Archive

Abstract:

The paper is concerned with the radial vibration of a spherial shell whose young's modulus is a function of the radial distance from the sphere and the poisson's ratio is taken to be constant. The frequency equations for the period of vibration has been determined by perturbation method considering the vibration parameters to be small.

Keywords:

spherical shell,radial vibration,period of vibration,

Refference:

I. Love, A.E.H. (1944), A Treatise on the Mathematical theory of Elasticity, Dover Publication (1944) p-142.

II. Paris, G. (1963): Jour. Of Sci. and Engng. Res., 7,1-4.

III. Charaborty, J.G., Radial and rotatory vibration of a spherical shell of aeolotropic elastic material, Bull. Cal. Math. Soc. Vol.147,no.4 (1965)

IV. Sur, S.P., Radial and rotatory vibration of a Spherical shell of aeolotropic elastic material, Bull. Cal. Math. Soc. Vol..47, no.4 (1965).

V. De, P.K. (1968): Bull. Cal. Math. Soc. 60, no.4.

VI. Pan, M.(1975): pH.D.(Se.) Thesis, C.U.

VII. Sengupta, P.R. and Roy, S.K., Radial vibration of a sphere of general visco elastic solid, Garlands Beitr. Geophysik, Leipzig, 92, 5, s. 435-442(1983).

VIII. Ezzat, M.A., Fundamental Solution in Generalized megneto-thermo-elasticity with two relaxation times for perfect conductor cylindrical region, Int. J. Eng. Sci., 42, pp 1503-1519 (2004).

IX. Rakshit, M. and Mukhopadhyay., B. An electro-magneto-thermo-visco-elastic problem I n an infinite medium with a cylindrical hole, Int. J. Eng. Sci. 43,pp.925-936, (2005).

X. Sengupta, S., Roy, I., Chakraborty, H.S., Redial vibration of a non-homogeneous anisotropic elastic spherical shall with inclusion, J. Mech. Cont. and Math. Sci. Vol .2, no.1, pp1-9, (2007).

TWO DIMENSIONAL WAVE PROPAGATION IN A HIGHER ORDER VISCOELASTIC PLATE UNDER THE INFLUENCE OF INITIAL STRESS AND MAGNETIC FIELD

Authors:

D. P. Acharya, Indrajit Roy, H. S. Chakraborty

DOI NO:

https://doi.org/10.26782/jmcms.2008.06.00006

Abstract:

The aim of the present paper is to investigate the propagation of waves in a magnetovisco-elastic initially stressed electrically conducting plate of finite thickness involving time rate of strain and stress of higher order. The initial stress is assumed to be of the nature of hydrostatic tension or compression. The normal mode analysis is used to obtain the wave velocity equations for the waves propagated in the plate bounded by stress free plane boundaries. The wave velocity equations in different cases, obtained in this paper may be considered as more general in the sense that the results presented by other authors may be obtained as special cases in the absence of additional fields. Numerical computations are carried out and the effects of higher order viscoelasticity, magnetic field and initial stress on the phase velocity ratio are exhibited graphically.

Keywords:

visco-elastic plate,initial stress,magnetic fluid,wave propagation,

Refference:

1) X. Wang and H. L. Dai: Magnetothermodynamic stress and perturbation
of magnetic field vector in an orthotropic thermoelastic cylinder, Int. J. Engng. Sci, 42 (2004), 539-556.
M. A. Ezzat: Fundamental solution in generalized magneto thermoelasticity
with two relaxation times for perfect conductor cylindrical region, Int. J. Engng. Sci, 42 (2004), 1503-1519.
3) Rakshit M. and Mukhopadhyay B. : An electro-magneto-thermo-visco
elastic problem in an infinite medium with a cylindrical hole, Int. J. Engng. Sei, 43 (2005), 925-936.
4) Bakshi A., Bera R. K. and Debnath L.: A study of magneto-thermo elastic
problems with thermal relaxation and heat sources in a three-dimensional infinite rotating elastic medium, Int. J. Engng. Sci, 43 (2005), 1419-1434.
5) Roy Choudhuri S. K. : Magneto-thermo-elastic waves in an infinite
perfectly conducting solid without energy dissipation, J. Tech. Phys., 47 (2006), 63-72.
6) M. I. A. Othman and Y. Song: The effect of rotation on the reflection of
magneto-thermoelastic waves under thermoelasticity without energy dissipation, Acta Mech., 184 (2006), 189-204.
Higuchi M., Kawamura R. and Tanigawa Y.: Magneto-thermo-elastic
stresses induced by a transient magnetic field in a conducting solid circular cylinder, Int. J. Solids Struct., 44 (2007) 5316-5335.Acharya D. P. and Sengupta P. R.: Magneto-thermo-elastic waves in an
initially stressed conducting Layer, Gerlands Beitr. Geophys., 87 (1978), 229-239.
9) Das S. C., Acharya D. P. and Sengupta P. R.: Magneto visco-elastic surface
waves in stressed conducting media, Sildhani , 19 (1994), 337-346.
10) Wang J. and Slattery S. P.: Thermoelasticity without energy dissipation for initially stressed bodies, Int. J. Math. Math. Sci, 31 (2002), 329-337.
11) Othman M. I. A. and Song Y.: Reflection of plane waves from an elastic
solid half-space under hydrostatic initial stress without energy dissipation, Int. J. Solids Struct., 44 (2007), 5651-5664.
12) Sharma M. D.: Effect of initial stress on reflection at the free surface of anisotropic elastic medium, J. Earth Syst. Sci., 116 (2007), 537-551.
13) Selim M. M.: Torsional waves propagation in an initially stressed dissipative
cylinder, AppL Math. Sci. 1 (2007), 1419-1427.
14) Gupta S., Chattopadhyay A. and Kumari P. : Propagation of shear wave in anisotropic medium, Appi. Math. Sci. 1 (2007), 2699-2706.
15) Yu C. P. and Tang S. : Magneto-elastic waves in initially stress’ conductors, Z. Angew. Math. Phys., 17 (1966), 766-775.
16) De S. N. and Sengupta P. R. : Magneto-elastic waves and disturbances in initially stressed conducting media, Pure Appi. Geophys. 93 (1972), 41-54.
17) Roy Choudhuri S. K. and Banerjee M.: Magneto-viscoelastic plane waves
in rotating media in the generalized thermoelasticity II, Int. J. Math. Math. Sci, 11 (2005), 1819-1834.
18) Addy S. K. and Chakraborty N. R.: Rayleigh waves in a viscoelastic half
space under initial hydrostatic stress in presence of the temperature field, Int. J. Math. Math. Sci, 24 (2005), 3883-3894.
19) Song Y. Q., Zhang Y. C., Xu H. Y. and B. H. Lu: Magneto
thermoviscoelastic wave propagation at the interface between two micropolar viscoelastic media, Appl. Math. Compu., 176 (2006), 785-802.
20) Sharma J. N. and Othman M. I. A.: Effect of rotation on generalized
thermo viscoelastic Rayleigh-Lamb waves, Int. J. Solids Struct., 44 (2007), 4243-4255.
21) Yin-feng Z. and Zhong-min W. : Transverse vibration characteristics of axially moving viscoelastic plate, Appl. Math. Mech., 28 (2007), 209-218.
22) Rakshit M. and Mukhopadhyay B. : Visco-elastic plane waves in two
dimensions using generalized theory of thermo-elasticity, Bull. Cal. Math. Soc, 99 (2007), 279-292.
23) Voigt W. : Theortische student uberdie elasticitats verhalinisse krystalle, Abh. Ges. Wiss Goetting, 34 (1887).
24) Sengupta P. R., De N., Kar M. and Debnath L.: Rotatory vibration of
sphere of higher order viscoelastic solid, Int. J. Math. Math. Sci, 17 (1994), 799-806.
25) Othman M. I. A. : Effect of rotation on plane waves in generalized thermo
elasticity with two relaxation times, Int. J. Solids Struct., 41(2004), 2939¬2956.
26) Ezzat M. A., Othman M. I., El-Karamany A. S. : Electromagneto-
thermoelastic plane waves with thermal relaxation in a medium of perfect conductivity, J. Thermal Stresses, 24 (2001), 411-432.
27) Rayleigh F. W. : On the free vibrations of an infinite plate of homogeneous isotropic elastic material, Proc, Math. Soc.20 (1989), 225-234.
28) Lamb H. : On waves in an elastic plate, Proc. Roy. Soc. (London), 93 (1916), 114-128.
29) Eringen A. C. : On Rayleigh surface waves with small wave lengths, Applied and Engineering Sciences, 1 (1973), 11-17.
30) Acharya D. P. and Mandal Asit : Effect of rotation on Rayleigh surface
waves under the linear theory of non-local elasticity, Ind. J. Theor. Phys., 52(1) (2004).

