Archive

Abstract:

An asymptotic method has been found to obtain approximate solution of a second of a second order Nonlinear Differential system based on the extension of Krylov-Bogoliubov-mitropolskii method, whose coefficients change slowly and periodically with time. Moreover a non-autonomous case also investigated in which an external periodic force acts in the system. The solutions for different initial conditions show a good agreement with those obtained by numerical method. The method is illustrated by examples.

Keywords:

Non-linear system, ,Varying coefficent,Periodic force,Asymptotic Method,

Refference:

I. Poincare H. Les Methods Nouvelles de ls Mecanique Celeste, Paris, 1892.

II. Wetzel, G.Z. Physio 38 (1926) 518.

III. Kramer’s H.A., G.Z. physik 39 (1926) 828.

IV. Beillouin L., Compt. Tend. 183(1926) 24.

V. Frshcnko S.F., Shkil N.I. and Nikolenko L.D., Asymptotic Method in the theory of linear differential Equation, (in Russia), Naukova Dumka, Kiev 1966 ( English translation, Amer Elsevier publishing co. INC. New York 1967.

VI. Nayfeh A.H., Perturbation Methods, J. Wiley, New York, 1973.

VII. Krylov N.N. and N.N., Bogoliubov, Introduction to Nonlinear Mechanics. Princeton University Presses, New Jersey, 1947.

VIII. Bogoliubov, N.N. and Yu. Mitropolskii, Asymptotic Method in the Theory of Nonlinear Oscillations, Gordan and Breach, New York, 1961.

IX. Mitropolskii Yu., Problemson Asymptotic Method of non-stationary Oscillations (in Russian), Izdat, Nauka, Moscow,(1964).

X. Bojadziev G. And Edwards j, On some asymptotic methods for non-oscillatory and processes, Nonlinear vibration problem 20(1981) 69-79.

XI. Murty I.S.N., A Unified Krylov-Bogoliubov method for second order Nonlinear Systems, Int. J. Nonlinear Mech. 6 (1971) 45-53.

XII. Shamsul Alam M., Unified Krylov-Bogoliubov- Mitropolskii method for Solving n-th order Nonlinear Systems with slowly varying coefficients, Journal of sound and vibration 256 (2003) 987-1002.

XIII. Hung Cheng and Tai Tsum Wu. An aging spring, Studies in Applied Mathematics 49(1970) 183-185.

XIV. K.C. Roy, Shamsul Alam M, Effect of higher approximation of Krylov-Bogoliubov-Mitropolskii solutions and matched asymptotic Solution of a differential system with slowly varying coefficients and damping near to a turning point, Vietnam Journal of Machanics, VAST, 26 (2004) 182-192.

XV. Shamsul Alam M, Perturbation theory for damped Nonlinear Systems with large damping, India J. Pure and APPL. Math. 32(2001) 1453-1461.

XVI. Shamsul Alam M, Bellal Hossain M. Shanta S.S., Approximate Solution if non-oscillatory systems with slowly varying coefficients, Ganit (Bangladesh J. of Math. Soc.) 21 (2001) 55-59.

XVII. Popov I.P., A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russia), Doll. Akad. Nauk. SSSR 111(1956) 308-310.

XVIII. Minorski N., Nonlinear Oscillations, Princeton, Von Nostrand Co. 1962.

XIX. G.N. Bojadziev and C.K. Hung Damped oscillation modeled by a 3-dimesionaltime dependent differential system, Acta Mech, 53(1984) 101-114.

XX. Shamsul Alam, Damped oscillation modeled by an n-th order time dependent quasi-linear differential system, Acta Mech. 169(2004) 111-122.

Journal Vol - 3 No -2, December 2008

THERMAL STRESSES IN AN IN-HOMOGENEOUS SPHERICAL SHELL

Authors:

A.De , M. Chaudhuri

DOI NO:

https://doi.org/10.26782/jmcms.2009.07.00001

Abstract:

I. The abstract of this paper is Nowinski obtained the thermo-elostic stresses and displacements in spherical shells and solid spheres with temperature deyendent propreties. Following Gibson. The present author has obtained the thermo-elostic stresses in an in-homogeneous spherical shell where the poisson's ratio, the co-efficieent of exponential thermal expansion very exponentially with the radial distance r from the centre of the shell.

Keywords:

thermal stress,spherical shells, thermo – electric stresses,

Refference:

I. Erdelyi, M.O.T. (1955) “Higher Trancendental Function”, McGraw-Hill Book Company, pp.40.

II. Gibson, R.E. (1969). “The thermo-elastic stresses in an in-homogeneous spherical shell” , ZAMP vol.20, pp.619.

III. Love, A.E.H. (1952) “A treatise on the mathematical theory of elasticity”, Cambridge UniversityPress, 4th Edn.

IV. MOllah, S.A. (1990) “Tharmal stresses in a non-homogeneous thin rotating circular disk having transient shearing stress applied on the outer edge” Ganit Journal of Bangladesh Mathematical Society Vol.10, pp.59-65.

V. Nowinski, J. (1959) “The thermo-elastic stresses and displacements in spherical shells and solid spheres” ZAMP, vol.10,pp.565.

VI. Saherical, B.K. (1965) “A stress distribution in a thin rotaiing circular dise having transient shearing stress applied on the outer edge”, Jour. Frank. Inst.vol.281, pp.315.

