Mathematical analysis of flexural vibrations of inhomogeneous rectangular plates and beams subjected to cyclic loadings of temperature change and external force

In this paper the Bolotin edge effect method is used to consider the free flexural vibrations of systems built up from rectangular plates. The constituent plates of the systems are considered either to lie in the same plane and form part of a plate continuous over line supports or to lie in planes at right angles to each other, as in box constructions. The application of the edge effect method to single-and multi-plate systems is described and the approximate frequency equations for two two-plate systems are given. The first 10 natural frequency parameters for these two systems for particular side ratios are compared with those obtained using a series solution and agreement is shown to be good. A few frequency parameters for a closed box computed using the edge effect method and the series solution are also compared. The range of plate systems to which the edge effect method may be applied with complete success and the range to which it may be applied with only partial success are indicated. The sources of errors in the edge effect solutions are indicated.

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Nonlinear flexural vibrations of rectangular plates subjected to in-plane forces using a new shear deformation theory

Thin-Walled Structures ◽

10.1016/0263-8231(87)90023-1 ◽

1987 ◽

Vol 5 (5) ◽

pp. 309-327 ◽

Cited By ~ 14

Author(s):

Alavandi Bhimaraddi

Keyword(s):

Shear Deformation ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Rectangular Plates ◽

Flexural Vibrations

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Nonlinear Flexural Vibrations of Rectangular Plates Subjected to Uniformly Distributed Periodic Forces

Transactions of the Japan Society of Mechanical Engineers ◽

10.1299/kikai1938.39.3334 ◽

1973 ◽

Vol 39 (327) ◽

pp. 3334-3341

Author(s):

Noboru YAMAKI ◽

Ken-ichi NAGAI

Keyword(s):

Rectangular Plates ◽

Flexural Vibrations

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Flexural Vibrations of Rectangular Plates

Journal of Applied Mechanics ◽

10.1115/1.4011349 ◽

1956 ◽

Vol 23 (3) ◽

pp. 430-436

Author(s):

R. D. Mindlin ◽

A. Schacknow ◽

H. Deresiewicz

Keyword(s):

Shear Deformation ◽

Classical Theory ◽

The Other ◽

Thin Plates ◽

Rectangular Plates ◽

Rotatory Inertia ◽

Simply Supported ◽

Independent Families ◽

Flexural Vibrations ◽

Elastically Supported

Abstract The influence of rotatory inertia and shear deformation on the flexural vibrations of isotropic, rectangular plates is investigated. Three independent families of modes are possible when the edges are simply supported. Coupling of the modes is studied for the case of one pair of parallel edges free and the other pair simply supported. The development of the coupling is traced by means of a solution for elastically supported edges. Special attention is given to the higher modes and frequencies of vibration which are beyond the range of applicability of the classical theory of thin plates.

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