In the present work, the effects of initial stress, magnetic field and non-homogeneity on wave propagation of free harmonic waves in isotropic material are discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement and different cases of the boundary conditions for the hollow cylinder are considered. The determination is concerned with the eigenvalues of the natural frequencies of the radial vibrations for different boundary conditions in the case of harmonic vibrations. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results in the absence of initial stress, magnetic field and non-homogeneity.
Abd-AllaAMFarhanAM (2008) Effect of the non-homogeneous on the composite infinite cylinder of orthotropic material. Journal Physics Letters A. 372: 756–760.
2.
Abd-AllaAMMahmoudSR (2010a) Effect of the rotation on propagation of thermoelastic waves in a non-homogeneous infinite cylinder of isotropic material. The International Journal of Mathematical Analysis. 42(4): 2051–2064.
3.
Abd-AllaAMMahmoudSR (2010b) Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylindrical under the hyperbolic heat conduction model. Meccanica. 45(4): 451–462.
4.
Abd-AllaAMMahmoudSR (2011) Magneto-thermo-viscoelastic interactions in an unbounded non-homogeneous body with a spherical cavity subjected to a periodic loading. Applied Mathematical Sciences. 29(5): 1431–1447.
5.
Abd-AllaAMMahmoudSR (2012) Analytical solution of wave propagation in non-homogeneous orthotropic rotating elastic media, in press. Journal of Mechanical Science and Technology. 3(26): 1–10.
6.
Abd-AllaAMMahmoudSRAl-ShehriNA (2010) Effect of the rotation on the radial vibrations in a non-homogeneous orthotropic hollow cylinder. The Open Mechanics Journal. 4: 32–38.
7.
Abd-AllaAMAbo-DahabSMHammadHAMahmoudSR (2011a) On generalized magneto-thermoelastic Rayleigh waves in a granular medium under influence of gravity field and initial stress. Journal of Vibration and Control. 17: 115–128.
8.
Abd-AllaAMMahmoudSRAbo-DahabSM (2011b) Wave propagation modeling in cylindrical human long wet bones with cavity. Meccanica. 6(46): 1413–1428.
9.
Abd-AllaAMMahmoudSRAl-ShehriNA (2011c) Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material. Applied Mathematics and Computation. 217(22): 8914–8922.
10.
Abd-Alla AM, Mahmoud SR and Abo-Dahab SM (2012a) On problem of transient coupled thermoelasticity of an annular fin. Meccanica DOI: 101007/s11012–011–9513–2.
11.
Abd-Alla AM, Yahya GA, Mahmoud SR and Alosaimi HS (2012b) Effect of the rotation, magnetic field and initial stress on peristaltic motion of micropolar fluid. Meccanica DOI: 101007/s11012–011–9528–8.
12.
Abo-DahabSMMohamedRA (2010) Influence of magnetic field and hydrostatic initial Stress on wave reflection from a generalized thermoelastic solid half-space. Journal of Vibration and Control. 16(5): 685–699.
13.
AhmedSMAbo-DahabSM (2010) Propagation of Love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium. Journal of Vibration and Control. 16(12): 1845–1858.
14.
BuchananGR (2003) Free vibration of an infinite magneto-electro-elastic cylinder. Journal of Sound and Vibration. 268: 413–426.
15.
ChapraSC (2004) Applied Numerical Methods with Matlab for Engineering and Science. New York: McGraw-Hill.
16.
ChenWQLeeKYDingHJ (2004) General solution for transversely isotropic magneto-electro-thermo-elasticity and potential theory method. International Journal of Engineering Science. 42: 1361–1379.
17.
ChenWQLeeKYDingHJ (2005) On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates. Journal of Sound and Vibration. 279: 237–251.
18.
DingHJWangHMHouPF (2003) The transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems. International Journal of Solids and Structures. 40: 105–123.
19.
HouPFLeungAYT (2004) The transient response of magneto-electro-elastic hollow cylinders. Smart Materials and Structures. 13: 762–776.
20.
HouPFWangHMDingHJ (2003) Analytical solution for the axisymmetric plane strain electroelastic dynamics of a special non-homogeneous piezoelectric hollow cylinder. International Journal of Engineering Science. 41: 1849–1868.
21.
HouPFDingHJLeungAYT (2006) The transient responses of a special non-homogeneous magneto-electro-elastic hollow cylinder for axisymmetric plane strain problem. Journal of Sound and Vibration. 291: 19–47.
22.
HuangJHWuTL (2000) Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phase. International Journal of Solids and Structures. 37: 2981–3009.
23.
HuangJHLiuHKDaiWL (2000) The optimized fiber volume fraction for magnetoelectric coupling in piezoelectric-piezomagnetic continuous fiber reinforced composites. International Journal of Engineering Science. 38: 1207–1217.
Lekhnitskii SG (1981) Theory of Elasticity of an Anisotropic Body. Moscow: Mir Publishers.
26.
LiuJXLiuXLZhaoYB (2001) Green’s functions for anisotropic magneto-electro-elastic solids with an elliptical or a crack. International Journal of Engineering Science. 39: 1405–1418.
27.
MahmoudSR (2010a) Effect of the non-homogeneity on wave propagation on orthotropic elastic media. International Journal of Contemporary Mathematical Sciences. 45(5): 2211–2224.
28.
MahmoudSR (2010b) Wave propagation in cylindrical poroelastic dry bones. Applied Mathematics & Information Sciences. 2(4): 209–226.
29.
Mahmoud SR (2012) Influence of rotation and generalized magneto-thermoelastic on Rayleigh waves in a granular medium under effect of initial stress and gravity field, in press. Meccanica DOI: 101007/s11012–011–9535–90.
30.
MahmoudSRAbd-AllaAMAl-ShehriNA (2011) Effect of the rotation on plane vibrations in a transversely isotropic infinite hollow cylinder. International Journal of Modern Physics B. 25(26): 3513–3528.
31.
MarinM (1998) A new approach of uniqueness in elastodynamics. Bulletin of the Korean Mathematical Society. 35(1): 63–74.
32.
MarinM (2010a) Harmonic vibrations in thermoelasticity of microstretch materials. Journal of Vibration and Acoustics. 4(132): 29–37.
33.
MarinM (2010b) Harmonic vibrations in thermoelasticity of microstretch materials. ASME Journal of Vibration and Acoustics. 132: 1–6.
34.
Martin Sadd H (2005) Elasticity: Theory, Applications and Numerics: Elsevier Butterworth-Heinemann, ISBN 0-12-605811-3, New York.
35.
PanE (2001) Exact solution for simply supported and multilayered magneto-electro-elastic plates. ASME Journal of Applied Mechanics. 66: 608–618.
36.
PanEHeyligerPR (2002) Free vibrations of simply supported and multilayered magneto-electro-elastic plates. Journal of Sound and Vibration. 252: 429–442.
37.
Sadd MH (2009) Elasticity: Theory, Applications and Numerics. London: Elsevier.
38.
SharmaJNKumarR (2004) Asymptotics of wave motion in transversely isotropic plates. Journal of Sound and Vibration. 274: 747–759.
39.
ToudeshkyHHMofakhamiMRHashemiSH (2009) Sound transmission into a thick hollow cylinder with the fixed end boundary condition. Applied Mathematical Modeling. 33: 1656–1673.
40.
WangXShenYP (2002) The general solution of three-dimensional problems in magneto-electro-elastic media. International Journal of Engineering Science. 40: 1069–1080.
41.
WangXShenYP (2003) Inclusions of arbitrary shape in magneto-electro-elastic composite materials. International Journal of Engineering Science. 41: 85–102.