VII. Timoshenko, S. and Goodier, J.N. (1966)” Theory of elasticity” 4th Edn. McGraw Hill Book Co. New York, pp.406-434.

NONLINEAR FREE VIBRATIONS ANALYSIS AND BEHEVIOR OF THIN SHALLOW SPHERICAL ELASTIC SHELLS OF VARIABLE THICKNESS

Authors:

Utpal Kumar Mandal

DOI NO:

https://doi.org/10.26782/jmcms.2009.07.00002

Abstract:

Large amplitude (nonlinar) free vibration analysis of thin shallow spherical elastic shalls of vairable thickness with tangentially clamped immovable edges has boon performed by using both (i) coupled governing differential equations derived in the Von Karman sense in trimes of displacement components as well as (ii) decoupled nonlinear governing differential equations on the basis of Berger approximation (i.e. neglection second strain invariant e2) derived from energy expression applying Hamilton`s principal and Euler`s variational equations. The governing differential equations are solved by Galerkin error minimizing technique incorporating clamped immovable edge conditions. A parametric study is presented to understand the effects of various parameters on nonlincear dynamic behavior of such structures and the same reveals some interesting features.

Keywords:

non linear vibration,spherical elastic shell,Berger approximation,Galerkin error ,

Refference:

I. R. Archer and S. Lang, “Nonlinear dynamic behavior of shallow spherical shells, ” AIAAJ., no.2, pp.30-36, 1969.

II. J. Ramachandran, “Vibration of shallow spherical shells at large amplitudes” Journal of Applied Mechanics, ASME, vol.41, no.3, pp.811-812, 1974.

III. J. Ramachandran, “Large amplitiude vibration of shallow spherical shell with concentrated mass,” Journal of Applied Mechanics, ASME, vol.43, no.2, pp. 363-365, 1976.

IV. P. Biswas, “Nonlinear Vibrations of a shallow shell of Variable Thickness,” Transactions of 11th International Conference on structural Mechanics in Reactor Technology (SMIRT-11), Tokyo, Japan, volSD2,05/5, pp.491-494. 1991.

V.U.K. Mandal and P.Biswas, “Nonliner tharmal vibrations on elastic shallow spherical shall under liner and parabolic temperature distributions,” Journal of Applied Mechanics, ASME, vol.66, np.3, pp.814-815.1991.

VI. Ghassan Odeh, “Nonliner dynamics of shallow Spherical caps subjected to peripheral, Netherlands, vol.33,pp.155-164, 2003.

VII. Wang Tono-gang and Dai Shi-liang, “Thermoelastically coupled axisymmetric nonlinear vibration of shallow spherical and conical shells,” Applied Mathematics and Mechanics, vol.24, no.4, pp.430-439, 2004.

VIII. W.A. Nash and J.R. Modeer, “Certain Approximate Analysis of the Nonlinear Behavior of Plates and Shallow Shells,” proceedings of Symposium on the Theory oh Thin Elastic Shells, Delft, The Netherlands, pp.331-353, 1969.

IX. A.P. Bhattacharyee, “Nonlinear Flexural Vibrations of Thin Shallow translational Shell, ” Journal of mechanics, ASME, vol.43, no.1, pp.180-181, 1976.

X. G.C. Sinharay And B.Banerjee, ” A new Approach to Large Deflection Analysis of Spherical and Cylindrical Shells under Thermal load,” Mechanics research Communication, vol.12, no.2, pp.53-64. 1985.

XI. G.C. Sinharay And B.Banerjee, ” Large Amplitude Free Vibrations of shallow spherical shell and Cylindrical Shell- A New Approach,” International Journal of Nonlinear Mechanics, vol.20, no.2, pp. 69-78., 1985.

XII. H.m. Berher, ” A new approachto the analisis of large Deflections of Plates,” Journal of Applied Mechanics, ASME, vol.22, pp.563-572, 1955.

XIII. B. Budiansky, “Buckling of Clamped Shallow spherical shell,” Proceedings of Symposium on the Theory of Thin Elastic Shalls, Delft, The Netherlands, pp.64-94, 1959.

XIV. S.P. Timoshenko and S. Woinowskty-Krieger, ” Theory of Plates and Shells, McGraw Hill, New York, 1959.

XV. U.K. Mandal, ” Nonlinear Vibrations of structures including Thermal Loading, ” Ph.D.Thesis, University of North Bengal, West Bengal India,2006.

OSCILLATORY HYDROMAGNETIC COUETTE FLOW OF A VISCO-ELASTIC RIVLIN-ERICKSEN FLUID

Authors:

Goutam Chakraborty, Supriya Panja

DOI NO:

https://doi.org/10.26782/jmcms.2009.07.00003

Abstract:

In this paper oscillatory Couette Flow of a visco-elastic Rivlin-Ericknes fluid thoruge a porous medium within two non-conducting paralled plates in presence of a transverse unifrom magnatic field in a rotating system has been studied.

