Critical Length of a Column in View of Bifurcation Theory

[摘要] The paper investigates nonlinear eigenvalue problem for a vertical homogeneous rod loaded with its own weight only. The critical length of the rod, for which the rod loses its stability, is found by use of bifurcation theory. Dependence of maximal deflections of the rods on their lengths is given.

[关键词] ritical length of column;eigenvalue problem;bifurcation theory;approximation of solution;Bessel function