Leipholz column with shear and compressibility

Abstract

The influence of rotary inertia, shear, and axis extensibility on the stability boundary of a generalized Leipholz column is analyzed. Namely, we consider the problem of determining the stability boundary for an elastic column, fixed at one and free at the other end, loaded by uniformly distributed tangential forces along its length and a concentrated force at the top having fixed direction. The constitutive equations for the column are taken in the form suggested by Haringx. First, the nonlinear differential equations of motion are derived. These equations are then linearized, around the trivial solution, and the critical (flutter) load is determined numerically. It is found that axis compressibility increases the critical load, while the finiteness of shear stiffness, rotary inertia, and constant compressive force decrease the critical load. The influence of the pulsating component of the compressive force on the stability is also analyzed.