A practical error estimator for finite element predicted natural frequencies of membrane vibration problems

Journal of Sound and Vibration

Volumn 195, Issue 5, 1996, Pages 739-756

  Zhao, Chongbin ^a   Steven, G P ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ESTIMATOR; ERROR ESTIMATOR CRITERION; FINITE ELEMENT MESH; FINITE ELEMENT MESH DESIGN CRITERION;

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; ERROR ANALYSIS; FINITE ELEMENT METHOD; MEMBRANES; NATURAL FREQUENCIES;

VIBRATIONS (MECHANICAL);

EID: 0030570972     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1996.0459     Document Type: Article

References (31)

1. C. ZHAO and G. P. STEVEN 1996 Communications in Numerical Methods in Engineering 12, 63-73. An asymptotic formula for correcting finite element predicted natural frequencies of membrane vibration problems.
2. LORD RAYLEIGH 1877 Theory of Sound. New York: Dover Publications.
3. P. M. MORSE 1936 Vibration and Sound. New York: McGraw-Hill Book Co.
4. G. R. SHARP 1967 Journal of Sound and Vibration 5, 1-8. Finite transform solution of the symmetrically vibrating annular membrane.
5. N. Y. OLCER 1967 Journal of Sound and Vibration 6, 365-374. General solution to the equation of the vibrating membrane.
6. P. A. A. LAURA 1967 Journal of the Acoustical Society of America 42, 21-26. Calculation of eigenvalues for uniform fluid waveguides with complicated cross sections.
7. P. A. A. LAURA, E. ROMANELLI and M. J. MAURIZI 1972 Journal of Sound and Vibration 20, 27-38. On the analysis of waveguides of doubly-connected cross-section by the method of conformal mapping.
8. K. NAGAYA 1978 Journal of Applied Mechanics 45, 153-158. Vibrations and dynamic response of membranes with arbitrary shape.
9. K. SATO 1976 Journal of Sound and Vibration 19, 535-540. Free vibration analysis of a composite rectangular membrane consisting of strips.
10. J. P. SPENCE and C. O. HORGAN 1983 Journal of Sound and Vibration 87, 71-81. Bounds on natural frequencies of composite circular membranes: Integral equation methods.
11. P. A. A. LAURA, L. ERCOLI and R. O. GROSSI 1985 Journal of Sound and Vibration 101, 299-306. Transverse vibration of composite membranes of arbitrary boundary shape.
12. H. P. W. GOTTLIED 1986 Journal of Sound and Vibration 110, 395-411. New types of vibration modes for stepped membranes.
13. V. H. CORTINEZ and P. A. A. LAURA 1992 Journal of Sound and Vibration 156, 217-225. Vibrations of non-homogeneous rectangular membranes.
14. A. W. LEISSA 1969 Vibration of Plates (NASA SP-160). Washington DC: U.S. Government Printing Office.
15. A. W. LEISSA 1973 Vibration of Plates (NASA SP-288). Washington DC: U.S. Government Printing Office.
16. A. W. LEISSA 1967 Journal of Sound and Vibration 6, 145-148. Vibration of a simply supported elliptical plate.
17. A. W. LEISSA, J. C. MCBAIN and R. E. KIELB 1984 Journal of Sound and Vibration 96, 159-173. Vibration of twisted cantilevered plates - summary of previous and current studies.
18. I. BABUSKA and W. C. RHEINBOLDT 1978 SIAM Journal of Numerical Analysis 15, 736-754. Error estimates for adaptive finite element computation.
19. I. BABUSKA and W. C. RHEINBOLDT 1978 International Journal of Numerical Methods in Engineering 12, 1597-1615. A posteriori error estimates for the finite element method.
20. I. BABUSKA and A. MILLER 1987 Computer Methods in Applied Mechanical Engineering 61, 1-40. A feedback finite element method with a posteriori error estimation: Part I - The finite element method and some basic properties of the a posteriori error estimator.
21. D. W. KELLY 1984 International Journal of Numerical Methods in Engineering 20, 1491-1506. The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method.
22. D. W. KELLY, J. P. DE, S. R. GAGO and O. C. ZIENKIEWICZ 1983 International Journal of Numerical Methods in Engineering 19, 1593-1619. A posteriori error analysis and adaptive processes in the finite element method: Part 1 - Error analysis.
23. J. T. ODEN, L. DEMKOWICZ, W. RACHOWICZ and T. A. WESTERMANN 1989 Computer Methods in Applied Mechanical Engineering 77, 113-180. Towards a univeral h-p adaptive finite element strategy: Part 2 - A-posteriori error estimation.
24. W. RACHOWICZ, J. T. ODEN and L. DEMKOWICZ 1989 Computer methods in Applied Mechanical Engineering 77, 181-212. Toward a universal h-p adaptive finite element strategy: Part 3-Design of h-p meshes.
25. O. C. ZIENKIEWICZ and J. Z. ZHU 1987 Internation of Journal of Numerical Methods in Engineering 24, 337-357. A simple estimator and adaptive procedure for practical engineering analysis.
26. O. C. ZIENKIEWICZ and J. Z. ZHU 1992 International Journal of Numerical Methods in Engineering 33, 1365-1382. The superconvergent patch recovery and a posteriori error estimates: Part 2 - Error estimates and adaptivity.
27. C. ZHAO and G. P. STEVEN 1995 Communications in Numerical Methods in Engineering 11, 13-23. Analytical solutions of mass transport problems for error estimation of finite/infinite element methods.
28. R. D. COOK and J. AVRASHI 1992 Computer and Structures 44, 619-626. Error estimation and adaptive meshing for vibration problems.
29. Y. M. XIE and G. P. STEVEN 1993 Communications in Numerical Methods in Engineering 9, 671-680. Explicit formulas for correcting finite element predictions of natural frequencies.
30. C. ZHAO and G. P. STEVEN 1996 Computers and Structures (in press). A posteriori error estimators/correctors for natural frequencies of membrane vibration problems.
31. C. ZHAO and G. P. STEVEN 1996 Computers and Structures 59, 949-963. A posteriori error estimators/correctors for natural frequencies of thin plate vibration problems.