Keywords:

hydromagnetic Couette flow, visco-elstic fluid,Rivlin –Ericksen fluid,

Refference:

I. Couette, M. (1890)- Ann.Chin, Phys., 21,433-510.

II. Tikekar, V.G. (1968) – Jour. Ind. Inst. Sci., 50,244.

III. Sengupta, P.R. and Ray, T.K. (1990) – Arch. Mech., 42,6, 717.

IV. Chakraborty, G. and Sengupta, P.R. (1992) – Proc. Int. AMSE Conf. Calcutta(India), 4, 171.

V. Sengupta, P.R. and PANJA, S. (1991)- Proc.Math. Soc. B.H.U.7, 41.

FIRST ORDER REACTANT IN MHD TURBULENCE BEFORE THE FINAL PERIOD OF DECAY IN A ROTATING SYSTEM

Authors:

M.A.K. Azad, M.A.Aziz, M.S.Alam Sarker

DOI NO:

https://doi.org/10.26782/jmcms.2009.07.00004

Abstract:

Following Deissler`s approach, the decay of MHD turbulence at times before the final period for the concentrantion fluotuations of a dilute contaminant undergoing a first order chemical reaction in a rotating system is studied. Here two and three point correlatoins between fluctuating quantitles have been third order correlations. The correlations equations are converted to spectrum over all wave numbers, the solution is obtained and this solution gives the Decay law of magnetic energy for the concentration fluctuations before the final period in a rotating system.

Keywords:

MHD turbulence, ,concentration fluctuations, ,energy spectrum, ,magnetic energy,

Refference:

I. Deissler, R.G.(1958): On the decay of homogeneous turbulence before the final period, Phys.Fluid,1,111-121.

II. Deissler, R.G.(1960): Decay law of homogeneous turbulence for time before the final period., Phys.,Fluid, 3, 176-187.

III. Loefter, A.L and Deisssler, R.G.(1961): Decay of temperature flucations in homogeneous turbluence before the final period, Int. J. Heat mass Transfer, 1,, 312-324.

IV. Kumar, P. and Patel, S.R.(1974): First order reactant in homogeneous turbulence before the final period for the case of multi-point and single time, Physics of fluids, 14, 1362.

V. Kumar, P. and Patel, S.R.(1975): First order reactant in homogeneous turbulence before the final period for the case of multi-point and multi-time, Int.Engng.Sci, 13,305-315.

VI. Patel, S.R.(1976): First order reactant in homogeneous turbulence Numberical results, Int. J.Engng.Sci, 14, 75.

VII. Sarker, M.S.A and Kishor,N(1991): Decay of MHD turbulence brfore thr final prriod, Int.J.Engng,Sci., 29, 1479-485.

VIII. Chandrasekher, S. (1951): Proc,Roy,Soc., London, A204, 435-449.

IX. Sarker,M.S.A and Islam,M.A(2001): Decay of MHD turbulence brfore thr final prriod for the case of multi-point and multi-time, Indian J.Pure appl. Math,32(7), 1065-1076.

X. Islam,M.A and Sarker,M.A.S (2001): First order reactant in MHD brfore thr final prriod of delay for the case of multi-point and multi-time, Indian J.Pure appl. Math,32(8), 1173-1184.

XI. Sarker,M.S.A and Islam, M.A(2001): Decay of dusyt fluid turbulence brfore thr final prriod in a rotating system, J.Math and Math. Sci, 16, 35-48.

XII. Corrsin, S. (1951b): J. Applied physics, 22,469.

XIII. Sarker,M.S.A and AAzad M.A.K. (2004): Decay of MHD turbulence brfore thr final prriod for the case of multi-point and multi-time in a rotating system, Rajshahi University Studies, Part-B vol.32, 177-192.

XIV. Dixit, T. and Upadhyay, B.N (1989a): Astrophysics and Space Sci.153, 257.

XV. Funada, T., Tuitiya, Y. and Ohji, M. (1978): J.Phy.Soc., Japan, 44 1020.

XVI. Kishor, N. and Dixit, T.()1979: J. Sci.Rce., B.H.U., 30(2),305.

XVII. Kishor, N. and Singh, S.R. (1984): Astrophysics and Space Sci., 104, 121.

XVIII. Kishor, N. and Golsefid, Y.T. ()1988: Astrophysics and Space Sci., 105, 89.

XIX. Kishor, N. and Sarker, M.S.A.(1990b): Astrophysics and Space Sci., 172,279.

XX. Sarker, M.S.A (1998): Rajshani Univ. Studies Part-B, in press.

XXI. Sarker, M.S.A. and Islam,M.A. (2001): Ph.D.Thesis, Dept. of Mathematics, R.U., 56-70.

ASYMPTOTIC SOLUTION OF FOURTH ORDER OVER DAMPED SYMMETRICAL NONLINEAR SYSTEMS

Authors:

M.Ali Akbar, Anup Kumar Datta, Md.Eliyas Karim

DOI NO:

https://doi.org/10.26782/jmcms.2009.07.00005

Abstract:

A fourth order nonlinear differention equation modeling an over-damped symmetrical system is considered. A perturbation technique is developed in this artical for obtaining the transient responsewhen the eigenvalues are in integral multiple. The results obtained by the presented technique agree with those results obtained by the numerical method nicely. An example is solved to illustrated method.

Keywords:

over-damped symmetrical system ,transient response,forth order non-linear differential equation,eigen values,

Refference:

I. Ali Akber, M., A.C. Paul and M.A. Sattar, An Asymptotic Method of krylov-Bogoliubov for fourth order over-damped nonlinear system, Geint, J. Bangladesh Math. Soc., vol.22, pp. 83-96, 2002.

II. All Akbar, M.M. Shamsul Alam and M.A. Sattar, Asymptotic Method for Forth order Damped Nonliner System, Ganit, J. Bangladesh Math. Soc., vol.23, pp. 83-96, 2002.

