Improved eigenfrequencies and eigenmodes in free vibration analysis

Computers and Structures

Volumn 73, Issue 1-5, 1999, Pages 79-89

  Wiberg, Nils Erik ^a   Bausys, Romualdas ^a   Hager, Patrik ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; MATRIX ALGEBRA; PROBLEM SOLVING; VIBRATIONS (MECHANICAL);

EIGENFREQUENCIES; EIGENMODES; FREE VIBRATION ANALYSIS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0033208026     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(98)00265-X     Document Type: Article

References (32)

1. Babuska I., Zienkiewicz O.C., Gago J., Oliveira E.R. Accuracy estimates and adaptive refinements in finite element computations. 1986;Wiley, New York.
2. Oden JT, editor. Reliability in computational mechanics Proceedings of the Workshop on Reliability in Computational Mechanics, Austin, Texas October 1989. Comput. Meth. Appl. Mech. Engng 1990;82.
3. Zienkiewicz O.C., Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Meth. Engng. 24:1987;333-357.
4. Oden J.T., Demkowicz L., Rachowicz W., Westerman T.A. Toward a universal h-p adaptive finite element strategy: Part 2, a posteriori error estimates. Comput. Meth. Appl. Mech. Engng. 77:1989;113-180.
5. Strouboulis T., Haque K.A. Recent experiences with error estimation and adaptivity, Part I: review of error estimators for scalar elliptic problems. Comput. Meth. Appl. Mech. Engng. 97:1992;399-436.
6. Strouboulis T., Haque K.A. Recent experiences with error estimation and adaptivity, Part II: error estimation for h-adaptive approximations on grids of triangles and quadrilaterals. Comput. Meth. Appl. Mech. Engng. 100:1992;359-430.
7. Zienkiewicz O.C., Zhu J.Z. The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput. Meth. Appl. Mech. Engng. 101:1992;207-224.
8. Babuska I., Strouboulis T., Upadhyay C.S., Gangaraj S.K., Copps K. Validation of a posteriori error estimators by numerical approach. Int. J. Numer. Meth. Engng. 37:1994;1073-1123.
9. Friberg O., Möller P., Makovicka D., Wiberg N.E. An adaptive procedure for eigenvalue problems using hierarchical finite element method. Int. J. Numer. Meth. Engng. 24:1987;319-335.
10. 0 eigenproblems in finite element analysis. Engng Comput. 10:1993;243-256.
11. Mackie R.I. Improving finite element predictions of modes of vibration. Int. J. Numer. Meth. Engng. 33:1992;333-344.
12. Zienkiewicz O.C., Zhu J.Z. The superconvergent patch recovery and a posteriori error estimators. Part 1: The recovery technique. Int. J. Numer. Meth. Engng. 33:1992;1331-1364.
13. Zienkiewicz O.C., Zhu J.Z. The superconvergent patch recovery and a posteriori error estimators. Part 2: Error estimates and adaptivity. Int. J. Numer. Meth. Engng. 33:1992;1365-1382.
14. Wiberg N-E., Abdulwahab F. Patch recovery based on superconvergent derivatives and equilibrium. Int. J. Numer. Meth. Engng. 36:1993;2703-2724.
15. Wiberg N-E., Abdulwahab F., Ziukas S. Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. Int. J. Numer. Meth. Engng. 37:1994;3417-3440.
16. Wiberg N-E., Li X.D. A postprocessed error estimate and an adaptive procedure for a semidiscrete finite element method in dynamic analysis. Int. J. Numer. Meth. Engng. 37:1994;3585-3603.
17. Wiberg N-E., Abdulwahab F., Ziukas S. Improved element stresses for node and element patches using superconvergent patch recovery. Commun. Appl. Numer. Meth. 11:1995;619-627.
18. Wiberg N-E., Bausys R. Error estimation for eigenfrequencies and eigenmodes in dynamics. Pal J., Werner H. Computing in Civil and Building Engineering. 1995;611-616 Balkema, Rotterdam.
19. 2 norm error estimate. Commun. Appl. Numer. Meth. 10:1994;313-320.
20. Tabbara M., Blacker T., Belytschko T. Finite element derivative recovery by moving least square interpolants. Comput. Meth. Appl. Mech. Engng. 117:1994;211-223.
21. Gambolati G., Sartoretto F., Florian P. An orthogonal accelerated deflation technique for large symmetric eigenproblems. Comput. Meth. Appl. Mech. Engng. 94:1992;13-23.
22. Perdon A.M., Gambolati G. Extreme eigenvalues of large sparse matrices by Rayleigh quotient and modified conjugate gradients. Comput. Meth. Appl. Mech. Engng. 56:1986;251-264.
23. Gambolati G., Putti M. A comparison of Lanczos and optimization methods in the partial solution of sparse symmetric eigenproblems. Int. J. Numer. Meth. Engng. 37:1994;605-621.
24. Gambolati G., Pini G., Putti M. Nested iterations for symmetric eigenproblems. SIAM J. Sci. Comput. 16:1995;173-191.
25. Cho Y., Yong Y-K. A multi-mesh, preconditioned conjugate gradient solver for eigenvalue problems in finite element models. Comput. Struct. 58:1995;575-583.
26. Gambolati G., Bergamaschi L. Partial eigensolution for transient groundwater flow equations. Russell T.R., Ewing R.E., Brebbia C.A., Gray W.G., Pinder G.F. ICCMWR IX Numerical Methods in Water Resources. vol. 1:1992;175-192 Computational Mechanics/Elsevier Applied Sciences, Southampton/Oxford.
27. Kershaw D.S. The incomplete Cholesky-conjugate gradient method for the iterative solution of linear equations. J. Comput. Phys. 26:1978;43-65.
28. Meijerink J.A., van der Vorst H.A. An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comput. 31:1977;148-162.
29. Parlett B.N. The symmetric eigenvalue problem. 1980;Prentice-Hall, Englewood Cliffs, NJ.
30. Bathe K-J. Finite element procedures in engineering analysis. 1982;Prentice-Hall, Englewood Cliffs, NJ.
31. Gambolati G. Solution of large-scale eigenvalue problems. Papadrakakis M. Solving large scale problems in mechanics: the development and application of computational solution methods. 1993;125-156 Wiley, New York.
32. Gupta K.K. Development of a finite dynamic element for free vibration analysis of two-dimensional structures. Int. J. Numer. Meth. Engng. 12:1978;1311-1327.