Initial and boundary conditions in multidimensional wave digital filter algorithms for plate vibration

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 51, Issue 8, 2004, Pages 1648-1663

  Tseng, Chien Hsun ^a   Lawson, Stuart ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; EQUATIONS OF MOTION; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS); VIBRATIONS (MECHANICAL);

COURANT-FRIEDRICHS-LEVY BOUND; GOLDEN SECTION SEARCH METHOD; KIRCHHOFF CIRCUIT; MINDLIN PLATE VIBRATION SYSTEM; MULTIDIMENSIONAL WAVE DIGITAL FILTERS;

DIGITAL FILTERS;

EID: 4344652891     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2004.832796     Document Type: Article

References (26)

1. A. Fettweis, "Digital filters related to classical filter networks," AEÜ, vol. 25, pp. 79-89, 1971.
2. A. Fettweis, "Wave digital filters: Theory and practice," Proc. IEEE, vol. 74, pp. 270-327, 1986.
3. A. Fettweis and G. Nitsche, "Transformation approach to numerical integrating PDEs by means of WDF principles," Multidim. Syst. Signal Processing, vol. 2, pp. 127-159, 1991.
4. A. Fettweis, "Numerical integration of partial differential equations using principles of multidimensional wave digital filters," J. VLSI Signal Processing, vol. 3, pp. 7-24, 1991.
5. G. Nitsche, "Numerische Lösung Partieller Differentialgleichungen mit Hilfe von Wellendigitalfiltern," Ph.D. dissertation, Fakultät Electrotech. Info., Ruhr-Universität, Bochum, Germany, 1993.
6. X. Liu and A. Fettweis, "Multidimensional digital filtering by using parallel algorithms based on diagonal processing," Multidim. Syst. Signal Processing, vol. 1, pp. 51-66, Mar 1990.
7. A. Fettweis and K. Meerkötter, "On parasitic oscillations in digital filters under looped conditions," IEEE Trans. Circuits Syst., vol. CAS-24, pp. 475-481, Sept. 1977.
8. C. T. Mullis and R. A. Roberts, "Synthesis of minimum roundoff noise fixed point digital filters," IEEE Trans. Circuits Syst., vol. CAS-23, pp. 551-562, Sept. 1976.
9. A. Fettweis, "Discrete passive modeling of physical systems described by PDEs," in Proc. EUSIPCO-92, 6th Eur. Signal Processing Conf., vol. 1, Brussels, Belgium, 1992, pp. 55-62.
10. G. Hemetsberger, "Stability verification of multidimensional Kirchoff circuits by suitable energy functions," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, vol. 6, Adelaide, Australia, 1994, pp. 13-16.
11. C. Q. Xu, S. C. Bass, and X. Wang, "Accommodating linear and nonlinear boundary conditions in wave digital simulations of PDE systems," J. Circuits Syst. Comput., vol. 7, pp. 563-597, 1997.
12. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics.-1: Fundamental and General Techniques, 2nd ed. New York: Springer-Verlag, 1991.
13. A. Fettweis, H. Levin, and A. Sedlmeyer, "Wave digital lattice filters," Int. J. Circuit Theory Applicat., vol. 2, pp. 203-211, 1974.
14. H. Krauss, R. Rabenstein, and M. Gerken, "Simulation of wave propagation by multidimensional digital filters," J. Simulation Practice Theory, vol. 4, pp. 361-382, 1996.
15. C. H. Tseng and S. S. Lawson, "Incorporating initial and boundary conditions into the multidimensional wave digital filter," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, Orlando, FL, May 2002.
16. S. D. Bilbao, "Wave and scattering methods for the numerical integration of partial differential equations," Ph.D dissertation, Dept. Elect. Eng., Stanford Univ., Stanford, CA, 2001.
17. Computer Solutions Europe AB, Partial Differential Equation Toolbox, The Math Works, Natick, MA, 1996.
18. K. F. Graff, Wave Motion in Elastic Solids. New York: Dover, 1975.
19. R. D. Mindlin, "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates," Trans. ASME J. Appl. Mech., vol. 18, pp. 31-38, 1951.
20. K. Liew, C. Wang, Y. Xiang, and S. Kitipornchai, Vibration of Mindlin Plates: Programming the p-Version Ritz Method, first ed. Amsterdam, The Netherlands: Elsevier, 1998.
21. E. Hinton and B. S. Al-Janabi, Numerical Methods and Software for Dynamic Analysis of Plates and Shells, E. Hinton, Ed. Swansea, U.K.: Pineridge Press, 1987.
22. H. Huang, Static and Dynamic Analyzes of Plates and Shells. London, U.K.: Springer-Verlag, 1989.
23. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. New York: McGraw-Hill, 1959.
24. M. D. Waller, Chladni Figures: A Study in Symmetry. London, U.K.: G. Bell and Sons, 1961.
25. R. Nouta, "The use of Jaumann structures in wave digital filters," Int. J. Circuit Theory Applicat., vol. 2, pp. 163-174, 1974.
26. A. A. Samarskij, Theorie der Differenzenverfahren (in German). Leipzig: Akademicshe Verlagsgesellschaft, 1984.