The effect of initial stress and magnetic field on wave propagation in human dry bones

S.r Mahmoud ,Abdelouahed Tounsi,Ahmed T Ali ,K S Al-Basyouni

doi:10.1186/1687-2770-2014-135

Abstract

The aim of the present paper is to study the influence of initial stress and magnetic field on the 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 elastodynamics are solved in terms of displacements. The natural frequency of plane vibrations in the case of harmonic vibrations has been obtained. The frequencies and phase velocity are calculated numerically, the effects of initial stress and magnetic field are discussed. Comparisons are made with the result in the absence of initial stress and magnetic field.

Highlights

The investigation of wave propagation over a continuous medium has very important application in the fields of engineering, medicine and in bioengineering
The results indicate that the effect of initial stress P∗ and magnetic field H is very pronouced
6 Conclusion This study has presented the effect of initial stress P∗ and magnetic field H on surface wave dispersion in bone

Summary

Introduction

The investigation of wave propagation over a continuous medium has very important application in the fields of engineering, medicine and in bioengineering. Abd-Alla et al [ , ] studied the effect of rotation, magnetic field and initial stress on peristaltic motion of micropolar fluid and investigated the effect of rotation on a non-homogeneous infinite cylinder of orthotropic material. The equations of elastodynamics for transversely isotropic material under the effect of initial stress and magnetic field are solved in terms of displacement potentials. Substituting equations ( a) and ( b) into equations ( a) and ( b), we obtain the final solution of displacement components in the following form: ur =. Substituting equations ( a) and ( b) into equations ( a)-( d), we obtain the final solution of the stress components of solid in the following form: ei(zγ –tω ) r. Elimination of these unknowns would give us the frequency equation as follows:

B B B B

Conclusion