Quasi-optimization of the slender geometrically nonlinear supporting system with non-prismatic element under the specific load

Abstract

This paper is devoted to the issue of free vibrations of a geometrically nonlinear column with a nonprismatic element modelling the supporting structure subjected to the specific load. The boundary problem was formulated on the basis of the Hamilton’s principle and its solution was obtained using the Lindstedt - Poincare’s small parameter method (a perturbation method). Within the range of the kinetic criterion of the static equilibrium, an influence of the shape of a rod of variable crosssection on the values of free vibrations and the bifurcation load of the system was determined. Presented quasi-optimization issue has been reduced to defining the ranges of physical and geometrical parameters where an increase of the bifurcation load is the biggest in comparison with the reference system.