III. Ali Akbar, M.M. Shamsul Alam and M.A. Satter, 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.

IV. Bogoliubov, N.N. and Yu. Mitropolskii, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordan and Breach, New York, 1961.

V. Krylov, N.N. and N.N. Bogoliubov, Introduction to Nonlinear Mechanics, Princeton University Press, New Jersey, 1947.

VI. Mulholland, R.J., Nonlinear Oscillations of Third Order Differential Equation, Int.J. Nonlinear Mechanics, vol.6, pp.279-294, 1971.

VII. Murty, I.S.N., B.L. Deekshatulu and G.Krishna, on an Asymptotic Method of Krylov-Bogoliubov for Over-damped Nonlinear Systems, J.Frank. Inst., vol.288, pp.49-65, 1969.

VIII. 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.

IX. Osiniskii. Z., Vibration of a one degree Freedom system with Nonlinear Internal Friction and Rrlaxation, Proceedings of intermations Symposium of Nonlinear Vibrations, vio.111, pp. , . 314-325 Kiew, Lazst, Akand, Nauk Ukr. SSR, 1963.

X. Popov, I.P., A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russian), Doll. Akad. USSR Vol.3, pp.308-310, 1956.

XI. Sattar, M.A., An asymmetric method for second Order Critically Damped Nonlinear Equations, J.Frank.Inst., vol. 321, pp.109-113, 1986.

XII. Sattar, M.A., An Asymptotic Method for Three-dimensional Over-damped Nonlinear Systems, Habit, J. Bangladesh Math. Soc., Vol.13, pp.1-8, 1993.

XII. Shamsul Alam, M., Asymptotic Methods for second-order Over-damped and Critically Damped Nonlinear Systems, Soochow J. Of Math., Vol.27, pp.187-200, 2001.

XIII. Sattar, M.A., An Asymptotic Method for Three-dimensional Over-damped Nonlinear Systems, Ganit, J. Bangladesh Math. Soc., Vol.13, pp.1-8, 1993.

XIV. 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.

XV.Shamsul Alam,M., Some special conditions of third order Over-damped Nonlinear Systems, Indian J. Pure APPL. Math., Vol. 33, pp.727-742, 2002.

ON SOME FIXED CONVERGENCE THEOREMS FOR MANN ITERATIVE PROCESS

Authors:

M.Zulfiker Ali, M.Asaduzzaman

DOI NO:

https://doi.org/10.26782/jmcms.2009.07.00006

Abstract:

In this paper, we find a more generalized contractive mapping that is applied to prove some convergence theorems of Mann Iteration Procedure. Our proof is comparatively easy. Actually, here we generalized some theorems of Rhoades(3), Qihou(1). Ganguly and Bandyopadhy(8) Kannan(12) to develop the concept on convergence of Mann Iteration Procedure.

Keywords:

Contractive mapping,Convergence theorems,Mann Iteration procedure,

Refference:

I. Qihou, L.: The convergence theorems of the sequence of Ishikawa iterates for quasi convergence mapping, J.Math.Anal.Appl. 146(1990), 301-305.

II. Kalishankar Tiwary and S.C. Debnath: On Ishikawa Iterations, Indian J.Pure and Appl.Math., 26(8) (1995). 743-750.

III. B.E. Rhoades: Some fixed point Iterations , Soochow J.Math. 19(1993), 377-80.

IV. B.E. Rhoades: A General Principle for Mann Iterations, Indian J. Pure and APPL.Math, 26(8)(1995), 751-762.

V. B.E. Rhoades: A comparison of contractive definitions, Trams. Amer.Math. Soc.b(1977), 257-290.

VI.B.E. Rhoades: Some fixed point Iteration procedures, Internet, J.Math.& Math. Sci. vol.14, no.1,(1991), 1-16.

VII. M.K. Chakraborty and B.K.Lahiri: Indian J.Math. 18(1976),81-89.

VIII. D.K.Ganguly and D. Bandyepadhyay: Soochow J.Math. 17(1991), 269-285.

IX. Ishikawa, S.: Fixed point by new Iteration method, Proc. Amer. Meth. Soc.44(1974), 147-150.

X.Ishikawa, S.: Fixed point and Iteration of a non-expansive mapping in a Banach space, Prof.Amar.Math.Soc.59(1976), 65-71.

XI. W.R. Mann: value methods in Iterations, Proc. Amer. Math. Soc. 4(1953), 506-510.

XII. R. Kannan: Construction of fixed points of class of Nonlinear mapping, J. Math. Anal. APPL. 41(1973), 430-438.

XIII. M.M.Vainberg: Variational Method of Monotone Operators in the Theory of Nonlinear Equations, John Wiley & Sons (1973).

XIV. V. Berinde: On the convergence of the Ishikawa Iteration in the class of quasi-contractive operators, Acta. Math. Univ. Comeniance, vol. LXXIII,1 (2004), 119-126.

XV. Arif Rafiq: A convergence theorems for Mann fixed point Iteration procedure, Applied Mathematics E-Notes, 6(2006), 289-293.

XVI. Krishna Kumar: The equivalence of Mann and Ishikawa Iteration for the class of uniformly pseudo-contraction, Thai. J. Math. Vol. 2(2004), no.2, 217-225.

