An elastically supported geometrically nonlinear slender system subjected to a specific load in respect of bifurcational load and free vibrations

摘要

The formulation of and solution to the problem of stability and free vibrations of a geometrically nonlinear column, supported at the loaded end by a spring with linear characteristics, are discussed in the paper. The considered system was subjected to a follower force directed towards the positive pole (load formulated by L. Tomski). The boundary problem was formulated using Hamilton's principle and the straightforward expansion method. A series of numerical simulations were based on the mathematical model. The distribution of internal forces in the column's elements and the bifurcation load dependent on the system's parameters were determined for the tangent problem. In the case of free vibrations, the characteristic curve in the plane, load natural frequency, was assigned to different parameters of the considered system. Experimental research was carried out to confirm the accuracy of the assumed mathematical model. The above research relied on modal analysis and the determination of the natural frequency of the system for the chosen values of an external load.