УСТОЙЧИВОСТЬ СТЕРЖНЯ ПРИ ДЛИТЕЛЬНОМ ОСЕВОМ СЖАТИИ

Abstract

The analysis of the classical problem of the lateral stability of a rod under action of the long-term axial compression is carried out. The transverse motion of rod significantly depends on the way of the load application. L. Eyler solved two static maximum tasks: in the linear approximation the critical load and the possible forms of stability loss are found, and at the nonlinear approach all possible equilibrium forms are found (Euler's elastics). In the work by M.A. Lavrent'ev and A.Yu. Ishlinsky, taking into account the transverse inertial forces, it is examined the case of load, sufficiently exceeding the Euler one. It is established that the one of the forms with the large number of waves has the maximum rate of growth. In this paper basing by the nonlinear dynamic model it is shown that at the initial moments of loading the form predicted by M.A. Lavrent'ev and A.Yu. Ishlinsky appears, and then it passes into the steady Euler's elastic. In this case the final form depends on the method of the rod ends support. Keywords: rod, dynamic stability, longitudinal waves, lateral vibrations, parametric resonance, beating, Euler's elastics.