AN EXTENSION OF THE KRYLOV-BOGOLIUBOV-MITROPOLSKII(KBM) METHOD FOR THIRD ORDER CRITICALLY DAMPED NONLINEAR SYSTEM

Authors:

M Ali Akbar, M, S. Uddin , Mo. Rokibullslam

DOI NO:

https://doi.org/10.26782/jmcms.2008.06.00007

Abstract:

Krylov-Bogolov-Mitropolskii (KBM) method has been extended and applied to certain third order non-oscillatory nonlinear systems characterizing critically damped .stems, For different· set oj tnisia! Conditions as well as for different eigenvalues the solutions obtained by the extended (KBM), ·method show good coiricidetlce with those obtained by the numerical method. The method is iIIustrated by all example

Keywords:

microstretch layer,wave propagation,micropolarity,wave velocity,

Refference:

1) Ali Akbar, M., M. Shamsul Alam and M. A. Sattar, A Simple Technique for Obtaining Certain Over-damped Solutions of an n-th Order Nonlinear Differential Equation, Soochow Journal of Mathematics Vol. 31(2), pp. 291-299, 2005.
2) Bogoliubov, N. N. and Yu. Mitropolskii, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordan and Breach, New York, 1961.
3) Bojadziev, G. N., Damped Nonlinear Oscillations Modeled by a 3-dimensional Differential System, Acta Mechanica, Vol. 48, pp. 193-201, 1983.
4) Krylov, N. N. and N. N. Bogoliubov, Introduction to Nonlinear Mechanics, Princeton University Press, New Jersey, 1947.
5) Mendelson, K. S., Perturbation Theory for Damped Nonlinear Oscillations, J. Math. Physics, Vol. 2, pp; 3413-3415, 1970.
6) Murty, I. S. N., Deekshatulu, B. L. and Krishna, G. On an Asymptotic Method of Krylov-Bogoliubov for Over-damped Nonlinear Systems, J. Frank. Inst., Vol. 288, pp. 49-65, 1969.
7) Murty, I. S. N., and Deekshatulu, B. L., Method of Variation of Parameters for Over-Damped Nonlinear Systems, J. Control, Vol. 9, no. 3, pp. 259¬266,1969.
8) Murty, I. S. N., A Unified Krylov-Bogoliubov Method for Solving Second Order Nonlinear Systems, Int. J. Nonlinear Mech. Vol. 6, pp. 45-53, 1971.
9) Popov, I. P., A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russian), Doki. Akad. USSR Vol. 3, pp. 308-310, 1956.
10) Rokibul Islam, M., M. Ali Akbar, M. Samsuzzoha and Afroza Ali Soma, A New Technique for Third Order • Critically Damped Non-linear Systems, Research Journal Applied Science (Accepted for Publication).
11) Sattar, M. A., An asymptotic Method for Second Order Critically Damped Nonlinear Equations, J. Frank. Inst., Vol. 321, pp. 109-113, 1986.
12) Sattar, M. A., An Asymptotic Method for Three-dimensional Over-damped Nonlinear Systems, Ganit, J. Bangladesh Math. Soc., Vol. 13, pp. 1-8, 1993.
13) Shamsul Alam, M. and M. A. Sattar, An Asymptotic Method for Third Order Critically Damped Nonlinear Equations, J. Mathematical and Physical Sciences, Vol. 30, pp. 291-298, 1996.
14) Shamsul Alam, M., Asymptotic Methods for Second Order Over-damped and Critically Damped Nonlinear Systems, Soochow Journal of Math. Vol. 27, pp. 187-200, 2001.
15) Shamsul Alam, M., Bogoliubov’s Method for Third Order Critically Damped Nonlinear Systems, Soochow J. Math. Vol. 28, pp. 65-80, 2002.
16) Shamsul Alam, M., On Some Special Conditions of Third Order Over-damped Nonlinear Systems, Indian J. pure appl. Math. Vol. 33, pp. 727-742, 2002.
17) Shamsul Alam, M., A Unified Krylov-Bogoliubov-Mitropolskii Method for Solving n-th Order Nonlinear Systems, J. Frank. Inst. Vol. 339, pp. 239-248, 2002.
18) Shamsul Alam, M., On Some Special Conditions of Over-damped Nonlinear Systems, Soochow J. Math. Vol. 29, pp. 181-190, 2003.

