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This investigation is concerned with analytically determining the dynamic buckling load of an imperfect cubic-quintic nonlinear elastic model structure struck by an explicitly time-dependent but slowly varying load that is continuously decreasing in magnitude. A multi-timing regular perturbation technique in asymptotic procedures is utilized to analyze the problem. The result shows that the dynamic buckling load depends, among other things, on the first derivative of the load function evaluated at the initial time. In the long run, the dynamic buckling load is related to its static equivalent, and that relationship is independent of the imperfection parameter. Thus, once any of the two buckling loads is known, then the other can easily be evaluated using this relationship.
Budiansky B, Hutchinson JW. Dynamic buckling of imperfection – Sensitive structures, Proceedings of XI International Congr. Applied Mechanics, Springer – Verlag, Berlin; 1966.
Hutchinson JW, Budiansky B. Dynamic buckling estimates. AIAA J. 1966;4:525-530.
Koiter WT. On the stability of elastic equilibrium (in Dutch), Thesis, Delf, Amsterdam. English translation issued as NASA TTF. 1945;10:1967-833.
Koiter WT. Elastic stability and post-buckling behavior, in nonlinear problems. ed. B.E. Langer, University of Wisconsin Press, Maduson; 1963.
Sadovsky Z, Teixeira AP, Guedes Soares C. Degradation of the compressive strength of rectangular plates due to initial deflection, Thin-Walled Structures. 2005;43:65-82.
Bisagni C. Dynamic buckling of fibre composite shells under impulsive axial compression. Thin-Walled Structures. 2005;43:499-514.
Kevorkian J. Perturbation techniques for oscillatory systems with slowly varying coefficients. SIAM Rev. 1987;29:391-461.
Kuzmak GE. Asymptotic solutions of nonlinear second order differential equations with variable coefficients. Pure Math Manuscript. 1959;23:515-526.
Luke, J.C.; A perturbation method for nonlinear dispersive wave problems, Proc. Roy. Soc. London Ser. A, (1966) 292, 403-412.
Kroll NM, Morton PL, Rosenbluth MN. Free-electron lasers with variable parameter wigglers. IEEE J., Quantum Electron. 1981;17:1436-1468.
Li YP, Kevorkian J. The effects of wiggler taper rate and signal field gain rate in free-electron lasers. IEEE J. Quantum Electron. 1971;24.
Askogan O, Sofiyev AV. Dynamic buckling of spherical shells with variable thickness subjected to a time-dependent external pressure varying as a power function of time. J. of Sound and Vibration. 2002;4:693-703.
Kubiak T. Dynamic buckling of thin-walled composite plates with varying width wise material properties. Int. J. of Solids and Struct. 2005;45:5555-5567.
Wooseok J, Waas AM. Dynamic bifurcation buckling of an impacted column. Int. J. of Eng. Science. 2008;46:958-967.
Kolakowski Z. Static and dynamic interactive buckling regarding axial extension mode of thin-walled channels. J. of Theoretical and Applied Mechanics. 2010;48:703-714.
Kowal-Michalska K. About some important parameters in dynamic buckling analysis of plates structures subjected to pulse loading. Mechanics and Mechanical Eng. 2010;14(2):269-279.
Bisagni C, Vescovini R. Analytical formulation for local buckling and post-buckling analysis of stiffened laminated panels. Thin-Walled Structures. 2009;47:318-334.
Patel SN, Datta PK, Sheikh AH. Buckling and dynamic instability analysis of stiffened shell panels. Thin-Walled Structures. 2006;44:321-333.
Reda AM, Forbes GL. Investigation into the dynamic effects of lateral buckling of high temperature/ high pressure offshore pipelines, Proc. of Acoustics. Paper No. 83 Fremantte; 2012.
Ette AM, Chukwuchekwa JU, Osuji WI, Udo-Akpan IU, Ozoigbo GE. Asymptotic investigation of the buckling of a cubic–quintic nonlinear elastic model structure stressed by static load and a dynamic step load. IOSR Journal of Mathematics (IOSR-JM). 2018;14(1):16-30.
Ette AM, Chukwuchekwa JU, Udo–Akpan IU, Osuji WI. Asymptotic analysis of the static and dynamic buckling of a column with cubic - quintic nonlinearity stressed by a step load. Journal of Advances in Mathematics and Computer Science. 2019;30(6):1-35.
Carrier GF, Krook M, Pearson CE. Functions of a single variables: Theory and technique, McGraw-Hill, New York; 1960.
Amazigo JC. Buckling of stochastically imperfect columns on nonlinear elastic foundations, Quart. Appl. Math. 1971;29:403-409.
Amazigo JC. Asymptotic analysis of the buckling of externally pressurized cylinders with random imperfections. Quart. Appl. Math. 1974;32:429-442.