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.

Circumferential Waves of Infinite Hollow Poroelastic Cylinders

2005 ◽  
Vol 73 (4) ◽  
pp. 705-708 ◽  
Author(s):  
M. Tajuddin ◽  
S. Ahmed Shah
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Phase Velocity ◽  
Elastic Solid ◽  
Frequency Equation ◽  
Saturated Porous Media ◽  
Biot’S Theory ◽  
Phase Velocity And Attenuation ◽  
Special Case ◽  
Circumferential Waves

Employing Biot’s theory of wave propagation in liquid saturated porous media, the frequency equation of circumferential waves for a permeable and an impermeable surface of an infinite hollow poroelastic cylinder is derived in the presence of dissipation and then discussed. Phase velocity and attenuation are determined for different dissipations and then discussed. By ignoring liquid effects, the results of purely elastic solid are obtained as a special case.

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 Propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses

1988 ◽  
Vol 1 (4) ◽  
pp. 271-286 ◽  
Author(s):  
Lokenath Debnath ◽  
Pijush Pal Roy
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Couple Stress ◽  
Frequency Equation ◽  
Initial Stresses ◽  
Wave Number ◽  
Edge Waves ◽  
Approximate Representation ◽  
Couple Stresses ◽  
Special Cases

The propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses is examined. Based upon an approximate representation of a laminated medium by an equivalent anisotropic continuum with average initial and couple stresses, an explicit form of frequency equation is obtained to derive the phase velocity of edge waves. Edge waves exist under certain conditions. The inclusion of couple stresses increases the velocity of wave propagation. For a specific compression, the presence of couple stresses increases the velocity of wave propagation with the increase of wave number, whereas the reverse is the case when there is no couple stress. Numerical computation is performed with graphical representations. Several special cases are also examined.

scholarly journals Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Spherical Shell ◽  
Wave Number ◽  
Biot’S Theory ◽  
Impervious Surfaces ◽  
Axially Symmetric ◽  
Spherical Shells ◽  
Biot's Theory

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.

scholarly journals Longitudinal Wave in a Thermally Conducting Elastic Medium

2019 ◽  
Vol 8 (4) ◽  
pp. 8769-8771
Keyword(s):  
Temperature Field ◽  
Phase Velocity ◽  
Elastic Medium ◽  
Longitudinal Wave ◽  
Frequency Equation ◽  
Damping Coefficient ◽  
Wave Number ◽  
Longitudinal Wave Propagation ◽  
Thermally Conducting ◽  
Equations Of Motions

The longitudinal wave propagation in a thermally conducting elastic medium has been investigated. Considering the equations of motions of longitudinal wave in displacement and temperature field, the frequency equation has been derived. The dispersion and damping equations have been derived for the propagation of longitudinal wave in four materials i.e Copper, Steel, Aluminum, and Lead. Effect of Phase velocity and damping coefficient are shown graphically. It is found that the increase in wave number results the decrease in Phase velocity and increase in damping coefficient.

Rayleigh-Type Wave Propagation on a Micropolar Cylindrical Surface

1993 ◽  
Vol 60 (4) ◽  
pp. 857-865 ◽  
Author(s):  
K. Mrithyumjaya Rao ◽  
M. Pratap Reddy
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Phase Velocity ◽  
Rayleigh Wave ◽  
Frequency Spectrum ◽  
Cylindrical Surface ◽  
Couple Stress ◽  
Cutoff Frequency ◽  
Particle Displacement ◽  
Azimuthal Direction

A detailed study of a Rayleigh wave propagating on the surface of a micropolar elastic circular cylinder in an azimuthal direction is considered. At the cutoff frequency if the particle displacement is purely azimuthal and equivoluminal, then only this type of wave exists. A number of deviations from the results of the classical theory are observed. For example, the phase velocity corresponding to the same branch is given to be single valued, whereas it seems to be multivalued at some intervals. Due to the micropolar effect there exists an extra wave whose frequency spectrum is also obtained. The dependence of the microrotation and couple stress amplitudes on depth are evaluated. The frequency of the Rayleigh wave increases due to the micropolar effect.

PROPAGATION OF LOVE WAVE IN FIBER-REINFORCED MEDIUM OVER A NONHOMOGENEOUS HALF-SPACE

2014 ◽  
Vol 06 (05) ◽  
pp. 1450050 ◽  
Author(s):  
SANTIMOY KUNDU ◽  
SHISHIR GUPTA ◽  
SANTANU MANNA ◽  
PRALAY DOLAI
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Half Space ◽  
Love Wave ◽  
Graphical Representation ◽  
Separation Of Variables ◽  
Classical Equation ◽  
Wave Number ◽  
Fiber Reinforced

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

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