Dispersion of Flexural Waves in an Elastic, Circular Cylinder

1960 ◽  
Vol 27 (3) ◽  
pp. 513-520 ◽  
Author(s):  
Yih-Hsing Pao ◽  
R. D. Mindlin
Keyword(s):  
Circular Cylinder ◽  
Phase Velocity ◽  
Propagation Constant ◽  
Direct Determination ◽  
Short Wave ◽  
Frequency Equation ◽  
Flexural Waves ◽  
Asymptotic Equations ◽  
Frequency Phase

In this paper it is shown how the branches of Pochhammer’s frequency equation for flexural waves in a circular cylinder may be constructed approximately with the aid of a grid of simpler curves and asymptotic equations for long and short wave lengths. With very little computation, in comparison with that required in the direct determination of the roots of Pochhammer’s equation, a qualitative view is obtained of the relations between frequency, phase velocity, group velocity, and propagation constant, for any branch, as well as some information as to the shapes of the modes.

scholarly journals Effect of Rotation on Wave Propagation in Hollow Poroelastic Circular Cylinder

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
A. M. Abd-Alla ◽  
S. Alqosami
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Phase Velocity ◽  
Frequency Equation ◽  
Wave Number ◽  
Elastic Behavior ◽  
Hollow Circular Cylinder ◽  
Poroelastic Material ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

The objective of this paper is to study the effect of rotation on the wave propagation in an infinite poroelastic hollow circular cylinder. The frequency equation for poroelastic hollow circular cylinder is obtained when the boundaries are stress free and is examined numerically. The frequency, phase velocity, and attenuation coefficient are calculated for a pervious surface for various values of rotation, wave number, and thickness of the cylinder which are presented for nonaxial symmetric vibrations for a pervious surface. The dispersion curves are plotted for the poroelastic elastic behavior of the poroelastic material. Results are discussed for poroelastic material. The results indicate that the effect of rotation, wave number, and thickness on the wave propagation in the hollow poroelastic circular cylinder is very pronounced.

scholarly journals Phase Velocity and Attenuation of Longitudinal Shear Vibrations of Hollow Poroelastic Cylinders

2014 ◽  
Vol 19 (2) ◽  
pp. 337-346
Author(s):  
S. Ahmed Shah ◽  
S. Javvad Hussaini
Keyword(s):  
Cylindrical Shell ◽  
Phase Velocity ◽  
Longitudinal Shear ◽  
Frequency Equation ◽  
Circular Cylinders ◽  
Physical Parameters ◽  
Flexural Mode ◽  
Second Mode ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

Abstract The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.

scholarly journals Instantaneous local wave vector estimation from multi-spacecraft measurements using few spatial points

2004 ◽  
Vol 22 (7) ◽  
pp. 2633-2641 ◽  
Author(s):  
T. D. Carozzi ◽  
A. M. Buckley ◽  
M. P. Gough
Keyword(s):  
Signal Processing ◽  
Phase Velocity ◽  
Wave Vector ◽  
Direct Determination ◽  
Space Mission ◽  
3 Dimensional ◽  
Local Wave ◽  
Local Properties ◽  
Vector Estimation

Abstract. We introduce a technique to determine instantaneous local properties of waves based on discrete-time sampled, real-valued measurements from 4 or more spatial points. The technique is a generalisation to the spatial domain of the notion of instantaneous frequency used in signal processing. The quantities derived by our technique are closely related to those used in geometrical optics, namely the local wave vector and instantaneous phase velocity. Thus, this experimental technique complements ray-tracing. We provide example applications of the technique to electric field and potential data from the EFW instrument on Cluster. Cluster is the first space mission for which direct determination of the full 3-dimensional local wave vector is possible, as described here.

scholarly journals On Rayleigh waves in a thinly layered laminated thermoelastic medium with stress couples under initial stresses

1988 ◽  
Vol 1 (3) ◽  
pp. 161-176
Author(s):  
Pijush Pal Roy ◽  
Lokenath Debnath
Keyword(s):  
Phase Velocity ◽  
Initial Stress ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Frequency Equation ◽  
Initial Stresses ◽  
Displacement Fields ◽  
Thermoelastic Medium ◽  
Couple Stresses

A study is made of the propagation of Rayleigh waves in a thinly layered laminated thermoelastic medium under deviatoric, hydrostatic, and couple stresses. The frequency equation of the Rayleigh waves is obtained. The phase velocity of the Rayleigh waves depends on the initial stress, deviatoric stress, and the couple stress. The laminated medium is first replaced by an equivalent anisotropic thermoelastic continuum. The corresponding thermoelastic coefficients (after deformation) are derived in terms of initially isotropic thermoelastic coefficients (before deformation) of individual layers. Several particular cases are discussed for the determination of the displacement fields with or without the effect of the couple stress.

The Dispersion of Flexural Waves in an Elastic, Circular Cylinder—Part 2

1962 ◽  
Vol 29 (1) ◽  
pp. 61-64 ◽  
Author(s):  
Yih-Hsing Pao
Keyword(s):  
Circular Cylinder ◽  
Frequency Equation ◽  
Flexural Waves

In the first part of this paper, a method was developed for the construction of the branches of Pochhammer’s frequency equation for flexural waves in a circular cylinder. The method was applied to the portions of the branches with real propagation constants. The method is now extended and applied to those portions having imaginary propagation constants.

Asymptotics of Flexural Waves in Isotropic Elastic Plates

1997 ◽  
Vol 64 (2) ◽  
pp. 336-342 ◽  
Author(s):  
N. A. Losin
Keyword(s):  
Material Parameter ◽  
Velocity Dispersion ◽  
Three Dimensional ◽  
Analytical Form ◽  
Short Wave ◽  
Frequency Equation ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Explicit Formulas ◽  
Longitudinal Waves

The long and short-wave asymptotics of order O(k6h6) for the flexural vibrations of an infinite, isotropic, elastic plate are studied. The differential equation for the flexural motion is derived from the system of three-dimensional dynamic equations of linear elasticity. All coefficients of the differential operator are presented as explicit functions of the material parameter γ = cs2/cL2, the ratio of the velocities squared of the flexural (shear) and extensional (longitudinal) waves. Relatively simple frequency and velocity dispersion equations for the flexural waves are deduced in analytical form from the three-dimensional analog of Rayleigh-Lamb frequency equation for plates. The explicit formulas for the group velocity are also presented. Variations of the velocity and frequency spectrums depending on Poisson’s ratio are illustrated graphically. The results are discussed and compared to those obtained and summarized by R. D. Mindlin (1951, 1960), Tolstoy and Usdin (1953, 1957), and Achenbach (1973).

The Direct Determination of I131 in Heterogeneous Fecal Specimens

1961 ◽  
Vol 41 (4) ◽  
pp. 380-384 ◽  
Author(s):  
Arthur F. Dratz ◽  
James C. Coberly
Keyword(s):  
Direct Determination
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