Elastic Instability of an Annular Plate Under Uniform Compression and Lateral Pressure

1980 ◽  
Vol 47 (3) ◽  
pp. 591-594 ◽  
Author(s):  
J. Tani
Keyword(s):  
Lateral Pressure ◽  
Annular Plate ◽  
Plate Theory ◽  
Axisymmetric Deformation ◽  
Elastic Instability ◽  
Uniform Compression ◽  
Combined Loads ◽  
Simultaneous Loading ◽  
Axisymmetric Equilibrium ◽  
Dynamic Version

The elastic instability of a thin clamped annular plate which has suffered a finite axisymmetric deformation due to simultaneous loading of uniform compression and lateral pressure is studied by examining the asymmetric small free vibration in the neighborhood of the nonlinear axisymmetric equilibrium state. The problem is solved by applying a finite-difference method to the dynamic version of the nonlinear von Karman plate theory. The numerical results indicate that there are the ranges of the magnitude of combined loads under which the axisymmetric deformation of the plate becomes unstable.

Elastic Instability of a Heated Annular Plate Under Lateral Pressure

1981 ◽  
Vol 48 (2) ◽  
pp. 399-403 ◽  
Author(s):  
J. Tani
Keyword(s):  
Critical Temperature ◽  
Finite Difference Method ◽  
Theoretical Analysis ◽  
Lateral Pressure ◽  
Annular Plate ◽  
Axisymmetric Deformation ◽  
Elastic Instability ◽  
Bifurcation Buckling ◽  
Vibration Problems ◽  
Dynamic Version

On the basis of the dynamic version of the nonlinear von Karman equations, a theoretical analysis is performed on the elastic instability of a uniformly heated, thin, annular plate which has suffered a finite axisymmetric deformation due to lateral pressure. The linear free vibration problems around the finite axisymmetric deformation of the plate are solved by a finite-difference method. By examining the frequency spectrum with various asymmetric modes, the critical temperature rise under which the axisymmetric deformation becomes unstable due to the bifurcation buckling is determined, which is found to jump up to 7.2 times within a range of very small lateral pressure.

Buckling of a thin annular plate under uniform compression

AIAA Journal ◽  
1971 ◽  
Vol 9 (9) ◽  
pp. 1701-1707 ◽  
Author(s):  
SAURINDRANATH MAJUMDAR
Keyword(s):  
Annular Plate ◽  
Uniform Compression

Buckling of an Elliptical Plate With Simply Supported Edge Under Uniform Compression

1976 ◽  
Vol 43 (3) ◽  
pp. 455-458 ◽  
Author(s):  
Kenzo Sato
Keyword(s):  
Plate Theory ◽  
Mathieu Functions ◽  
Elliptical Plate ◽  
Buckling Mode ◽  
Uniform Compression ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Thin Plate Theory ◽  
The Stability ◽  
Circular Functions

On the basis of the ordinary thin plate theory, the stability of a simply supported elliptical plate subjected to uniform compression in its middle plane is considered by the use of circular functions, hyperbolic functions, Mathieu functions, and modified Mathieu functions which are solutions of the equilibrium equation of the buckled plate. The first five eigenvalues for the buckling mode symmetrical about both axes are calculated numerically for a variety of aspect ratios of the ellipse. The limiting cases of a circular plate and of an infinitely long strip are also discussed.

Investigation of Fixed-Free Annular Plate Resonant Frequency Predictions

1988 ◽  
Vol 110 (3) ◽  
pp. 408-410 ◽  
Author(s):  
Alison Flatau ◽  
G. A. Flandro ◽  
W. K. Van Moorhem
Keyword(s):  
Free Boundary ◽  
Resonant Frequency ◽  
Elastic Plate ◽  
Annular Plate ◽  
Plate Theory ◽  
Outer Radius ◽  
Resonant Frequencies ◽  
Free Boundary Conditions ◽  
Annular Plates ◽  
Analytical Frequency

Nondimensional frequency parameters for predicting the resonant frequencies of annular plates with fixed-free boundary conditions as the plate inner to outer radius ratio approaches unity have been investigated experimentally. Frequency parameters have been determined by using modal analysis to measure resonant frequencies for annular plates of varied materials, thicknesses, and with radius ratios of 0.5 to 0.9. The data are compared to two different analytical frequency predictions which have been presented as solutions for resonance of fixed-free annular plates based on classical elastic plate theory.

