First-order shear deformation, p-version, finite element for laminated plate nonlinear vibrations

AIAA Journal

Volumn 43, Issue 6, 2005, Pages 1371-1379

  Ribeiro, Pedro ^a  

^a UNIVERSITY OF PORTO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; FINITE ELEMENT METHOD; FREQUENCY DOMAIN ANALYSIS; HARMONIC ANALYSIS; LAMINATES; NATURAL FREQUENCIES; PLATES (STRUCTURAL COMPONENTS); SHEAR DEFORMATION; STIFFNESS;

HARMONIC BALANCE METHOD; LAMINATED PLATE; NONLINEAR VIBRATIONS; SHEAR LOCKING;

VIBRATIONS (MECHANICAL);

EID: 20444476798     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.4025     Document Type: Article

References (29)

1. Han, W., and Petyt, M., "Geometrically Nonlinear Vibration Analysis of Thin, Rectangular Plates Using the Hierarchical Finite Element Method - I: The Fundamental Mode of Isotropic Plates," Computers and Structures, Vol. 63, No. 2, 1997, pp. 295-308.
2. Han, W., and Petyt, M., "Geometrically Nonlinear Vibration Analysis of Thin, Rectangular Plates Using the Hierarchical Finite Element Method-II: 1st Mode of Laminated Plates and Higher Modes of Isotropic and Laminated Plates," Computers and Structures, Vol. 63, No. 2, 1997, pp. 309-318.
3. Ribeiro, P., and Petyt, M., "Nonlinear Vibration of Composite Laminated Plates by the Hierarchical Finite Element and Continuation Methods," Composite Structures, Vol. 46, No. 3, 1999, pp. 197-208.
4. Ribeiro, P., and Petyt, M., "Multi-modal Geometrical Non-linear Free Vibration of Fully Clamped Composite Laminated Plates," Journal of Sound and Vibration, Vol. 225, No. 1, 1999, pp. 127-152.
5. Mei, C., and Decha-Umphai, K., "Finite Element Method for Nonlinear Forced Vibrations of Rectangular Plates," AIAA Journal, Vol. 23, No. 7, 1985, pp. 1104-1110.
6. Zienkiewicz, O. C., and Taylor, R. L., The Finite Element Method, 4th ed., McGraw-Hill, London, 1988.
7. Sathyamoorthy, M., "Nonlinear Vibration Analysis of Plates: A Review and Survey of Current Developments," Applied Mechanics Review, Vol. 40, No. 11, 1987, pp. 1553-1561.
8. Reissner, E., "The Effect of Transverse Shear Deformation on the Bending of Elastic Plates," Journal of Applied Mechanics, Vol. 12, No. 2, 1945, pp. 69-77.
9. Mindlin, R. D., "Influence of Rotatory Inertia and Shear on Flexural Vibrations of Isotropic, Elastic Plates," Journal of Applied Mechanics, Vol. 18, No. 1, 1951, pp. 31-38.
10. Petyt, M., Introduction to Finite Element Vibration Analysis, Cambridge Univ. Press, Cambridge, England, U.K., 1990, p. 35 and Chap. 6.
11. Mei, C., and Prasad, C. B., "Effects of Large Deflection and Transverse Shear on Response of Rectangular Symmetric Composite Laminates Subjected to Acoustic Excitation," Journal of Composite Materials, Vol. 23, No. 6, 1989, pp. 606-639.
12. Reddy, J. N., and Chao, W. C., "Large Deflection and Large-Amplitude Free Vibrations of Laminated Composite-Material Plates," Computers and Structures, Vol. 13, Nos. 1-3, 1981, pp. 341-347.
13. Hinton, E., and Owen, D. R. J., Finite Element Software for Plates and Shells, Pineridge Press, 1984, Chap. 3.
14. Tessler, A., and Hughes, T. J. R., "A Three-Node Mindlin Plate Element with Improved Transverse Shear," Computer Methods in Applied Mechanics and Engineering, Vol. 50, No. 1, 1985, pp. 71-101.
15. Chen, W. C., and Liu, W. H., "Deflections and Free Vibrations of Laminated Plates-Levy Type Solutions,". International Journal of Mechanical Sciences, Vol. 32, No. 9, 1990, pp. 779-793.
16. Ganapathi, M., Varadan, T. K., and Sarma, S. M., "Nonlinear Flexural Vibrations of Laminated Orthotropic Plates," Computers and Structures, Vol. 39, No. 6, 1991, pp. 685-688.
17. Soldatos, K. P., and Messina, A., "The Influence of Boundary Conditions and Transverse Shear on the Vibration of Angle-Ply Laminated Plates, Circular Cylinders and Cylindrical Panels," Computer Methods in Applied Mechanics and Engineering, Vol. 190, No. 18-19, 2001, pp. 2385-2409.
18. Rank, E., Holzer, S., and Werner, H., "An Implementation of the h-p Version of the Finite Element Method for the Reissner-Mindlin Plate Problems," International Journal for Numerical Methods in Engineering, Vol. 30, No. 3, 1990, pp. 459-471.
19. Scapolla, T., "Avoiding Locking in Reissner-Mindlin Plates with High-Order Hierarchic Bubble Plus Finite Elements," Journal of Computational and Applied Mathematics, Vol. 63, No. 1-3, 1995, pp. 291-299.
20. Brockman, R. A., "Dynamics of the Bilinear Mindlin Plate Element," International Journal for Numerical Methods in Engineering, Vol. 24, No. 12, 1987. pp. 2343-2356.
21. Qian, G.-L., Hoa, S.V., and Xiao, X., "A New Rectangular Plate Element for Vibration Analysis of Laminated Composites," Journal of Vibration and Acoustics, Vol. 120, No. 1, 1998, pp. 80-86.
22. Reddy, J. N., "Theory and Analysis of Laminated Composite Plates," Mechanics of Composite Materials and Structures, edited by C. A. M. Scares, C. A. M. Soares, and M. J. M. Freitas, Kluwer Academic, Dordretch, The Netherlands, 1999, pp. 1-62.
23. Szabó, B. A., and Mehta, A. K., "p-Convergent Finite Element Approximations in Fracture Mechanics," International Journal for Numerical Methods in Engineering, Vol. 12, No. 3, 1978, pp. 551-560.
24. Szabó, B. A., and Babuska, I., Finite Element Analysis, Wiley, New York, 1991.
25. Bardell, N. S., "Free Vibration Analysis of a Flat Plate Using the Hierarchical Finite Element Method," Journal of Sound and Vibration, Vol. 151, No. 2, 1991, pp. 263-289.
26. Vinson, J. R., and Sierakowski, R. L., The Behavior of Structures Composed of Composite Materials, Martinus Nijhoff, Dordrecht, The Netherlands, 1987, pp. 43-47.
27. Noor, A. K., and Burton, W. S., "Stress and Free Vibration Analyses of Multilayered Composite Plates," Composite Structures, Vol. 11, No. 3, 1989, pp. 183-204.
28. Sivakumaran, K. S., "Frequency Analysis of Symmetrically Laminated Plates with Free Edges," Journal of Sound and Vibration, Vol. 125, No. 2, 1988. pp. 211-225.
29. El Kadiri, M., Benamar, R., and White, R. G., "The Non-linear Free Vibration of Fully Clamped Rectangular Plates: Second Non-linear Mode for Various Plate Aspect Ratios," Journal of Sound and Vibration, Vol. 228, No. 2, 1999, pp. 333-358.