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Two types of non-holonomic constraints (imposing a prescription on velocity)are analyzed, connected to an end of a (visco)elastic rod, straight in itsundeformed configuration. The equations governing the nonlinear dynamics areobtained and then linearized near the trivial equilibrium configuration. Thetwo constraints are shown to lead to the same equations governing thelinearized dynamics of the Beck (or Pfluger) column in one case and of the Reutcolumn in the other. Therefore, although the structural systems are fullyconservative (when viscosity is set to zero), they exhibit flutter anddivergence instability. In addition, the Ziegler's destabilization paradox isfound when dissipation sources are introduced. It follows that these featuresare proven to be not only a consequence of 'unrealistic non-conservative loads'(as often stated in the literature), rather, the models proposed by Beck, Reut,and Ziegler can exactly describe the linearized dynamics of structures subjectto non-holonomic constraints, which are made now fully accessible toexperiments.

Flutter instability and Ziegler destabilization paradox for elastic rods subject to non-holonomic constraints