DYNAMIC BEHAVIOR OF A THIN ELASTIC ROD UNDER THE LONGTERM LONGITUDINAL COMPRESSION

Abstract eng:
A 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.

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