Harnessing centrifugal and Euler forces for tunable buckling of a rotating elastica

We investigate the geometrically nonlinear deformation and buckling of a slender elastic beam subject to time-dependent ‘fictitious’ (non-inertial) forces arising from unsteady rotation. Using a rotary apparatus that accurately imposes an angular acceleration around a fixed axis, we demonstrate that dynamically coupled centrifugal and Euler forces can produce tunable structural deformations. Specifically, by systematically varying the acceleration ramp in a highly automated experimental setup, we show how the buckling onset of a cantilevered beam can be precisely tuned and its deformation direction selected. In a second configuration, we demonstrate that Euler forces can cause a pre-arched beam to snap-through, on demand, between its two stable states. We also formulate a theoretical model rooted in Euler's elastica that rationalizes the problem and provides predictions in excellent quantitative agreement with the experimental data. Our findings demonstrate an innovative approach to the programmable actuation of slender rotating structures, where complex loading fields can be produced by controlling a single input parameter, the angular position of a rotating system. The ability to predict and control the buckling behaviors under such non-trivial loading conditions opens avenues for designing devices based on rotational fictitious forces.