Postbuckling of composite laminated plates under biaxial compression combined with lateral pressure and resting on elastic foundations

1998 ◽  
Vol 33 (4) ◽  
pp. 253-261 ◽  
Author(s):  
H-S Shen
Keyword(s):  
Lateral Pressure ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Laminated Plates ◽  
Combined Loading ◽  
Graphical Form ◽  
Biaxial Compression ◽  
Elastic Foundations ◽  
Plate Aspect Ratio ◽  
Limiting Case

A postbuckling analysis is presented for a simply supported, composite laminated rectangular plate subjected to biaxial compression combined with lateral pressure and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the classical laminated plate theory, including plate-foundation interaction. The analysis uses a perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of antisymmetric angle-ply and symmetric cross-ply laminated plates subjected to combined loading and resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, the plate aspect ratio, the total number of plies, fibre orientation and initial lateral pressure, is studied. Typical results are presented in dimensionless graphical form.

Multi-Frequency Multi-Modal Excitation of a Heated Annular Plate

2006 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh
Keyword(s):  
Nonlinear Dynamics ◽  
Internal Resonance ◽  
Radial Direction ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Plate Theory ◽  
Frequency Excitation ◽  
The Difference

The forced nonlinear dynamics of a pre-buckled thermally loaded annular plate are investigated. The plate is modeled using the von Ka´rma´n plate theory and the heat equation. The heat, which is generated by the difference between the uniformly distributed temperatures at the inner and outer boundaries, is assumed to symmetrically flow in the radial direction. The amount of heat affects the natural frequencies, which may give rise to different internal resonance conditions. The method of multiple scales is used to examine the system axisymmetric responses when it is driven by an external multi-frequency excitation. The plate responses could be very complex exhibiting Hopf and cyclic-fold bifurcations, quasi-periodicity, chaos, and multiplicity of attractors.

Buckling of a Thin Annular Plate Under Uniform Compression

1958 ◽  
Vol 25 (2) ◽  
pp. 267-273
Author(s):  
N. Yamaki
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Critical Loads ◽  
Equilibrium Equation ◽  
Annular Plate ◽  
Elastic Stability ◽  
Infinite Strip ◽  
Uniform Compression ◽  
The Stability

Abstract This paper deals with the elastic stability of a circular annular plate under uniform compressive forces applied at its edges. By integrating the equilibrium equation of the buckled plate, the problem is solved in its most general form for twelve different combinations of the boundary conditions of the edges. For each case cited the lowest critical loads are calculated with the ratio of its radii as the parameter. It is clarified that the assumption of symmetrical buckling, which has been made by several researchers, often leads to the overestimate for the stability of the plate. Discussions for the limiting cases of the circular plate and infinite strip also are included.

Non-linear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations

2000 ◽  
Vol 35 (2) ◽  
pp. 93-103 ◽  
Author(s):  
Hui-Shen Shen
Keyword(s):  
Thermal Loading ◽  
Lateral Pressure ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Laminated Plates ◽  
Graphical Form ◽  
Elastic Foundations ◽  
Non Linear ◽  
Shear Deformable ◽  
Two Parameter

A non-linear bending analysis is presented for a simply supported shear deformable composite laminated plate subjected to a combined uniform lateral pressure and thermal loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy's higher-order shear deformation plate theory, including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of antisymmetric angleply and symmetric cross-ply laminated plates subjected to thermomechanical loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences due to a number of effects e.g. foundation stiffness, plate aspect ratio, total number of plies, fibre orientation and initial thermal bending stress, are studied. Typical results are presented in a dimensionless graphical form.

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