Overview

There are several ways of investigating instabilities. The fact that rotorcraft dynamic issues must invariably be described by multiple-degrees-of-freedom systems of equations drives our attention to mathematical techniques that can deal with them. All too often these techniques, while giving accurate indications of stability levels, also lead to a loss of understanding of the physics involved. At the heart of any instability issue is the condition wherein there is an energy source and one or more motion-induced force ( s) that are in phase with velocities and grow with response level. Perhaps the clearest example of this principle is the action of a person on a swing. To initiate and increase the amplitude of the oscillatory motion, the "person" must pull on the swing ropes at the bottom of the swing amplitude to generate a gravity moment in phase with the angular velocity of the swing. This approach to issues of instability forms the basis of examining the instabilities of shafting (to be examined in a subsequent chapter), as well as forming the basis of the method of force-phasing matrices, to be discussed in a subsequent section.

Other approaches to investigating instabilities require dealing with multiple-degrees-of freedom equation sets and the use of sophisticated eigenvalue calculations. Within this broad class of methods are the methods associated with periodic coefficients and with the marriage of frequency-domain data of one subsystem with the analytic description of another. Both of these issues have application to all aircraft aeroelasticity...