XVII. D.R.Smart: Fixed point theorems, Cambridge University Press (1974).

ROTATORY VIBRATION OF AN ANISOTROPIC IN-HOMOGENEOUS ANNULAR DISK

Authors:

A.De, S.Banik

DOI NO:

https://doi.org/10.26782/jmcms.2009.07.00007

Abstract:

The aim of the present paper is to investigate rotatory vibration of an isotropic inhomogeneous elastic disk when the elastic constants and also the density of the material varies exponentially as the n-th power of the distance from the center and thinks such problem was not attempted before by any previous investigator and the corresponding results are shown graphically.

Keywords:

Rotator vibration,Isotropic,Inhomogeneous ,Elastic disk,

Refference:

I. Bhowmick, Monoj Roy & Sengupta, P.R.(1986): The effect of non-homogeneous on rotatory vibration of spherical shell., Indian Journal of Theoretical physics, vol.35, no.4, 1987.

II. Biswas, p.(1983): Nonlinear free vibrations of heated elastic plates. Indian Journal of Pure and Applied Mathematics., 14(10), 1199-1203, October, 1983.

III. Biswas, p.(1983): Nonlinear vibration of a non-isotropic Trapezoidal plate., Indian Journal of Pure and Applied Mathematics,14(2), 265-269, Feb. 1983.

IV. Biswas,p. & Kapoor, (1984): Nonlinear free vibrations of orthotropic circular plates at elevated temperature. Journal of Indian Institute of Science., 65(B), pp-(87-93), 1984.

V. Chakraborty, A. & Bera, R.K. (2002): Nonlinear vibration and stability of a shallow unsymmetrical orthotropic sandwich shell of double curvature with orthotropic core , Math.Appl., vol.43, pp. (1617-1630), 2002.

VI. Chakraborty,A. & Bera, R.K. (2006): Large amplitude vibration of thin homogeneous heated orthotropic sandwich elliptic plates. Journal of Thermal stress, vol.29, pp.(21-36), 2006.

VII. Chakraborty, J.G & Choudhuri, P.K. (1983): The Elastic plastic problem of a thin rotating disk with vibration thickness- Indian Journal of Pure & Applied Mathematics, 14(1), pp-(70-78), Jan 1983.

VIII. Chatterjee, D.(1968): Problem of rotatory vibration of an anisotropic elastic disk. Indian Journal of Mechanics & Mathematics; vol.6 no.1.

IX. Choudhuri P.K. & Dutta, S. (1989): Note on the small vibration of beams with varying Young’s modulus carrying a concentrated mass distribution.’ Indian Journal of Pure & Applied Mathematics, 20(1), 75-88, Jan-1989.

X. De, P.K. (1968): ‘Rotatory vibration of a sphere of variable modulus of elasticity.’ Bulletin of Calcutta Mathematics Society, vol. 60, no.4, p-(185-189).

XI. Kundu, J.C. & Basuli, S(1977): ‘Note on the vibration of circular plates of variable thickness.’ Indian Journal of Theoretical physics; vol.25, no.1, 1977.

XII. Mollah, S.A.(1977): Note on the vibration of circular plates of variable thickness.’ Indian Journal of Theoretical physics; Calcutta; vol.25, no.1, 1977.

XIII.Mollah, S.A.(1978): ” Vibration of rectangular plates of variable thickness under the combined action of uniform lateral loads and uniform tension’ Bulletin of Calcutta Mathematics Society; vol.70. no.4

XIV. Sinharoy, G.C. & Bera, R.K.(1993): Large amplitude vibration of thin homogeneous orthotropic elastic plates under uniform heating revisited.’ International Journal of Engineering Science, vol-31, no.6, pp.883-892.1993.

POINT WISE QUASICONTINUTTY AND BAIRE SPACES

Authors:

Sucharita Chakrabarti, Saibal Ranjan Ghosh , Hiranmany Dasgupta

DOI NO:

https://doi.org/10.26782/jmcms.2010.01.00001

Abstract:

In this paper, it is proved that the notions of point wise semi-continuity and quasicontinuity are the same even when the mapping is not globally semi-continuity. The concept of removable quasicontinuity at a point is introdeced with some of its applications [Theorem 4.1]. Finally, a set of sufficient conditions for a topological space to be a Baire space is formulated. In particular, it was shown that if every mappimg from a topological space X to an infinite T2 space is quasicontinuity then X is a Baire space.

Keywords:

baire space,topological space,quasicontinuity,

Refference:

I. Biswas, N. Atti Accad. Naz. Lincei. Sci.Fis. Mat. Natur. Series 8. Vol 48(1970), 399

II. Crossely, S.G. and Hildebra, S.K. Texas J. Sci.22(1971), 99-112.

III. Das, P. Prgr. M.M., Vol.2, No.1(1973),33-34.

IV.Das , P.I.J.M.M., Vol.2,No.1(1974),31-44

V. Dasgupta, H. and Lahiri, B.K. Acta Ciencia Indica. Vol.XII m No.1(1986),35-39.

VII. Ghose, S.R. and dasgupta, H.Bull.Cal.Math.Soc.97(2005),(4),283-296.

VIII. Halfer, E.Proc. Amer. Math.Soc. 11(1960), 688-691.

IX. Husain, T.Prace, Mathematyczne.10(1966),1-7.

X. Kuratowski, K. Topology, Academic Press. Vol1,1966.

XI. Levine, N. Amer.Math.Monthly.70(1963),36-41.

XII. Lin, S-Y.T. and Lin, Y-F.T. Canad. Bull.21 (1978), 183-186.

XIII. Long, P.E. Amer.Math.Monthly.76(1969, 930-932.

XIV. Long, P.E. Charles, E.Merril Publ. Co., Columbus, Ohio, 1971.

XV. Neubrunn, T.Math. Slovaca 26(1976),97-99

XVI. Neubrunnova, A.Mat. Cas. 23(1973)374-380

XVII. Tong, Jing Cheng Internet. J.Math. and Math.Sci. Vol.7(1983) No.1, 197-199.

XVIII. Tong,Jing Cheng Internet. J.Math. And Math. Sci. Vol.7(1984) No.3, 619-620

XIX. Wilansky, A. Topology for analysis, Ginn, Walthham, Mass, 1970.

MULTIPLE TIME SCALE METHOD FOR OVER-DAMPED PROCESSES IN BIOLOGICAL SYSTEM

Authors:

Md. Abdul Kalam Azad, M. Ali Akbar , M. Abdus Sattar

DOI NO:

https://doi.org/10.26782/jmcms.2010.01.00002

Abstract:

An over-damped solution of a nonlinear system has been investigated by multiple time scale method when one of the roots of the roots of the unperturbed equation is much smaller then the outhers. The anymptotic solunion shows excellent agreement with the numerical solution. An example is givin to biological system.

Keywords:

multiple time scale,over-damped process biological system,

Refference:

I. Bogoliubov, N.N. and Yu. Mitropolskii, “Asymptotic Methods in the theory of nonlinear osillation,” Gordan and Breach, New York, 1961.

II. Bojadziev, G.N., “Damped nonlinear oscillations modeled by a 3-dimensional system”, Acta Mechanica, Vol.48, pp.193-201, 1983.

III.FitzHugh, R., Impulse and physiological states in theoretical models of nerve membrane”, J. Biophys., Vol.1 pp.445-466,1961.

IV.Goh. B.S., Global stability in many species systems, The American Naturalist, Vol.111, pp.135-143, 1977.

V. Hsu, I.D., and Kazarinoff, “An applicable Hopf bifurcation formula and instabity of small periodic solution of the field-noice modle” , J.Math. Anal.Applic., Vol.55, pp.61-89, 1976.

VI. Kalam A.A., M.Samsuzzoha, M.Ali Akbar and M.Alhaj, “KBM asymptotic method for over-damped processes in biological and biochemical system.” GANIT, Bangladesh Math.Soc., Vol.26, pp.1-10,2006.

VII. Krylov, N.N. and N.N. Bogoliubov, “Introduction to nonlinear mechanics”. Princeton University Press New Jersey, 1947.

VIII. Lefwver, R.and G. Nicolis, “Chemical instabilities and sustained oscillations”.J.Theor.Biol., Vol.30, pp.267-248, 1971.

IX. Lotka, A.J., “The growth of mixed popluation”, J. Wash. Acad. Sci. Vol.22, pp.461-469, 1932.

X. Murty, L.S.N. and B.L. Deekshatulu, “Method of variation of paeameters for over-damped nonlinear systems”, J.Control . Vol.9(3), pp.259-266, 1969.

XI. Murty, I.S.N., B.L.Deekshatulu and G. Krishna, “On asymptotic method of krylov-Bogoliubov for over-damped nonlinear systems”, J.Frak. Inst. Vol.288,pp.49-65, 1969.

XII. Popov, I.P. “A generalization of the Bogoliubov asymptiotic method in the theory of nonlinear oscillation(In Russian).”, Dokl. Akad. Nauk. SSSR. Vol.3,pp.308-310, 1956.

XIII. Sattar. M.A., “An asymptotic method for second order critically damped nonlinear equation”. J.Frank.Inst. Vol.321,pp.109-113, 1986.

XIV. Shamsul Alam M., “An asymptotic method for second order over-damped and critically damped nonlinear systems”. Soochow Journal of Math. Vol.27(2), pp. 187-200, 2001.

XV.Shamsul Alam, M., “A unified Krylov-Bogoliubov-Mitropolskii method for solving n-order systems”, J.Franklin Inst., Vol.339, pp.239-248, 2002.

XVI. Shamsul Alam M., “On some special conditions of over-damped nonlinear systems”, Soochow Journal of Math. Vol.29(2),pp.181-190, 2003.

XVII.Shamsul Alam, M., M. Abul Kalam Azad and M.A. Hoque “A general Struble’s technique for solving an n-th order weakly nonlinear differential system with damping”, Int. J. Nonlinear Mech., Vol.41,pp.905-918, 2006.

XVIII. Troy, W.C., “Oscillating Phenomena in nerve condition equation”, Ph.D.Dissertation, SUNY at Buffelo, 1974.

XIX. Volterra, V., “Variazioni e fluttuazioni del numero d’individue in species animali conviventi”, Memorie del R. Comitato Talassografico Italiano, Vol.131, pp.1-142, 1927.

A PROBLEM OF COUPLED THERMO-ELASTICITY IN A SEMI-INFINITE ELASTIC NON-SIMPLE MEDIUM

Authors:

Nlrmalya kr. Bhattacharyya.

