Stability of rotating shafts made of piezoelectric fiber composites

In the paper, theoretical fundamentals of stabilisation of a rotating shaft by making use of piezoclectric elemcnts are presented. The shaft is made of an active piezoelectric fiber composite - the state-of-the-art structural material which has just emerged in the field of ''smart'' engineering. Irrespective of the kind of material the rotating shafts are made of, they exhibit flutter-type instability brought about by the presence of internal friction. At a certain critical rotation speed the system loses its stability and starts to perform self-excited vibrations. The paper discusses a method protecting the shaft from such a phenomenon or, at least, shifting it away by incorporation of piezoelectric fibers embedded in a polymer matrix and electrodes bonded to each lamina of the active composite. The constitutive equations of the laminate are derived and used in formulation of equations of motion of the rotating shaft. The analysis of stabilisation reveals that the desired effect can be achieved by application of three and more pairs of the electrodes enabling generation of a constant bending moment regardless of the rotary motion. Proportional and velocity feedbacks in the control system are examined and compared. The critical threshold is determined by investigating the eigenvalues corresponding to the governing equations linearised around non-trivial equilibrium position. The equations themselves were earlier found via a uni-modal Galerkin's discretisation of the partial differential equations of motion. The applied method proves to be efficient as, an increase in the critical speed by two and more times is observed after activation of the proposed stabilisation method.