High-Frequency Extensional Vibrations of Plates

1956 ◽  
Vol 23 (2) ◽  
pp. 277-283
Author(s):  
T. R. Kane ◽  
R. D. Mindlin
Keyword(s):  
Plane Stress ◽  
High Frequency ◽  
Circular Disk ◽  
Thin Plates ◽  
Axially Symmetric ◽  
Thick Plates

Abstract The equations of generalized plane stress are applicable to the extensional vibrations of plates only for the low modes of motion of thin plates. In this paper equations are derived which are applicable to both low and high modes of thin plates and to low modes of thick plates. As an example, the equations are solved for the case of axially symmetric vibrations of a circular disk and comparisons are made with the theory of generalized plane stress and with experiments.

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.

Stress Analysis of Holes in Thick Plates

2004 ◽  
Vol 1-2 ◽  
pp. 153-158 ◽  
Author(s):  
S. Quinn ◽  
Janice M. Dulieu-Barton
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Plate Surface ◽  
Flat Plates ◽  
Thick Plates ◽  
Concentration Factors ◽  
Stress Concentration Factors

A review of the Stress Concentration Factors (SCFs) obtained from normal and oblique holes in thick flat plates loaded in uniaxial tension has been conducted. The review focuses on values from the plate surface and discusses the ramifications of making a plane stress assumption.

Scattering of High-Frequency Flexural Oscillations in Thin Plates

1999 ◽  
Vol 4 (4) ◽  
pp. 461-479 ◽  
Author(s):  
Gavin R. Thomson ◽  
Christian Constanda
Keyword(s):  
High Frequency ◽  
Thin Plates

High Frequency Ultrasonic Measurements

1988 ◽  
Vol 21 (5) ◽  
pp. 133-136
Author(s):  
N Zarsav
Keyword(s):  
High Frequency ◽  
Polymer Coating ◽  
Steel Sheet ◽  
Lamb Waves ◽  
Thin Plates ◽  
Design Features ◽  
Degree Of Cure ◽  
Double Probe ◽  
Ultrasonic Measurements

The use of high frequency ultrasonic Lamb waves to measure the thickness of thin plates and foils, is discussed and the feasibility of their application to the determination of the degree of cure of polymer coating on coated tin plated steel sheet (as used by the food can industry) is evaluated. The paper also discusses briefly the design features of the purpose built precision double probe ultrasonic goniometer used to carry out these measurements.

Dependence of the Frequency Spectrum of a Circular Disk on Poisson’s Ratio

1957 ◽  
Vol 24 (1) ◽  
pp. 53-54
Author(s):  
R. L. Sharma
Keyword(s):  
Frequency Spectrum ◽  
Poisson’S Ratio ◽  
Circular Disk ◽  
Intermediate Frequency ◽  
Poisson's Ratio ◽  
Axially Symmetric ◽  
Frequency Range ◽  
Flexural Vibrations ◽  
Circular Disks

Abstract The results of computations of frequencies of axially symmetric flexural vibrations of circular disks are given for an intermediate frequency range and for several values of Poisson’s ratio.

Accurate Calculation of Stress Distributions in Multiholed Plates

1965 ◽  
Vol 87 (3) ◽  
pp. 331-335 ◽  
Author(s):  
L. E. Hulbert ◽  
F. W. Niedenfuhr
Keyword(s):  
Computer Program ◽  
Plane Stress ◽  
Symmetric Groups ◽  
Thin Plates ◽  
Stress Distributions ◽  
Accurate Calculation ◽  
Point Matching ◽  
Shallow Shells ◽  
Matching Technique ◽  
Stress Functions

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

Symmetric Flexural Vibrations of a Clamped Circular Disk

1956 ◽  
Vol 23 (2) ◽  
pp. 319
Author(s):  
H. Deresiewicz
Keyword(s):  
Shear Deformation ◽  
Frequency Spectrum ◽  
Transverse Shear ◽  
Circular Disk ◽  
Transverse Shear Deformation ◽  
Axially Symmetric ◽  
Rotatory Inertia ◽  
Flexural Vibrations ◽  
Clamped Edges

Abstract The frequency spectrum is computed for the case of free, axially symmetric vibrations of a circular disk with clamped edges, using a theory which includes the effects of rotatory inertia and transverse shear deformation.

Planar inductors using NiZn ferrite thin plates and the application to high-frequency DC-DC converters

1993 ◽  
Vol 29 (6) ◽  
pp. 3231-3233 ◽  
Author(s):  
I. Sasada ◽  
T. Yamaguchi ◽  
K. Harada ◽  
Y. Notohara
Keyword(s):  
High Frequency ◽  
Thin Plates

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

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