On stability of elastic rod planar equilibrium configurations

The Jacobi test is used to analyze the stability of planar equilibrium configurations for clamped–clamped and clamped–hinged elastic rods. The governing equilibrium equation and Jacobi equation are derived from variational principles, and their solution is presented in terms of the Jacobi elliptical functions. The critical equation, which determines the stability properties of rod equilibrium, is solved numerically. The results of the analysis are presented in graphical form as instability regions on bifurcation diagrams.