STEADY UNIDIRECTIONAL FLOW OF A MICROPOLAR FLUID OF FINIT DEPTH DUE TO TANGENTIAL STRESS APPLIED AT THE SURFACE

Authors:

P. C. Ghosh

DOI NO:

https://doi.org/10.26782/jmcms.2008.06.00008

Abstract:

The paper is concerned with the investigation of the steady unidirectional flow of a Micropolar fluid of finite depth due to tangential stress applied at the surface. Numerically it is found that the velocity component (u) of the Micropolar fluid increases to a significant extent over the classical fluid.. The miocropolar effect increases the velocity of the classical fluid and rotation component a increases with the increase of the depth

Keywords:

micropolar fluid,unidirectional floe,tangential stress ,

Refference:

1. Eringen, A.C. Theory of Micropolar fluids. J. Math. Mech. 16.1 (1967)
2. Willson, A.J. Basic Flows of Micropolar liquid. Appl. Sci. REs. 20, 338 (1969)
3. Willson, The flow of a Micropolar liquid layer down on inclined plane. Proc. Camb. Phil. Soc. 64, 513 (1968)
4. Willson, A.J. Boundary layer in Micropolar liquid, Proc. Camb. Phil. Soc. 67, 469 (1970)
5. Goldstem, Proc. Land. Math. Soc. (2), 34 (1931).51.
6. Schlichting, H. Boundary layer theory, p. 230, New York. Mc-Graw¬Hill Co. 1955.
7. Whittake, A.G. and Robinson, C. The calculus of observation, p. 125, Blackie and Son, 1944.

Gupta, P.S. and Gupta, A.S. Steady flow of Micropolar Liquids, Acta Mechanica, 15, 141-149 (1972).
Ghosh, P.C. and Sengupta, P.R. N.B.U. review (Sc. and Tech.) Vol 4 (No.– 2); (1983).
Ghosh, P.C. and Sengupta, (1983), Journal of Technology, (Shibpur E. College), Vol — XXVII, No. 1
Lamb, H. (1975) Hydrodynamics, Cambridge University Press, Sixth
Batchelor, G. K. (1967) An Introduction of fluid Dynamics, Cambridge University Press, Cambridge.
Panja,S (2006), J. Mech. Cont. Sci. Vol 1, No. 1, July, 2006, pp 46-52

NUMERICAL TREATMENT OF NON-DARCIAN EFFECT ON PULSATILE MHD POWER-LAW FLUID FLOW WITH HEAT TRANSFER IN A POROUS MEDIUM BETWEEN TWO ROTATING CYLINDERS

Authors:

Mokhtar A. Abd Elnaby, Nabil T.M. Eldabe, Hanaa A. Asfour

DOI NO:

https://doi.org/10.26782/jmcms.2008.12.00001

Abstract:

The problem of unsteady magneto hydrodynamic flow with heat transfer of a non-Newtonian fluid obeying power low fluid in a porous medium between two coaxial cylinders is investigated when the inner cylinder is at rest and the outer cylinder rotates with constant velocity, taking into account pulsation the pressure gradient and Darcy dissipation term. A Rung-Kutta-Merson method and a Newtown Iteration in a shooting and matching technique are used to obtain the solution of the system Equations of the problem. The velocity and temperature distributions are obtained as a perturbation technique. During this work we calculate an estimation of the global error by using Zadunaisky technique. The effects of behaviour index, Reynolds number, steady state part of the pressure gradient, the amplitude of the oscillatory part, the magnetic parameter, the permeability parameter, Forschheimer number, Prandtl number, Eckert number on the velocity and temperature distributions of Newtown and non- Newtown fluid are evaluated and depicted graphically.