DOI NO:

https://doi.org/10.26782/jmcms.2010.01.00003

Abstract:

The object of present praper is to investigate one- dimensional dynamical problem of coupled thermo- elasticity in a semi infinite elastic non - simple medium when its surface is under suddenly applied constant pressure. The solution of the problem has been deduced using Laplace transfrom in Bromwich integral from. The author determined the value of the surface displacements in non - simple medium for small values of time t numerically and presented graphically.

Keywords:

thermo-elasticity,non-simple medium,surface displacements,

Refference:

I. Chen. P.J., & Gurtin, M.E. (1968): ZAMP, Vol. 19, pp.614.

II. Chen, P.J., Gurtin, M.E. & Williams, W.O. (1969): ZAMP, Vol.20,PP.107.

III. Nowacki, W. (1962) : “Thermoelasticity” Addison Wesley Publising Co.pp.5,8,11,40,133,159, N.Y..

IV. Iesan, D. (1970): ZAMP, Vol.21,pp.583.

V. Chakraborty, S.(1972) : Bulletin of calcutta Mathematical Society, Vol.64, pp.129.

VI. Erdelyi, A. (1954) : Tales of Integral Transforms, McGraw Hill Book col. Inc Vol.1, New York.

VII. Das, N.C., Lahiri, A., & Bhakta , P.C. , Bull. Cal. Math. Soc., 90, pp-235-250 (1998)

VIII. Kar, T.K., Lahiri, A., J.Math., NBU., Vol-1, No.-2, (2008), pp-165-172.

THE EFFECT OF GRAVITY ON THE PROPAGATION OF WAVES IN AN ELASTIC LAYER IMMERSED IN AN INFINITE LIQUID

Authors:

Prabir Chandra Bhattacharyya

DOI NO:

https://doi.org/10.26782/jmcms.2010.01.00004

Abstract:

The object of the present paper is to investigate the propagation of waves in an elastic layer immersed in an infinite liquid and under the influence of gravity. The corresponding velocity equation has been derived. In the limiting case the wave velocity equation so obtained is in good agreement with the corresponding classical problem when gravitational effects are vanishing small.

Keywords:

elastic layer, propagation of waves,effect of gravity,

Refference:

I. Voigt, W (1887) : Theorestische Studien iiber die elasticitats varhattnisse der krystalle- I,II. Abh.Konigh Ges derwise. Gottingen 34.

II. Biot, M.A. (1965) : Mechanics of incmental deformation. Willy, New York, pp 44-45, 273-81.

III. Bromwich, T.J.I.A (1898) : Proc.London.Math.Soc.30, 98-120.

IV. Love, A.E.H (1952) : The Mathematical Theory of Elasticity, Dover, pp-164.

V. De, S.N. and Sengupta, P.R. (1974) : J. Acoust.Soc.Amer., Vol.55. No.5 pp.919-21.

VI. De, S.N. and Sengupta, P.R (1975) : Gerlands. Beitr Geophysik, Lepizing 84, 6. s 509-514.

VII. Bhattacharyya, P.C. and Sengupta, P.R. (1984) : Influence of gravity on propagation of waves in a composite elastic layer, Ranchi, Uni. Math. Jour. Vol-15(1984).

VIII. Acharya, D.P., Roy I and Chakraborty, H.S. (2008) : On interface Waves in second order thermo- visco elastic solid media under the influence of gravity, J.Math. Sci., Vol-3 No.3 (2008). pp 286-298.

DECAY OF FIRST ORDER REACTANT IN INCOMPRESSIBLE MHD TURBULENT FLOW BEFORE THE FINAL PERIOD FOR THE CASE OF MULTI-POINT AND MULTI-TIME IN A ROTATING SYSTEM

Authors:

M.L.Rahman

DOI NO:

https://doi.org/10.26782/jmcms.2010.01.00005

Abstract:

Following Deissler's approach the decay for the concentration fluctuation of a dilute contaminant undergoing a first order chemical reaction in MHD turbluent flow at times before the final period in a rotating system for the case of multi-point and multi-time correlation equations is studied. Two-point, two-time and three-point, correlation eqyations have been obtained and to make the set of equations determinate, the trams containing quadruple correlations in compraison with second and third order correlation terms. The solution obtained gives the decay law for the concentration fluctuations before the final period in a rotating system.

Keywords:

MHD turbulent flow, rotating system,concentration fluctuation,

Refference:

I. S.Chandrasekher, Proc. R.Soc. London A204(1951) 435.

II. S.Corrsin J.Appl.Phys. 22(1951) 469.

III. R.G. Deissler, Phys. Fluid 1 (1958) 111.

IV.R.G. Deissler, Phys. Fluid 3(1960) 176.

V. P.Kumar and S.R. Patel, Phys, Fluid 17 (1971) 1364.

VI. P.Kumar and S.R. Patel, Int J. Eng.Soc. 13(1975) 305.

VII. A.L. Loeffler and R.G. Deissler, Int J.Heat Mass transfer 1(1961) 312.

VIII. S.R. Patel, Int J.Eng. Sci. 12(1975)159.

IX. S.A. Sarker and N. Kishore, Int J.Eng. Sci. 29 (1991)1479.

X. S.A. Sarker and M.A. Islam, Indian J.Pure and Appl. Math. 8(2001)32.

STEADY FLOW OF MICROPOLAR FLUID UNDER UNIFORM SUCTION

Authors:

Goutam Chakraborty, Supriya Panja

DOI NO:

https://doi.org/10.26782/jmcms.2010.01.00006

Abstract:

This paper is concerned with the steady flow of a micropolar fluid an infinite flat plate subjected to unifrom suction.

