First, a brief history of the development of the analyses of large amplitude vibration is given. Second, nonlinearities exhibited by beams, plates, rings, and shells undergoing large amplitude vibrations are discussed. It is shown that, in case of large amplitude vibrations, the modal equations for multilayered beams and plates are qualitatively the same as the modal equation for shells. © 1987, Sage Publications. All rights reserved.

K. A V Pandalai

BEAMS AND GIRDERS - COMPOSITE

DOMES AND SHELLS - COMPOSITE

MATHEMATICAL TECHNIQUES - NONLINEAR EQUATIONS

PLATES - COMPOSITE

VIBRATIONS - MATHEMATICAL MODELS

FREE FLEXURAL VIBRATION

LARGE AMPLITUDE VIBRATION

Composite materials

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Large Amplitude Free Flexural Vibration of Structures

Journal of Reinforced Plastics and Composites

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.

Journal of Sound and Vibration

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

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 Reinforced Plastics and Composites
ISSN	07316844
Open Access	No