Keywords:

Non-Darcain effect,Fluid flow ,Heat transfer,Rotating calender.,

Refference:

I. Long Q., Xua X.Y., Ramnarine K.V. and Hoskins P. Journal of Biomechanics 34(2001), 1229.

II. Phillips E.M. And Chiang S.H. Int. J.Engng Sci. 11(1973), 579.

III. McDonald D.A. “Blood flow in arteries”, Edward Arnold, London. 1974.

IV. Bitoun J.P. and Bellet D.: Biorheology, 23(1986), 51.

V. Ahmed S.A. and Giddens D.P.: J. Biomech, 17(1984),695.

VI. Lieber B. pH. D. Thesis, Georgia Institute of Technology, Atlanta (1985).

VII. Ojha M., Cobbold R.S.C., Johnston K.W. and Hummel R.J. Fluid. Mech. 203 (1989), 173.

VIII. Hong J.T., Tien C.L. and Kaviany M.Int. J. Heat Mass Transfer. 28 No. 11(1985), 2149.

IX. Andresson H.I., Bech K.H. and Dandapat B.S. Int. J. Nonlinear Mechanics. 27No.6(1992),929.

X. Nakayama A. Transactions of the ASME. 114(1992), 642.

XI. Nakayama A. Int. J. Heat and Fluid. 14 no.3(1993). 278.

XII. Agrawal A.K. and Sengupta S. Int. J. Heat and Fluid Flow. 11. No.1(1990), 54.

XIII. Mokhtar A. Abdelnaby, Nabil T.M Eldabe and Mohammed Y. Abo zeid: J.Ind.Theo.Phys. (2006), in press. 4164.

XIV. Nabil T.M. Eldabe, Sadeek G. and Asma F. El-Sayed. Phys. Soc. Japan. 64(1995), 4165.

XV. Batra R.L. and Biggani Das: Fluid Dynamic Research, 9 (1992), 133.

XVI. Ibrahim F.N. phys. D: APPL. Phys. 24(1991), 1293.

XVII. Zadunaisky, P.E: Numer. Math. 27(1976),21.

TORSIONAL VIBRATION OF AN IN-HOMOGENEOUS ELASTIC CONE

Authors:

A.De, M. Chaudhuri

DOI NO:

https://doi.org/10.26782/jmcms.2008.12.00002

Abstract:

The object of this paper is to study the torsional vibration of an in-homogeneous elastic cone. For in-homogeneous of the material considered it is assumed that the elastic constants and the density of the material very exponentially as the radial distance. Two broad cases of end condition have been taken into account. Displacements and stresses for a particular case have been obtained and are shown in tabular from and graphically for different values of radial distance.

Keywords:

Torrtion vibration,Elastic cone,In-homogeneous,Stress,

Refference:

I. Abramovitz, M.: Handbook of Mathematical Functions, Dover and Publications, New York, 1970 stegun,A.

II. Banerjee, A.: ‘Torsional vibration in a circular cylinder’, Bull. Calcutta. Math. Soc. 72, 309-314, 1989.

III. Bullen, K.E. An Introduction to the Theory of Seismology 2nd. Edn. Cambridge University Press, 1976.

IV. Bhanja, N.: ‘ Torsional vibration problem for a cone of spherically anisotropic material, Ind. Jour. Mech. Math. Vol-8,2,160-167,1970.

V. Campbell, J.D.: ‘Torsional vibration in a circular cylinder and Q.J.M.A.

VI. M.25, 74-84, 1972. Tsao, M.C.C

VII. Davies, R.M. “Torsional vibration in a circular cylinder “, Surveys of Mechanics, Cambridge University Press, 1959.

VIII. Koslky, H. “Torsional vibration in stress waves in solids.

IX. Love, A.E.H.: “The Mathematics Theory of Elasticity” 4th Edn. Cambridge University Press, 1962.

X. Mitra, A.K.: “Torsional vibration in a circular cylinder” J.Sci. Engng. Res. No.2, 251-28, 1961.

XI. Mondal, N.C: “Free Torsional vibration of a non-homogeneous semi-solid circular cylinder” Proc. Indian Bath. Sci. Acad. 52A, 512-20, 1986.

XII. Mukherjee, S. : ‘ Torsional vibration of an isotropic material.’ Ind. Jour, Mech. Math. Vol. V, 1967.

XIII. Rao, Y.B. : ‘ Torsional vibration in an isotropic homogeneous infinitely long solid circular cylinder with rigid boundary.’ Proc. Indian Natn. Sci. Acad. 52A, 497-501, 1986.

XIV. Watson, G.N.: ” A treatise on Theory of Bessel Functions”.

XV. Cambridge University Press, NY 10022, USA, 1922.

XVI. Watson, G.N.: ” The Theory of Bessel Functions” 2nd Ed., Cambridge University Press,1948.

DEVELOPMENT OF SECONDARY FLOW AND UNSTEADY SOLUTION THROUGH A CURVED DUCT

Authors:

Rabindra Nath Mondal, Md. Sharif Uddin , Md. Azmol Huda, Anup Kumar Dutta

DOI NO:

https://doi.org/10.26782/jmcms.2008.12.00003

Abstract:

In this paper, development of secondary flow and unsteady by using the spectral method. Numberical calculations are carried out for the Grashof number Gr=1000 over a wide range of the Dean number,0≤Dn≤1000, and the curvature,0<ẟ≤0.5, where the outer well is heated and the inner wall is cooled. First steady solutions are obtained by the Newton-Raphson Iteration method. As a result, we obtain five branches of asymmetric steady solutions with one -two-four-six and eight-vortex Solution at the same Dean number. Then,time evolution calculations of the unsteady solutions are performed, and it is found that the steady flow turns into chaotic flow through periodic flows, no matter with the curvature is Finally, the complete unsteady Solution, covering the wide range of dn and ẟ are shown by a phase diagram.

Keywords:

Secondary flow,Curved duct,Chaotic flow,Vortex Solution,

Refference:

I. Berger, S.A. Talbot, L. And Tai, L.S., Flow in curved pipes, Annual Review of Fluid Mechanics, Vol 35, pp. 461-512,1983.

II. Dean, W.R.., Note on the motion of Fluid in a curved pipe, Philosophical.

III. Ito, H., Flow in curved pipes, JSME International Journal, vol.30, pp.543-552,1987.

IV. Mondal, R.N. 2006. Isothermal and non-isothermal flows through curved ducts with square and rectangular cross sections, PH.D. Thesis, Department of Mechanical Engineering, Okayama University, Japan.

V. Mondal, R.N., Kaga, Y., Hyakutake, T. and Yanase, S., Effect of curvature and convective heat transfer in curved square duct flows, Trans. ASME, Journal of Fluids Engineering, vol.128(9), pp. 1013-1023,2006.

ON INTERFACE WAVES IN SECOND ORDER THERMO-VISCOELASTIC SOLID MEDIA UNDER THE INFLUENCE OF GRAVITY

Authors:

D.P. Acharya, Indrajit Roy, H.S. Chakraborty.

DOI NO:

https://doi.org/10.26782/jmcms.2008.12.00004

Abstract:

The aim of the present paper is to investigate interface waves (surface waves) of Earthquakes in second order thermo-viscoelastic solid media under the influence of gravity. The displacement components are expressed in terms of displacement potentials. The problem of surface waves, particularly, Rayleigh waves, Love waves and stoneley waves have been determined. All final results and Equations are in fair agreement with the corresponding classical results when the effect of temperature, viscosity and gravity are ignored.

Keywords:

Thermo-viscoelastic solid,Surface wave,Rayleigh wave,Wave velocity,,Gravity,

Refference:

I. Love AEH(1911) Some problems of Geodynamics. Dover, New York.

II. Stoneley R (1924) Elastic waves at the surface of separation of two solids. Proc. Roy. Soc. London A-106, pp. 416-428.

III. Bullen KE(1965) An introduction to the Theory of Seismology. Cambridge University Press,. London. pp.85-99.

IV. Jeffreys. Sir H (1970) The Earth, Cambridge University Press.

V. Bromwich TJIA(1898) On the influence of gravity on elastic waves and in particular on the vibrations of an elastic globe. Proc. London Math. Soc.30, pp.98-120.

VI. De SN and Sengupta PR (1975) Therm-elastic Rayleigh waves under the influence of gravity. Gerlands Betir. Geophysik. 84(6), pp.509-514.

VII. De SN and Sengupta PR (1976) Surface waves under the influence of gravity. Gerlands Betir. Geophysik.85(4), pp.311-318.

