Large Amplitude Response of Layered Circular Plates
Publication: Journal of Engineering Mechanics
Volume 121, Issue 1
Abstract
This paper deals with the Chebyshev series solution technique to the nonlinear static and dynamic response of cylindrically orthotropic, symmetrically laminated, cross-ply moderately thick plates. Considering the transverse shear and rotatory inertia, the governing equations of motion for the axisymmetric deformation of circular plates are expressed in terms of normal deflection , slope , and the stress function . The effects of transverse shear, rotatory inertia, material properties, number of layers, and boundary conditions on static and dynamic response of plates to uniformly distributed normal loads are studied, and the results are shown graphically. The effects of transverse shear and rotatory inertia on the central response are greatly influenced by the ratio of base radius to thickness, the materials, and the type of loadings.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Alwar, R. S., and Nath, Y. (1976). “Application of Chebyshev polynomials to the nonlinear analysis of circular plates.”Int. J. Mech. Sci., Vol. 18, 589–595.
2.
Alwar, R. S., and Nath, Y. (1977). “Nonlinear dynamic response of circular plates subjected to transient load.”J. of Franklin Inst., Vol. 303, 527–542.
3.
Berger, H. M. (1955). “A new approach to the analysis of large deflection of plates.”J. Appl. Mech., Vol. 22, 465–472.
4.
Chia, C. Y. (1980). Nonlinear analysis of plates . McGraw-Hill, New York, N.Y.
5.
Chia, C. Y. (1988). “Geometrically nonlinear behavior of composite plates: A review.”Appl. Mech. Rev., Vol. 41, 439–451.
6.
Chia, C. Y., and Sathyamoorthy. (1981). “Nonlinear vibration of circular plates with transverse shear and rotatory inertia.”J. of Sound and Vibration, Vol. 78, 131–137.
7.
Dumir, P. C., Kumar, R., and Gandhi, M. L. (1985). “Nonlinear axisymmetric vibration of orthotropic thin circular plates on elastic foundation.”J. of Sound and Vibration, Vol. 103, 273–283.
8.
Dumir, P. C., Kumar, R., and Gandhi, M. L. (1986). “Nonlinear axisymmetric vibration of orthotropic thin circular plates with elastically restrained edges.”Computers and Struct., Vol. 22, 677–686.
9.
Ebcioglu, I. K. (1964). “A large deflection theory of anisotropic plates.”Ingenieur-Archive, Vol. 33, 396–403.
10.
Fox, L., and Parker, I. B. (1968). Chebyshev polynomials in numerical analysis . Oxford University Press, London, England.
11.
Fu, Y. M., and Chia, C. Y. (1989). “Multi-mode nonlinear vibration and postbuckling of anti-symmetric imperfect angle-ply cylindrical thick panel.”Int. J. Nonlinear Mech., Vol. 24, 365–381.
12.
Hermann, G. (1955). “Influence of large amplitudes on flexural motions of elastic plates.”Technical note 3578, National Advisory Committee for Aeronautics, Washington, D.C.
13.
Houbolt, J. C. (1950). “A recurrence matrix solution for the dynamic response of elastic aircraft.”J. Aeronautical Sci., Vol. 17, 540–550.
14.
Kunukkaseril, V. X., and Venkateshan, S. (1979). “Axisymmetric nonlinear oscillations of isotropic layered circular plates.”J. of Sound and Vibration, Vol. 64, 295–302.
15.
Librescu, L., and Reddy, J. N. (1989). “A few remarks concerning several refined theories of anisotropic composite laminated plates.”Int. J. Engrg. Sci., Vol. 27, 515–527.
16.
Medwadowski, S. J. (1958). “A refined theory of elastic orthotropic plates.”J. Appl. Mech., Vol. 25, 437–443.
17.
Nash, W. A., and Kanematsu, H. (1971). “Finite amplitude response of circular plates subjected to dynamic loading.”Instability of continuous systems (IUTAM), H. Leipholz, ed., Springer-Verlag KG Berlin, Germany, 311–316.
18.
Nash, W. A., and Modeer, J. R. (1960). “Certain approximate analyses of the nonlinear behavior of plates and shallow shells.”Proc., Symp. on the theory of thin elastic shells, Interscience Publishers, Inc., New York, N.Y., 331–354.
19.
Nath, Y., and Alwar, R. S. (1980). “Nonlinear dynamic analysis of orthotropic circular plates.”Int. J. Solid Struct., Vol. 16, 433–443.
20.
Nath, Y. (1982). “Large amplitude response of circular plates on elastic foundation.”Int. J. Nonlinear Mech., Vol. 17, 285–296.
21.
Nath, Y., and Jain, R. K. (1983). “Nonlinear dynamic analysis of orthotropic annular plate resting on elastic foundation.”Earthquake Engrg. and Struct. Dynamics, Vol. 11, 785–796.
22.
Nowinski, J. L. (1963). “Nonlinear vibrations of elastic circular plates exhibiting rectilinear orthotropy.”ZAMP, Vol. 14, 113–124.
23.
Raju, K. K., and Rao, G. V. (1976). “Axisymmetric vibration of circular plates including the effects of geometric nonlinearity, shear deformation and rotatory inertia.”J. of Sound and Vibration, Vol. 47, 179–184.
24.
Rao, G. V., and Raju, K. K. (1980). “Large amplitude axisymmetric vibrations of orthotropic circular plates elastically restrained against rotation.”J. of Sound and Vibration, Vol. 69, 175–180.
25.
Ruei, K. H., Jiang, C., and Chia, C. Y. (1984). “Dynamic and static nonlinear analysis of cylindrically orthotropic circular plates with nonuniform edge constraints.”ZAMP, Vol. 33, 387–400.
26.
Sathyamoorthy, M. (1984). “Multiple mode large amplitude vibration of circular plates with transverse shear and rotatory inertia.”Int. J. Nonlinear Mech., Vol. 19, 341–348.
27.
von Karman, T. (1910). “Festigkeitsprobleme im machinebau.”Encyklopadie der Mathematishen Wissenschaften, Vol. IV.
28.
Wu, C. I., and Vinson, J. R. (1969). “Influence of large amplitude transverse shear deformation, and rotatory inertia on lateral vibrations of transversely isotropic plates.”J. Appl. Mech., 254–260.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jan 1, 1995
Published in print: Jan 1995
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.