A Theory of Two‐Dimensional Longitudinal and Flexural Vibrations in Rectangular Isotropic Plates

Physics ◽  
1935 ◽  
Vol 6 (7) ◽  
pp. 234-246 ◽  
Author(s):  
Harold Osterberg ◽  
John W. Cookson
Keyword(s):  
Two Dimensional ◽  
Isotropic Plates ◽  
Flexural Vibrations

Selected topics in the history of the two-dimensional biharmonic problem

2003 ◽  
Vol 56 (1) ◽  
pp. 33-85 ◽  
Author(s):  
VV Meleshko
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Review Article ◽  
Creeping Flow ◽  
Two Dimensional ◽  
Historical Overview ◽  
Biharmonic Problem ◽  
Isotropic Plates ◽  
History Of ◽  
Analytical Approaches

This review article gives a historical overview of some topics related to the classical 2D biharmonic problem. This problem arises in many physical studies concerning bending of clamped thin elastic isotropic plates, equilibrium of an elastic body under conditions of plane strain or plane stress, or creeping flow of a viscous incompressible fluid. The object of this paper is both to elucidate some interesting points related to the history of the problem and to give an overview of some analytical approaches to its solution. This review article contains 758 references.

Axially Symmetric Extensional Vibrations of a Circular Disk With a Concentric Hole

1959 ◽  
Vol 26 (4) ◽  
pp. 541-545
Author(s):  
O. G. Gustafsson ◽  
T. R. Kane
Keyword(s):  
High Frequency ◽  
Circular Disk ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Dimensional Theory ◽  
Isotropic Plates

Abstract In a paper by T. R. Kane and R. D. Mindlin, a two-dimensional theory was developed for high-frequency extensional vibrations of elastic, isotropic plates. This theory is now used to study vibrations of a circular disk with a concentric hole.

Elastic deformations of infinite strips

1950 ◽  
Vol 46 (1) ◽  
pp. 164-181 ◽  
Author(s):  
H. G. Hopkins
Keyword(s):  
Boundary Conditions ◽  
Mathematical Problem ◽  
The Other ◽  
Transverse Displacement ◽  
Two Dimensional ◽  
Airy Stress Function ◽  
Elastic Deformations ◽  
Isotropic Plates ◽  
Edge Force ◽  
Harmonic Equation

ABSTRACTIn this paper, Fourier integrals are used to solve some elastic problems of generalized plane stress and small transverse displacements in infinitely long, rectangular, isotropic plates stressed only at their edges. The Airy stress function and the transverse displacement satisfy the two-dimensional bi-harmonic equation, and the basic mathematical problem is to solve this equation subject to different sets of boundary conditions. Little attention has been given hitherto to problems in which some of the boundary conditions depend directly upon displacements. Here the general problem is solved when one long edge is fixed, and stresses or displacements are arbitrarily prescribed at the other, with no stresses and displacements at infinity. The problem of a concentrated edge force is discussed in detail and numerical values of the stresses at the fixed edge are given.

Fracture Analyses for Interface Corners in Elastic Materials Subjected to Thermal Loading

2011 ◽  
Vol 462-463 ◽  
pp. 277-283
Author(s):  
Chyan Bin Hwu ◽  
Tai Liang Kuo ◽  
Chun Chih Huang
Keyword(s):  
Thermal Effects ◽  
Thermal Loading ◽  
Stress Singularity ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Surface Integral ◽  
Elastic Materials ◽  
Isotropic Plates ◽  
Anisotropic Elastic ◽  
The One

By employing the Stroh formalism for two-dimensional anisotropic thermoelasticity, fracture analyses of interface corners between two dissimilar anisotropic elastic materials under thermal loadings are considered in this paper. It was proved that the consideration of thermal effects will not influence the stress singularity but will induce heat flux singularity if the singularity of the temperature field is not permissible. To calculate the stress intensity factors via path independent H-integral, it was found that the one proposed previously for the mechanical loading conditions should be modified by adding an additional surface integral accounting for the thermal effects. Two examples considering cracks and corners in isotropic plates are presented to show the correctness and validity of the modified H-integral.

Flexural vibrations of prestressed isotropic plates

1995 ◽  
Vol 76 (3) ◽  
pp. 2397-2399
Author(s):  
A. S. Kosmodamianskii ◽  
A. M. Kravtsov ◽  
S. A. Priimenko
Keyword(s):  
Isotropic Plates ◽  
Flexural Vibrations
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