VIII. Das TK and Sengupta PR(1992) Effect of gravity on visco-elastic surface waves in solids involving time rate of strain and stress of first order. Sadhana. 17(2), pp.315-323.

IX. Das TK, Sengupta PR, and Debnath L (1995). Effect of gravity on visco-elastic surface waves in solids involving time rate of strain and stress of higher order. Int. J. Math. Sci. 18(1), pp. 71-76.

X. Ghosh NC, Roy I and Biswas PK. (2000) Effect of gravity and couple-stress on thermo-visco-elastic Rayleigh waves involving stress rate and strain rate. J.Bih. Math. Soc. 20, pp.89-99.

XI. Boot MA (1965) Mechanics of incremental deformations, Theory of elasticity and viscoelasticity of initially stressed stressed solids and fluids, including thermodynamic foundation and application to finite strain, John Wiley & Sons, New York. 44-45, 273-281.

XII. Mukherjee A and Sengupta PR(1991) Surface waves in thermo visco-elastic media of higher order. Ind. J. Pure. APPL. Math.22(2), pp.159-167.

On Some Properties of Anti Fuzzy Subgroups

Authors:

Samit Kumar Majumder , Sujit Kumar Sardar

DOI NO:

https://doi.org/10.26782/jmcms.2008.12.00005

Abstract:

In this paper some properties of anti fuzzy subgroups have been introduced.

Keywords:

Fuzzy set,Fuzzy subgroup,Anti-fuzzy subgroup,

Refference:

I. Kandasamy w.b. Vasantha, Samarandache Fuzzy Algebre- American Research Press, Rehoboth (2003), 22-26.

II. Majumder. S.K and Sardar. S.K; On fuzzy Magnified Translation (Communicated).

III. Rosenfeld. A, Fuzzy groups, J. Math. Anal. APPL. 35(1971), 512-517.

IV. Zadeh. L.A, Fuzzy Sets, Inform And Control 8(1965) 338-365.

TOROSIONAL VIBRATION OF A LARGE THICK COMPOSITE PLATE UNDER SHEARING FORCES APPLIED ON THE FREE PLANE SURFACE

Authors:

P.C. Bhattachryya

DOI NO:

https://doi.org/10.26782/jmcms.2008.12.00006

Abstract:

In this paper dynamic stresses and displacements are calculated in a large thick composite plate due to Torsional vibration under sharing forces applied on the free plane boundary being in contact with a rigid foundation. The applied shearing force on the free plane boundary is expressed in terms of Four lier -- Bessel integrals; in particular, case of Gaussian load has been treated in details to find distributions of stresses and displacements.

Keywords:

Torrtional vibration,Composite plate,Shearing force,Plane surface.,

Refference:

I. Chatterjee, P.P (1957), Proc. Th. And Appl. Mech P. 129.

II. Love, A.E.H. (1994), A Treatise on the Mathematical theory of Elasticity.

III. Timoshenko and Goofier (1951), theory of Elasticity.

IV. Acharya, D P. and Mondal, A Effect of rotation on Rayleigh surface waves under the linear theory of non-local elasticity, Ind. J. Theory. Phys. 52(1) (2004).

V. Yu, Yi-Yuan(1954), Quar. Journal of Mech. And App. Math., Vol.7 p. 287.

VI. Sengupta, P.R. (1964), Bull. Cal. Math. Soc.vol.56 , No.1, march, 1967. Pp. 33-40.

VII. Sengupta, P.R. (1965), Bull. Cal. Math. Soc.vol.57, No.2 & 3, June and Sept. (1965), pp.69-70.

VIII. Bhattachryya, P.C. and Sengupta, P.R., propagation of waves in composite elastic layer, Jour. Sci. Res. Vol.3. (1981) pp.211-214.

IX. Sharma M.D. Effect of initial stress on reflection at the free surface of anisotropic elastic medium, J. Earth Syst. Sci. 116 (2007), pp.537-557.

X. Guptav, S. Chattopadhyaya, A and Kumari, P., Propagation of share waves in anisotropic medium ., Appl. Math. Sci., 1(2007) pp.2699-2706.

XI. Selim. M.M., Torsional Waves Propagation in an initially stresses dissipative cylender., Appl. Math. Sci. 1 (2007) pp.1419-1427