Structures loaded with a force acting along a fixed straight line, or the “Reut's column problem”

An elastic double pendulum subject to a force acting along a fixed straight line, the so-called “Reut's column problem”, is a structure exhibiting flutter and divergence instability, which was never realized in practice and thus debated whether to represent reality or mere speculation. It is shown, both theoretically and experimentally, how to obtain the Reut's loading by exploiting the contact with friction of a rigid blade against a freely-rotating cylindrical constraint, which moves axially at constant speed, an action recalling that of a bow's hair on a violin string. With this experimental set-up, flutter and divergence instabilities, as well as the detrimental effect of viscosity on critical loads, are documented indisputably, thus bringing an end to a long debate. This result opens a new research area, with perspective applications to mechanical actuators, high-precision cutting tools, or energy harvesting devices.