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.

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.

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.

An Experimental Method to Determine Poisson’s Ratio in a Small Beam Subject to Seismic Excitation

1997 ◽  
Author(s):  
Roberto Caracciolo ◽  
Alessandro Gasparetto ◽  
Marco Giovagnoni
Keyword(s):  
Experimental Method ◽  
Poisson’S Ratio ◽  
Iterative Procedure ◽  
Master Curve ◽  
Seismic Excitation ◽  
Poisson's Ratio ◽  
Strain Gauges ◽  
Frequency Range ◽  
Different Temperatures ◽  
Transverse Strains

Abstract An experimental method to determine Poisson’s ratio in a small beam subject to seismic excitation is presented. Poisson’s ratio is computed by measuring longitudinal and transverse strains by means of electric strain gauges. A first set of tests is carried out with different materials, and it is observed that the measured Poisson’s ratio decreases with frequency. However, to determine whether the observed decrease is true or it is due to an error caused by the plate effect of the beam, a second set of tests at different temperatures is carried out. Then, by applying the reduced variables method, a unique plot for Poisson’s ratio on a much broader frequency range is obtained, which allows to state that the decrease of Poisson’s ratio is true. An iterative procedure is described, which has been developed to gather the curves at different temperatures in a master curve.

Dispersion of Axially Symmetric Waves in Elastic Rods

1962 ◽  
Vol 29 (4) ◽  
pp. 729-734 ◽  
Author(s):  
Morio Onoe ◽  
H. D. McNiven ◽  
R. D. Mindlin
Keyword(s):  
Poisson’S Ratio ◽  
Large Range ◽  
Propagation Constant ◽  
Poisson's Ratio ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Complex Propagation

The relation between frequency and propagation constant, for axially symmetric waves in an infinitely long, isotropic, circular rod, as given by Pochhammer’s equation, is explored. A spectrum, covering a large range of frequencies, is developed for real, imaginary, and complex propagation constants, and the influence of Poisson’s ratio is described.

Longitudinal Pochhammer — Chree Waves in Mild Auxetics and Non-Auxetics

2018 ◽  
Vol 35 (3) ◽  
pp. 327-334 ◽  
Author(s):  
A. V. Ilyashenko ◽  
S. V. Kuznetsov
Keyword(s):  
Poisson’S Ratio ◽  
Wave Speed ◽  
Poisson's Ratio ◽  
Abnormal Behavior ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Shear Wave Speed ◽  
The Matrix ◽  
The Waves ◽  
Analytical Expressions

ABSTRACTThe exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.

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