Authors:Utpal Kumar Mandal,
Keywords:non linear vibration,spherical elastic shell,Berger approximation,Galerkin error ,
AbstractLarge 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.
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.
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