On the Occurrence of Simultaneous Resonances in Parametrically-Excited Rectangular Plates

1993 ◽  
Vol 115 (3) ◽  
pp. 344-352 ◽  
Author(s):  
G. L. Ostiguy ◽  
L. P. Samson ◽  
H. Nguyen
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Temporal Response ◽  
Governing Equations ◽  
Parametrically Excited ◽  
Damped System ◽  
Simultaneous Resonances ◽  
Deflection Theory ◽  
New Phenomena ◽  
Large Deflection Theory

The present work deals primarily with the problem of the occurrence of simultaneous resonances in parametrically-excited rectangular plates. The analysis is based on the dynamic analog of the von Karman’s large-deflection theory and the governing equations are satisfied using the orthogonality properties of the assumed functions. The temporal response of the damped system is determined by the generalized asymptotic method and various types of simultaneous resonances are investigated. An experimental investigation is performed to verify the analytical predictions and to possibly discover new phenomena not predicted by the theory. Experiments are conducted for four different sets of boundary conditions. Analytically defined simultaneous resonances are experimentally observed and isolated.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

Large Deflection Theory for Orthotropic Rectangular Plates Subjected to Edge Compression

1952 ◽  
Vol 19 (4) ◽  
pp. 446-450
Author(s):  
Syed Yusuff
Keyword(s):  
Large Deflection ◽  
Polytechnic Institute ◽  
Large Deflections ◽  
Rectangular Plates ◽  
Compression Tests ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Theoretical Results ◽  
Anisotropic Rectangular Plates

Abstract A theory is presented of the large deflections of orthotropic (orthogonally anisotropic) rectangular plates when the plate is initially slightly curved and its boundaries are subjected to the conditions prevailing in edgewise compression tests. Results are given of computations carried out for four different combinations of load and lamination in Fiberglas panels. These theoretical results duplicate the substantial variations in the load-strain and load-deflection diagrams obtained earlier in experiments at the Polytechnic Institute of Brooklyn.

Benchmark of Plate Forming and Weld Distortion Process

2005 ◽  
Vol 128 (3) ◽  
pp. 414-419
Author(s):  
James Gombas
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Large Deflection ◽  
Element Analysis ◽  
Manufacturing Simulation ◽  
Simulation Process ◽  
Weld Distortion ◽  
Deflection Theory ◽  
Large Deflection Theory

A circular flat plate with a perforated central region is to be formed by dies into a dome and then welded onto a cylindrical shell. After welding, the dome must be spherical within a narrow tolerance band. This plate forming and welding is simulated using large deflection theory elastic-plastic finite element analysis. The manufacturing assessment is performed so that the dies may be designed to compensate for plate distortions that occur during various stages of manufacturing, including the effects of weld distortion. The manufacturing simulation benchmarks against measurements taken at several manufacturing stages from existing hardware. The manufacturing simulation process can then be used for future applications of similar geometries.

Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume

2017 ◽  
Vol 17 (08) ◽  
pp. 1750091 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Constant Volume ◽  
Large Deflections ◽  
Buckling Loads ◽  
Geometrical Nonlinear ◽  
Deflection Theory ◽  
Large Deflection Theory

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

On the Large Axisymmetrical Deflection of Thin Plates Made of the Mooney-Rivlin Material

1974 ◽  
Vol 41 (3) ◽  
pp. 725-730 ◽  
Author(s):  
H. Abe´ ◽  
M. Utsui
Keyword(s):  
Large Deflection ◽  
Lateral Pressure ◽  
Three Dimensional ◽  
Thin Plates ◽  
Axially Symmetric ◽  
Dimensional Theory ◽  
Plate Equations ◽  
Basic Equations ◽  
Deflection Theory ◽  
Large Deflection Theory

A large deflection theory of axially symmetric and thin plates made of the Mooney-Rivlin material is developed by making a systematic and consistent approximation from the exact three-dimensional theory. The problem of a circular plate made of the neo-Hookean material subjected to uniform lateral pressure is investigated with the use of the basic equations just derived, and the results are compared with the solutions based on the von Karman plate equations.

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