Axially Symmetric Flexural Vibrations of a Circular Disk

1955 ◽  
Vol 22 (1) ◽  
pp. 86-88
Author(s):  
H. Deresiewicz ◽  
R. D. Mindlin
Keyword(s):  
Shear Deformation ◽  
Frequency Spectrum ◽  
Classical Theory ◽  
Circular Disk ◽  
Axially Symmetric ◽  
Rotatory Inertia ◽  
High Frequencies ◽  
Flexural Vibrations ◽  
Thickness Shear ◽  
Free Edges

Abstract At high frequencies, the flexural vibrations of a plate are described very poorly by the classical (Lagrange) theory because of neglect of the influence of coupling with thickness-shear vibrations. The latter may be taken into account by inclusion of rotatory inertia and shear-deformation terms in the equations. The resulting frequency spectrum is given, in this paper, for the case of axially symmetric vibrations of a circular disk with free edges and is compared with the spectrum predicted by the classical theory.

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.

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.

Flexural Vibrations of Rectangular Plates

1956 ◽  
Vol 23 (3) ◽  
pp. 430-436
Author(s):  
R. D. Mindlin ◽  
A. Schacknow ◽  
H. Deresiewicz
Keyword(s):  
Shear Deformation ◽  
Classical Theory ◽  
The Other ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Rotatory Inertia ◽  
Simply Supported ◽  
Independent Families ◽  
Flexural Vibrations ◽  
Elastically Supported

Abstract The influence of rotatory inertia and shear deformation on the flexural vibrations of isotropic, rectangular plates is investigated. Three independent families of modes are possible when the edges are simply supported. Coupling of the modes is studied for the case of one pair of parallel edges free and the other pair simply supported. The development of the coupling is traced by means of a solution for elastically supported edges. Special attention is given to the higher modes and frequencies of vibration which are beyond the range of applicability of the classical theory of thin plates.

Three-Dimensional and Shell-Theory Analysis of Axially Symmetric Motions of Cylinders

1956 ◽  
Vol 23 (4) ◽  
pp. 563-568
Author(s):  
George Herrmann ◽  
I. Mirsky
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Plate Theory ◽  
Wave Length ◽  
Three Dimensional ◽  
Approximate Theory ◽  
Axially Symmetric ◽  
Rotatory Inertia ◽  
Phase Velocities ◽  
Transition Wave

Abstract The frequency (or phase velocity) of axially symmetric free vibrations in an elastic, isotropic, circular cylinder of medium thickness is studied on the basis of the three-dimensional linear theory of elasticity and several different shell theories. To be in good agreement with the solution of the three-dimensional equations for short wave lengths, an approximate theory has to include the influence of rotatory inertia and transverse shear deformation, for example, in a manner similar to Mindlin’s plate theory. A shell theory of this (Timoshenko) type is deduced from the three-dimensional elasticity theory. From a comparison of phase velocities it appears that, to a good approximation, membrane and curvature effects on one hand, and on the other hand, flexural, rotatory-inertia, and shear-deformation effects are mutually exclusive in two ranges of wave lengths, separated by a “transition” wave length. Thus, in the full range of wave lengths, the associated lowest phase velocities may be determined on the basis of the membrane shell theory (for wave lengths larger than the transition wave length) and on the basis of Mindlin’s plate theory (for wave lengths smaller than the transition wave length).

The Effect of Rotatory Inertia and of Shear Deformation on the Frequency and Normal Mode Equations of Uniform Beams With Simple End Conditions

1961 ◽  
Vol 28 (4) ◽  
pp. 579-584 ◽  
Author(s):  
T. C. Huang
Keyword(s):  
Shear Deformation ◽  
Normal Mode ◽  
Transverse Shear ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
End Conditions ◽  
Flexural Vibrations

New frequency and normal mode equations for flexural vibrations of six common types of simple, finite beams are presented. The derivation includes the effect of rotatory inertia and transverse-shear deformation. A specific example is given.

Thickness‐Shear and Flexural Vibrations of a Circular Disk

1954 ◽  
Vol 25 (10) ◽  
pp. 1329-1332 ◽  
Author(s):  
R. D. Mindlin ◽  
H. Deresiewicz
Keyword(s):  
Circular Disk ◽  
Flexural Vibrations ◽  
Thickness Shear
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