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Application of translational edge restraint for vibration analysis of free edge Kirchhoff’s plate including rigid-body modes

Verma Y., Datta N.

Engineering Transactions

2018

Vol. 66, iss. 1

21--60

A comprehensive theoretical study of closed-form rigid-body modes of a free-free and translationally edge-restrained Euler-Bernoulli beam is presented. Accurate vibrational analysis of a free-free-free-free plate is not possible without the inclusion of degenerate rigid-body beamwise admissible functions. The trivial solution(s) of the beam frequency equation produce(s) a non-trivial modeshape, which satisfies the boundary conditions, has zero curvature, and is orthogonal to the other modeshapes. These frequency parameters are “trivial”, i.e. they lead to zero natural frequency, since their modeshapes have no curvature. Mathematicallygenerated orthogonal free-free (classical) beam-wise rigid-body modeshapes, and those generated from non-classical edged beams, have been both separately used as admissible functions in the Rayleigh-Ritz method (RRM) to generate the plate natural frequencies of a free-freefree-free rectangular uniform isotropic Kirchhoff’s plate. With respect to the increasing elastic support, the trifurcation and bifurcation of plate frequencies from the trivial to the flexural frequencies, is investigated. The completely free plate modeshapes are also presented. Also, combination of present closed-form rigid-body modes with polynomial functions, trigonometric functions is also demonstrated.

Vibrations of circular plate supported on a rigid concentric ring with transnational restraint boundary

Rao L. B., Rao C. K.

Engineering Transactions

2016

Vol. 64, iss. 3

259--269

This paper deals with frequency analysis of a circular plate supported on a rigid concentric ring with translational restrained boundary. Natural frequencies of such a circular plate are computed for different sets of elastic translational restraints, and for various values of the radius of the internal ring support. Results for different modes of plate vibrations are computed and presented in a tabular form suitable for use in design. The effect of plate boundary conditions such as translational restraints and the radius of concentric ring support on natural frequencies of the circular plate are studied. Exact frequency values presented in this paper are expected to serve as benchmark solutions for assessing the accuracy of other numerical methods being used in the literature.