Effect of Magnetic Field on Torsional Waves in Non-Homogeneous Aeolotropic Tube

Subject Areas : Engineering

R Kakar ¹ , S Kakar ² , K.C Gupta ³ , K Kaur ⁴

1 - Principal, DIPS Polytechnic College, Hoshiarpur
2 - Faculty of Electrical Engineering, SBBSIET Padhiana Jalandhar
3 - Faculty of Science, DIPS Polytechnic College, Hoshiarpur
4 - Faculty of Science, BMSCT, Muktsar

Received: 2012-07-04 Accepted : 2012-09-09 Published : 2012-09-30

Keywords: magnetic field, Aeolotropic Material, Viscoelastic Solids, Non-Homogeneous, Bessel Functions,

Abstract :

The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The elastic constants and non-homogeneity in viscoelastic medium in terms of density and elastic constant is taken. The frequency equations have been derived in the form of a determinant involving Bessel functions. Dispersion equation in each case has been derived and the graphs have been plotted showing the effect of variation of elastic constants and the presence of magnetic field. The obtained dispersion equations are in agreement with the classical result. The numerical calculations have been presented graphically by using MATLAB.

References:

[1] Kaliski S., Petykiewicz J., 1959, Dynamic equations of motion coupled with the field of temperatures and resolving functions for elastic and inelastic bodies in a magnetic field, Proceedings Vibration Problems 1(2):17-35.

[2] Narain S., 1978, Magneto-elastic torsional waves in a bar under initial stress, Proceedings Indian Academic Science 87 (5): 137-45.

[3] White J.E., Tongtaow C., 1981, Cylindrical waves in transversely isotropic media, Journal of Acoustic Society America 70(4):1147-1155.

[4] Das N.C., Bhattacharya S.K., 1978, Axisymmetric vibrations of orthotropic shells in a magnetic field, Indian Journal of Pure Applied Mathematics 45(1): 40-54.

[5] Andreou E., Dassios G., 1997, Dissipation of energy for magneto elastic waves in conductive medium, The Quarterly of Applied Mathematics 55: 23-39.

[6] Suhubi E.S., 1965, Small torsional oscillations of a circular cylinder with finite electrical conductivity in a constant axial magnetic field, International Journal of Engineering Science 2: 441.

[7] Abd-alla A.N., 1994, Torsional wave propagation in an orthotropic magneto elastic hollow circular cylinder, Applied Mathematics and Computation 63: 281-293.

[8] Datta B.K., 1985, On the stresses in the problem of magneto-elastic interaction on an infinite orthotropic medium with cylindrical hole, Indian Journal of Theoretical. Physics 33(4): 177-186.

[9] Acharya D.P., Roy I., Sengupta S., 2009, Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media, Acta Mechanics 202: 35–45.

[10] Liu M.F., Chang T.P., 2005, Vibration analysis of a magneto-elastic beam with general boundary conditions subjected to axial load and external force, Journal of Sound and Vibration 288(1-2): 399-411.

[11] Dai H.L., Wang X., 2006, Magneto-elastodynamic stress and perturbation of magnetic field vector in an orthotropic laminated hollow cylinder, International Journal of Engineering Science 44: 365–378.

[12] Tang L., Xu X. M., 2010, Transient torsional vibration responses of finite, semi-infinite and infinite hollow cylinders, Journal of Sound and Vibration 329(8): 1089-1100.

[13] Selim M., 2007, Torsional waves propagation in an initially stressed dissipative cylinder, Applied Mathematical Sciences 1(29): 1419 – 1427.

[14] Chattopadhyay A., Gupta S., Sahu S., 2011, Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer, Applied Mathematics and Mechanics 32(5): 571-586.

[15] Love A.E.H., 1911, Some Problems of Geodynamics, Cambridge University press.

[16] Thidé B., 1997, Electromagnetic Field Theory, Dover Publications.

[17] Chandrasekharaiahi D.S., 1972, On the propagation of torsional waves in magneto-viscoelastic solids, Tensor( N.S.) 23: 17-20.

[18] Watson G.N., 1944, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Second Edition.

[19] Green A.E., 1954, Theoretical Elasticity,Oxford University Press.

[20] Love A.E.H., 1944, Mathematical Theory of Elasticity, Dover Publications, Forth Edition.

[21] Timoshenko S., 1951, Theory of Elasticity, McGraw-Hill Book Company, Second Edition.

[22] Westergaard H.M., 1952, Theory of Elasticity and Plasticity, Dover Publications.

[23] Christensen R.M., 1971, Theory of Viscoelasticity, Academic Press.