The large amplitude free flexural vibrations of thin, orthotropic, eccentrically and lightly stiffened elastic rectangular plates are investigated. Clamped boundary conditions with movable in-plane edge conditions are assumed. A simple modal form of one-term transverse displacement is used and in-plane displacements are made to satisfy the in-plane equilibrium equations. By using Lagrange's equation, the modal equations for the nonlinear free vibration of stiffened plates are obtained for the cases when the stiffeners are assumed to be smeared out over the entire surface of the plate, and when the stiffeners are located at finite intervals. Numerical results are obtained for various possibilities of stiffening and for different aspect ratios of the plate. By particularizing the problem to different known cases, the results obtained here are compared with available analytical and experimental results, and the agreement is good. © 1979.

T. K. Varadan

K. A V Pandalai

STRUCTURAL ANALYSIS - Mathematical Models

Plates

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Large amplitude flexural vibration of eccentrically stiffened plates

Journal of Sound and Vibration

General conclusions regarding the non-linear vibration of structural components like curved beams, rings and thin shells are derived from the study of two specific examples, the circular ring and shallow spherical shell. It is shown that whereas the non-linear behaviour of flat plates and straight bars is generally of a hardening type, the behaviour of thin structural elements that have a finite curvature of the undeformed median surface in one or both principal axis directions may be of the hardening or softening type, depending on the structural parameters as well as on whether the shell is open or closed. It is seen that with careful judgment in the use of mode shapes of one or more terms, the resulting modal equations help one to appreciate much better the physics of the problem, whereas sophisticated mathematical models tend to obscure this. © 1978.

The role of median surface curvature in large amplitude flexural vibrations of thin shells

The large amplitude free flexural vibration of thin, elastic orthotropic stiffened plates is studied. The boundary conditions considered are either simply supported on all edges or clamped on all edges and the in-plane edge conditions are either immovable or movable. The governing dynamic equations are derived in terms of non-dimensional parameters describing the stiffening achieved, and the solutions are obtained on the basis of an assumed one-term vibration mode shape for various stiffener combinations. In all cases, the non-linearity is found to be of the hardening type (i.e., the period of non-linear vibration decreases with increasing amplitude). Some interesting conclusions are drawn as to the effect of the stiffening parameters on the non-linear behaviour. A simple method of predicting the postbuckling and static large deflection behaviour from the results obtained in this analysis is included. © 1978.

Large amplitude flexural vibration of stiffened plates

This report deals with the large amplitude (non-linear) free flexural vibration of thin, elastic, orthotropic skew plates clamped along all four edges. The analysis is based on the non-linear dynamic equations applicable for rectilinearly orthotropic skew plates, derived in terms of the stress function, F, and the lateral displacement, W. Solutions obtained on the basis of assumed vibration modes make use of Galerkin's method. Curves of amplitude versus period for clamped skew plates have been obtained for two types of orthotropy and, in each case, for different aspect ratios and sweep angles of the plate. The corresponding relationship for the isotropic case has also been obtained. The results when specialized for the cases of isotropic skew plates and orthotropic rectangular plates agree well with those in the literature. The results show that the non-linearity is of the "hardening" type, that is, the period of non-linear vibration decreases with increasing amplitude. © 1972.

Journal	Journal of Sound and Vibration
ISSN	0022460X
Open Access	No