Contact between two planar buckled beams pushed together transversely

In this paper we study the behavior of two buckled beams when they are pushed toward each other. The elastica model is adopted in the theoretical formulation. In the early stage, the buckled beams contact each other at one point. It then evolves to line contact when the external pushing force increases. The line-contact segment can be straight or curved. It is shown that there is no distributed force within the line-contact segment. In order to determine the stability of the deformation, the vibration method is adopted. To account for change of contact points during vibration, the equations of motion are reformulated into Eulerian forms and the squares of natural frequencies are solved. If any of the squares of natural frequencies is negative, the equilibrium is unstable. Experiments are conducted to measure the relation between the pushing force and the top clamp-line movement. For each stable deformation, several of the lowest natural frequencies are recorded and compared with the theoretical predictions. In displacement control the lowest two natural frequencies agree very well with the theoretical prediction. However, the measurement of natural frequencies for load control is less successful. Generally speaking, the deformation evolutions observed in experiments follow the load-deflection curves predicted theoretically for both displacement and load-control procedures.