Unbonded contact between a circular plate and an elastic foundation

1975 ◽  
pp. 99-109 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Circular Plate ◽  
Elastic Foundation

Large Amplitude Vibrations of Circular Plate on a Uniform Elastic Foundation

1972 ◽  
Vol 94 (1) ◽  
pp. 43-49 ◽  
Author(s):  
R. Bolton
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Single Mode ◽  
Linear Mode ◽  
Mode Amplitude ◽  
Plate Vibrations ◽  
Edge Conditions ◽  
Large Amplitude Vibrations ◽  
Mode Response

Herrmann’s equations, the dynamic analogues of the von Karman equations, are solved for a circular plate on a linear elastic foundation by assuming a series solution of the separable form involving unknown time functions. The spatial functions include both regular and modified Bessel functions and are chosen to satisfy the linear mode shape distributions of the plate as well as the usual edge conditions. Total differential equations governing the symmetric plate motions are derived using the Galerkin averaging techniques for a spatially uniform load. By extending the concept of normal modes to nonlinear plate vibrations, comparisons between normal mode response and single mode response, as functions of the first mode amplitude, are shown for different values of the elastic foundation parameter. Results are obtained for plates with simply supported and clamped edges and with both radially moveable and immoveable edges. These results are used to discuss the limitations of single-mode response of circular plates, both with and without an elastic foundation.

Bending of Circular and Ring-Shaped Plates on an Elastic Foundation

1954 ◽  
Vol 21 (1) ◽  
pp. 45-51
Author(s):  
Herbert Reismann
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Series Solution ◽  
Circular Disk ◽  
Symmetric Problem ◽  
Concentrated Load ◽  
Transverse Loads ◽  
Infinite Extent ◽  
Theory Of Plates ◽  
Pure Moment

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

Buckling of a Circular Plate Resting Over an Elastic Foundation in Simple Shear Flow

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Haoxiang Luo ◽  
C. Pozrikidis
Keyword(s):  
Shear Flow ◽  
Circular Plate ◽  
Elastic Foundation ◽  
Simple Shear ◽  
Body Force ◽  
The Body ◽  
Simple Shear Flow ◽  
Uniform Compression ◽  
Buckling Instability ◽  
Plate Buckling

The elastic instability of a circular plate adhering to an elastic foundation modeling the exposed surface of a biological cell resting on the cell interior is considered. Plate buckling occurs under the action of a uniform body force due to an overpassing simple shear flow distributed over the plate cross section. The problem is formulated in terms of the linear von Kármán plate bending equation incorporating the body force and the elastic foundation spring constant, subject to clamped boundary conditions around the rim. The coupling of the plate to the substrate delays the onset of the buckling instability and may have a strong effect on the shape of the bending eigenmodes. Contrary to the case of uniform compression, as the shear stress of the overpassing shear flow increases, the plate always first buckles in the left-to-right symmetric mode.

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