scholarly journals Effect of the initial stress and rotation on free vibrations in transversely isotropic human long dry bone

2015 ◽  
Vol 23 (1) ◽  
pp. 171-184 ◽  
Author(s):  
S. R. Mahmoud ◽  
M. Marin ◽  
K.S. Al-Basyouni
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Initial Stress ◽  
Isotropic Material ◽  
Transversely Isotropic ◽  
Free Vibrations ◽  
Harmonic Waves ◽  
Transversely Isotropic Material ◽  
Harmonic Vibrations ◽  
Dry Bone

Abstract The object of the present paper is to study the influence of the initial stress and rotation on wave propagation of harmonic waves in a human long dry bone as transversely isotropic material, subject to the boundary conditions that the outer and inner surfaces are traction free. The equations of elastodynamic are solved in terms of displacements. The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained. The frequencies and the phase velocity are calculated numerically, the effects of the initial stress and rotation are discussed. Comparisons are made with the result in the absence of rotation and initial stress.

EFFECT OF THE ROTATION ON PLANE VIBRATIONS IN A TRANSVERSELY ISOTROPIC INFINITE HOLLOW CYLINDER

2011 ◽  
Vol 25 (26) ◽  
pp. 3513-3528 ◽  
Author(s):  
S. R. MAHMOUD ◽  
A. M. ABD-ALLA ◽  
N. A. AL-SHEHRI
Keyword(s):  
Natural Frequency ◽  
Hollow Cylinder ◽  
Isotropic Material ◽  
Natural Frequencies ◽  
Transversely Isotropic ◽  
Axisymmetric Vibration ◽  
Harmonic Waves ◽  
Harmonic Vibrations ◽  
Transversely Isotropic Materials ◽  
Effects Of Rotation

In the present paper, a technique is presented for obtaining estimates for the natural frequencies of axisymmetric vibration for transversely isotropic material. The wave propagation of harmonic waves in hollow cylinder of transversely isotropic materials subjected to certain boundary conditions is studied. The two-dimensional equations of elastodynamic are solved in terms of displacement by using the technique of variables separation. The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained. The natural frequencies are calculated numerically and the effects of rotation is discussed. The numerical results obtained have been illustrated graphically to understand the behavior of natural frequency versus the ratio h. Comparisons are made with the result in the absence of rotation.

THE ANALYSIS OF DYNAMICAL RESPONSE OF TRANSVERSELY ISOTROPIC MATERIAL UNDER BLASTING LOAD

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1443-1448
Author(s):  
YUE-XIU WU ◽  
QUAN-SHENG LIU
Keyword(s):  
Isotropic Material ◽  
Peak Velocity ◽  
Transversely Isotropic ◽  
Normal Direction ◽  
Dynamical Response ◽  
Transversely Isotropic Material ◽  
Peak Acceleration ◽  
Loading Direction ◽  
Blasting Load ◽  
Explosion Load

To understand the dynamic response of transversely isotropic material under explosion load, the analysis is done with the help of ABAQUS software and the constitutive equations of transversely isotropic material with different angle of isotropic section. The result is given: when the angle of isotropic section is settled, the velocity and acceleration of measure points decrease with the increasing distance from the explosion borehole. The velocity and acceleration in the loading direction are larger than those in the normal direction of the loading direction and their attenuation are much faster. When the angle of isotropic section is variable, the evolution curves of peak velocity and peak acceleration in the loading direction with the increasing angles are notching parabolic curves. They get their minimum values when the angle is equal to 45 degree. But the evolution curves of peak velocity and peak acceleration in the normal direction of the loading direction with the increasing angles are overhead parabolic curves. They get their maximum values when the angle is equal to 45 degree.

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