Keywords:

micro polarfluid,steady flow, flate plate,uniform suction,

Refference:

I. Eringen, A.C. (1964)- Simple Microfluids; Int. Jour. Engng. Sci. 2, 205.

II. Hoyl, J.W. and Fabula, A.C. (1964)- The effect of additives on fluid.

III. Willson, A.J. (1969)- Basic flowes of a micropolar liquid; Appl. Sci. Res., 20,338.

IV. Willson, A.J. (1968)- The flow of a micropolar liquid layer down an inclined plane; Proc. Camb. Phil. Soc., 64,513.

V. Willson, A.J. (1970)- Boundary layer in micropolar liquid ; Proc. Camb. Phil. Soc.., 67,469.

VI. Sengupta, P.R. and Ghosh, P.C. (1982)- Asymptotic suction problem in the unsteady flow of micropolar liquid; Journal of Technology, XXVII, 1,21.

VII. Gupta, P.S. and Gupta, A.S (1972)- Steady flow of Micropolar Liquids; Acta Meachanica, 15,141.

MHD Free Convection Flow Of Fluid From A Vertical Flat Plate

Authors:

S.F. Ahmmed, M.S. Alam sarkar

DOI NO:

https://doi.org/10.26782/jmcms.2010.01.00007

Abstract:

A two dimensional natural convection flow of a viscous incompressible and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a unifrom transverse magnetic field. The governing equations are reduced to non-similar boundary layer equations by introducing coordinate transformations appropriate to the cases (i) near the leading edge (ii) in the region for away from the leading edge and (iii) for the entire regime from leading edge to down stream. the governing equations for the flow in the up stream regime are investigated by perturbation method for smaller values of the stream wise distributed magnetic field parameter. The equations governing the flow for large and for all have been investigated by employing the implicit finite difference method with Killer box scheme. The effect of prandit number pr and the magnetic filed parameter on the skin fricition as well as on the rate of heat transfer for the fluid of low prandtl number will be shown in tabular from. The effect of Pr and different level of velocity, in the boundary layer region, will also be shown graphically.

Keywords:

viscous incompressible fluid, convection flows,skin friction,heat transfer,

Refference:

I. Sparrow, E.M. and Gregg, J.L.: Buoyancy effects in forced convection flow and heat Transfer. ASME J. Appl. Mech., Vol.83, 133-134 (1959).

II. Merkin, J.H.: The effect of buoyancy forces on the boundary layer flow over semi-infinite vertical flat plate in a unifrom free stream, J. Fluid Mech., vol.35, pp.439-450 (1969).

III. Lioyd, J.R. and Sparrow, E.M, : Combined forced and free convection flow on a vartical surface. Int. J. Heat Transfer. vol.13, pp.434-438(1970).

IV. Wilks, G. and Hunt, R.: Continuous transformation computation of boundary layer equations between similarity regimes. J. Comp. Phys., vol.40, (1981).

V. Raju, M.S., Liu, X.R. and Law, C.K.: A formulation of combined forced and free convection past a horizontal and vertical surface . Int. J. Heat mass Transfer, vol.27 pp.2215-2224 (1984).

VI. Tingwei, G., Bachrun, P. and Daguent, M. (1982): Influence de la converction natural le convection force and dessus d’ume surface plane vertical vomise a un flux de rayonnement. Int. J. Heat Mass Transfer, vol.25 pp.1061-1065 (1982).

VII. Sparrow, E.M. and Cess, R.D.: Effect of magnetic filed on free convection heat transfer. Int. J. Heat Transfer, vol.3. pp.267-274 (1961).

VIII. Riley, N.: Magnetohydrodynamic free convection. J. Fluid Mech., vol.18, pp. 267-277(1964).

IX. Kuiken, H.K.: Magnetohydrodynamic free convection in a strong cross-field. J. Fluid Mech., vol.40,pp.21-38 (1970).

X. Sing, K.R. and Cowling, T.G.: Thermal convectiv in Magnetohydrodynamic boundary layer. J. Mech. Appl. Math. vol.16, pp.1-5 (1963).

XI. Crammer, E.M. and Pai, S.I.: Megnetofluid Dynamics for Engineering and applied Physicists. McGrow-Hill, New York, (1974).

XII. Wilks, G.: Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross-field. J. Appl. Phys., vol.27, pp.621-631, (1976).

XIII. Wilks, G. and Hunt, R: Magnetohydrodynamic free convection about a semi-infinite vertical plate at whose surface the heat flux is unifrom. J. Appl. Math. Phys. (ZAMP), vol.34, January, (1984).

XIV. Hossain, M.A. and Ahmed, M.: MHD forced and free convection boundary layer flow near the leading edge. Int. J. Heat Mass transfer, vol.33. pp.571-575 (1984).

XV. Hossain, M.A., Pop I. and Ahmed, M.: MHD Free Convection Flow From an isothermal plate inclined a small angle to the horizontal. J. Theo. Appl. Fluid Mech., Vol.1, pp.194-207, (1996).

XIV. Cebeci, T. and Bradshaw, P.: Physical and computational aspects of convective heat transfer. Springer, New York, (1984).