000022283 001__ 22283
000022283 005__ 20170622150005.0
000022283 04107 $$aeng
000022283 046__ $$k2015-05-25
000022283 100__ $$aMorozov, Nikita
000022283 24500 $$aDYNAMIC BEHAVIOR OF A THIN ELASTIC ROD UNDER THE LONGTERM LONGITUDINAL COMPRESSION

000022283 24630 $$n5.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000022283 260__ $$bNational Technical University of Athens, 2015
000022283 506__ $$arestricted
000022283 520__ $$2eng$$aA problem of thin rod longitudinal compression is a classical problem with the long history, but some new results were obtained recently. The bifurcation problem of the rod equilibrium under static compression was solved by L. Euler (1744). Also he found the possible nonlinear modes (the so-called Euler elastics) which rod takes under forces and moments applied to its ends. It has been found out by M.A. Lavrentiev and A.Yu. Ishlinsky (1949) that under the jump loading exceeding the Euler static critical load, the amplitudes of buckling modes with the large number of waves the maximal increase highly under of lateral buckling load. In the recent works of the authors the problem is solved in an assumption on the finite speed of longitudinal wave distribution in the rod. The parametric resonances are studied in the linear and nonlinear statements. It is found that due to these resonances the buckling under the load that is less than the Euler critical load may occur. This problem is examined also in the nonlinear statement. In this case vibrations have the form of beatings with the energy exchange between longitudinal and transversal vibrations whereas in the linear approach instead the amplitude grows unboundedly. We study also the long-term suddenly applied impact load, which exceeds the Euler critical load, and analyze the rod behavior in the initial moments of time while the compression wave does not return after reflection from the opposite rod end.

000022283 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000022283 653__ $$athin rod, longitudinal compression, dynamic stability, Euler elastica

000022283 7112_ $$aCOMPDYN 2015 - 5th International Thematic Conference$$cCrete (GR)$$d2015-05-25 / 2015-05-27$$gCOMPDYN2015
000022283 720__ $$aMorozov, Nikita$$iTovstik, Tatiana P.$$iTovstik, Petr$$iBelyaev, Alexandr
000022283 8560_ $$ffischerc@itam.cas.cz
000022283 8564_ $$s794736$$uhttps://invenio.itam.cas.cz/record/22283/files/C2849.pdf$$yOriginal version of the author's contribution as presented on CD, section: 
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000022283 962__ $$r22030
000022283 980__ $$aPAPER