An Application of Floquet Theory to Prediction of Mechanical Instability

The problem of helicopter mechanical instability is considered for the case where one blade damper is inoperative. It is shown that if the hub is considered to be nonisotropic the equations of motion have periodic coefficients which can not be eliminated. However, if the hub is isotropic the equations can be transformed to a rotating frame of reference and the periodic coefficients eliminated. The Floquet Transition Matrix method is shown to be an effective way of dealing with the nonisotropic hub and nonisotropic rotor situatioin. Time history calculations are examined and shown to be inferior to the Floquet technique for determining system stability. A smearing technique used in the past for treating the one damper inoperative case is examined and shown to yield unconservative results. It is shown that instabilities which occur when one oblade damper is inoperative may consist of nearly pure blade motion or they may be similar to the classical mechanical instability.