Experimental evidence of flutter and divergence instabilities induced by dry friction

Flutter and divergence instabilities have been advocated to be possible in elastic structures with Coulomb friction, but no direct experimental evidence has ever been provided. Moreover, the same types of instability can be induced by tangential follower forces, but these are commonly thought to be of extremely difficult, if not impossible, practical realization. Therefore, a clear experimental basis for flutter and divergence induced by friction or follower-loading is still lacking. This is provided for the first time in the present article, showing how a follower force of tangential type can be realized via Coulomb friction and how this, in full agreement with the theory, can induce a blowing-up vibrational motion of increasing amplitude (flutter) or an exponentially growing motion (divergence). In addition, our results show the limits of a treatment based on the linearized equations, so that nonlinearities yield the initial blowing-up vibration of flutter to reach eventually a steady state. The presented results give full evidence to potential problems in the design of mechanical systems subject to friction, open a new perspective in the realization of follower-loading systems and of innovative structures exhibiting ‘unusual’ dynamical behaviors.     

Vibration and stability of an elastic column subject to a generalized load

Summary The critical load of the divergence instability, eigenfrequency curves and the Rayleigh's quotient for a column with one clamped end, subject to a generalized load, have been established in the paper. In particular, it has been found that the way the external force is being applied results in the linear dependence of both the shearing force and the bending moment upon both the deflection and the deflection angle of the loaded end. Such a case of loading exists e.g. for a column which supports a transversally stabilized structure when the contact surfaces are cylindrical. Furthermore, it has been theoretically and experimentally proven, that the slope of some eigencurves can change from positive to negative with the increasing load value.This research has been supported by the State Committee for Scientific Research, Warsaw, Poland, 1995.     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)-THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol’d’s second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance