DYNAMIC BUCKLING OF A VISCOUSLY DAMPED CYLINDRICAL SHELL SUBJECTED TO A SLOWLY VARYING EXPLICITLY TIME DEPENDENT LOAD
Keywords:
Regular perturbation, dynamic buckling, cylindrical shell, slowly varying explicitly time dependent loadAbstract
This investigation is concerned with the dynamic buckling of an imperfect but viscously damped finite circular cylindrical shell stressed by an explicitly time dependent load that is slowly varying over the duration of loading. The formulation contains two small but independent parameters upon which regular perturbation procedure is initiated in asymptotic expansions. Homogeneous initial conditions and simple-supported boundary conditions are assumed. The explicitly time dependent loading is assumed infinitely differentiable and in particular, has right hand derivatives of all orders at the initial time. Besides, the loading history is dynamically slowly varying with a nontrivial value at the initial time. The result shows, among other things, that the dynamic buckling load depends on the first derivative of the load function evaluated at the initial time. All results which are asymptotically valid as the small parameters tend to zero, are also seen to be valid for different specializations and variants of the explicitly time dependent but slowly dynamic loading history
References
Lockhart, D. and Amazigo, J.C. (1975); Dynamic buckling of externally pressurized imperfect cylindrical shells, J. of Applied Mech. 42(2), 316-320.
Kriegesman, R., Mohle, M. and Rolfes, R. (2015); Sample size dependent probabilistic design of axially compressed cylindrical shell, Thin-Walled Structures, 96, 256-268.
Ganapathi, M., Gupta, S.S. and Patel, B.P. (2003); Nonlinear axisymmetric dynamic buckling of laminated angle-ply composite spherical caps, Comp. Structt., 59, 89-97.
Wang, A. and Tian, W. (2003); Twin-characteristic parametric solution of cylindrical shells under axial compression waves, Int. J. Solids Struct. 40, 3157-3175.
Aksogan, O. and Sofiyer, A.V. (2002); Dynamic buckling of cylindrical shells with variable thickness subjected to a time dependent external pressure varying as a power function of time, J. of Sound and Vibration. 254, 693-702.
Karogiozova, D. and Jones, N. (2000); Dynamic elasto-plastic buckling of circular cylindrical shells under axial impact, Int. J. of Solids and Struct. 37, 2005-2034.
Ette, A.M. (2004); on a two-parameter dynamic buckling of a lightly damped spherical shell cap trapped by a step load, J. Nigerian Math. Soc. 23, 7-26.
Kuzmak, G.E. (1959); Asymptotic solution of nonlinear second order differential equations with variable coefficients, Pure Math. Manuscript, 23, 515-526.
Kevorkian, J. (1987); Perturbation techniques for oscillatory systems with slowly varying coefficients, SIAM Rev. 29, 391-461.
Luke, J.C. (1966); A perturbation method for nonlinear dispersive wave problems, Proc. Roy. Soc. London, Ser A 292, 403-412.
Kevorkian, J. and Li, Y.P. (1988); Explicit approximation for strictly nonlinear oscillations with application to free-electron laser, Studies in Applied Math. 78(2), 111-165.
Kroll, N.M., Mortons, P.L. and Rosenbluth, M.N. (1981); Free-electron lasers with variable parameter wigglers, IEEE J. Quantum Electron, 17, 1436-1468.
Volmir, S.A. (1972); Nonlinear dynamics of plates and shells (in Russian) Science, Moscow.
Budiansky, B. and Roth, R.S. (1962); Axisymmetric dynamic buckling of clamped shallow spherical shells.collected papers on instability of shells structure, NASA TND
Budiansky, B. and Hutchinson, J.W. (1966); Dynamic buckling of imperfection sensitive structures, Proceedings of X1th Int. congr. Of Appl. Mech. Springer-Verlag, Berlin.
Amazigo, J.C. (1974); asymptotic analysis of the buckling of externally pressurized cylinders with random imperfections, Quart. Of Appl. Math. 32, 429-442.
Ozoigbo, G. E. and Ette, A. M. (2019), on the maximum displacement and static buckling of circular cylindrical shell,” Journal of Applied Mathematics and Physics, 7, 2868 – 2882.
Ette, A. M., Ozoigbo, G. E., Chukwuchekwa, J. U, W. I. Osuji, W. I and Udo – Akpanc, I. U. (2022). On the Dynamic Buckling of a Pre – Statically Loaded Cubic
Elastic Model Structure Struck by a Slowly Varying Explicitly Time Dependent Load, Mechanics of Solids, Vol.57, No. 2, 412 – 426
Ozoigbo, G. E., Ette, A. M., Chukwuchekwa, J. U., W. I. Osuji, W. I and Udo – Akpan, I. U. (2023). Nonlinear Analytical Investigation of Dynamic Buckling of a Spherical Shell Trapped under a Periodic Load, Mechanics of Solids.
Ozoigbo, G. E. and Ette, A. M., (2020), Perturbation approach to dynamic buckling of a statically pre – loaded, but viscously damped elastic structure,” Journal of Applied Mechanics and Technical Physics, 61, No. 6, 1001 – 1015
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