Nonlinear Free Vibration of Laminated Composite Plates
Publication: Journal of Engineering Mechanics
Volume 118, Issue 1
Abstract
In this paper the nonlinear vibration of composite plates has been presented. Usually in the nonlinear analysis of plates, the von Karman‐type formulation is followed because it is possible to obtain the complete solution once the solution for lateral displacement is assumed. In this paper an extension of the von Karman formulation has been presented for the first time. In this formulation the resulting governing equations are nonlinear in all the displacement parameters of the plate. Due to the highly nonlinear nature of the equations, the straightforward solution techniques usually adopted in the nonlinear plate analysis cannot be used. To circumvent this problem, a regular perturbation technique has been used to obtain the solution. Numerical results presented for simply supported plates indicate that the von Karman‐type formulation is quite satisfactory. This may also be viewed as a validation of the von Karman approach to nonlinear plate analysis.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bert, C. W. (1982). “Research on dynamics of composite sandwich plates, 1979–1981.” Shock and Vibration Digest, 14, 17–34.
2.
Bhimaraddi, A. (1987a). “Static and transient response of rectangular plates,” Thin‐Walled Structures, 5(1), 125–143.
3.
Bhimaraddi, A. (1987b). “Nonlinear flexural vibrations of rectangular plates subjected in‐plane forces using a new shear deformation theory.” Thin‐Walled Structures, 5(5), 309–328.
4.
Bhimaraddi, A. (1989a). “Nonlinear free vibration analysis of composite plates with initial imperfections and in‐plane loading.” Int. J. Solids and Structures, 25(1), 33–43.
5.
Bhimaraddi, A. (1989b). “Nonlinear vibrations of in‐plane loaded, imperfect, orthotropic plates using the perturbation technique.” Int. J. of Solids and Structures, 25(5), 563–575.
6.
Bhimaraddi, A., and Stevens, L. K. (1984). “A higher order theory for free vibration of orthotropic, homogeneous, and laminated rectangular plates.” J. Appl. Mech., 51 (March), 195–198.
7.
Chia, C. Y. (1988). “Geometrically nonlinear behavior of composite plates: A review.” Appl. Mech. Reviews, 41, 439–450.
8.
Leissa, A. W. (1981). “Advances in vibration, buckling and postbuckling studies on composite plates.” Composite Structures, Proc. 1st Int. Conference, Sept., Applied Science Publishers, 312–334.
9.
Magrab, E. (1979). Vibrations of elastic structural members. Sijthoff and Noordhoff, Amsterdam, The Netherlands.
10.
Nayfeh, A. H., and Mook, D. T. (1979). Nonlinear oscillations, John Wiley and Sons, New York, N.Y.
11.
Saada, A. S. (1974). Elasticity: Theory and applications. Pergamon Press, New York, N.Y.
12.
Sathyamoorthy, M. (1987). “Nonlinear vibration analysis of plates: A review and survey of current developments.” Appl. Mech. Reviews, 40 (Dec), 1553–1561.
Information & Authors
Information
Published In
Copyright
Copyright © 1992 ASCE.
History
Published online: Jan 1, 1992
Published in print: Jan 1992
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.