Acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval Newton/generalized bisection method

Journal of the Acoustical Society of America

Volumn 118, Issue 6, 2005, Pages 3662-3671

  Naka, Yusuke ^a   Oberai, Assad A ^a   Shinn Cunningham, Barbara G ^a  

^a BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC IMPEDANCE; BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; NUMERICAL METHODS; PROBLEM SOLVING;

ACOUSTIC EIGENVALUE EQUATIONS; FINITE ELEMENT SOLUTIONS; HELMHOLTZ OPERATORS; IN/GB METHODS;

ACOUSTICS;

ACCURACY; ACOUSTICS; ALGORITHM; ANALYTIC METHOD; ARTICLE; BUILDING; FINITE ELEMENT ANALYSIS; IMPEDANCE; INTERVAL NEWTON GENERALIZED BISECTION METHOD; PRIORITY JOURNAL; VALIDATION PROCESS; VIBRATION;

EID: 29244443994     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.2114607     Document Type: Article

References (19)

1. P. M. Morse and R. H. Bolt, "Sound waves in rooms," Rev. Mod. Phys. 16, 69-150 (1944).
2. L. Cremer and H. A. Müller, Principles and Applications of Room Acoustics, Vol. 2 (Applied Science Publishers, New York, 1982); english translation by T. J. Schultz.
3. A. D. Pierce, Acoustics-An Introduction to Its Physical Principles and Applications (Acoustical Society of America, New York, 1994).
4. D. T. Blackstock, Fundamentals of Physical Acoustics (Wiley-Interscience, New York, 2000).
5. H. Kuttruff, Room Acoustics, 4th ed. (Spon Press, London, 2000).
6. P. M. Morse, "The transmission of sound inside pipes," J. Acoust. Soc. Am. 11, 205-210 (1939).
7. S. R. Bistafa and J. W. Morrissey, "Numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances," J. Sound Vib. 263, 205-218 (2003).
8. S. L. Hodge, W. E. Zorumski, and W. R. Watson, "Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions," NASA Technical Memorandum 110174, 1995.
9. R. E. Moore, Methods and Applications of Interval Analysis (SIAM, Philadelphia, 1979).
10. A. Neumaier, Interval Methods for Systems of Equations (Cambridge University Press, Cambridge, 1990).
11. R. B. Kearfott, Rigorous Global Search: Continuous Problems (Kluwer Academic, Dordrecht, 1996).
12. T. Sunaga, "Theory of an interval algebra and its application to numerical analysis," in RAAG Memoirs (Gakujutsu Bunken Fukyu-kai, Tokyo, 1958), Vol. 2, pp. 29-46 (547-564).
13. Y. Yasuda, S. Sakamoto, A. Ushiyama, and H. Tachibana, "Reverberation characteristics in a room with unevenly-distributed absorbers: Numerical analysis," Acoust. Sci. Tech. 26, 388-390 (2005).
14. L. L. Beranek, "Acoustic impedance of commercial materials and the performance of rectangular rooms with one treated surface," J. Acoust. Soc. Am. 12, 14-23 (1940).
15. M. J. Schulte, A. Akkas, V. A. Zelov, and J. C. Burley, "Compiler support for interval arithmetic," in Proceedings of the 16th IEEE Instrumentation and Measurement Technology Conference, Venice, Italy, May 1999, pp. 1189-1193.
16. C. Hu, S. Xu, and X. Yang, "A review on interval computation-Software and applications," Int. J. Comput. Numer. Anal. Appl. 1, 149-162 (2002).
17. R. B. Kearfott, M. Dawande, K. Du, and C. Hu, "INTLIB: A portable FORTRAN 77 interval standard-function library," ACM Trans. Math. Softw. 20, 447-459 (1994).
18. K. Bodlund, "Monotonic curvature of low frequency decay records in reverberation chambers," J. Sound Vib. 73, 19-29 (1980).
19. E. R. Hansen, Topics in Interval Analysis (Clarendon, Oxford, 1969).