondas, S.A. in collaboration with the Microwave Heating Group of the Polythecnic University of Valencia where he was currently involved in the development of microwave heating components and applicators for industrial applications. From 2005 to 2007 he was Assistant Professor at the Applied Physics Department of the Polythecnic University of Catalonia, Spain. His current research interests include the areas of computer-aided techniques (FDTD) for the analysis of acoustic and photonic crystals, acoustic lens and musical instruments.

 
 

Antonio Soriano was born in Benaguasil (Valencia), Spain, in 1978. In 2001 he received the licenciado degree in physics, and the electronics engineering degree in 2005 from the University of Valencia. In 2007 he received the PhD in Computer Science from the University of Valencia. He was with the Applied Physics Departments in the Universities of Granada and Valencia from 2001 to 2004, and from 2004 to 2007 respectively. In 2007 he joined the Medical Physics Group at the Particle Physics Institute (IFIC) of the Spanish National Research Council (CSIC). His research interest is focused on numerical modelling of electromagentic wave-propagation using the FDTD technique.