Free-free Dynamic Systems, Inertia Relief

Abstract

Free-free systems can move as a rigid body through space, the structure is so-called unconstrained. The stiffness matrix [K] is singular and therefore the flexibility matrix [G] = [K] ^-1 does not exist. Launch vehicles, aircraft and spacecraft are examples of free-free moving dynamic systems. In this chapter, a method, the inertia relief, will be derived to analyse free-free systems. The motion as a rigid body will be eliminated and a new set of applied loads (relative forces) will be used to analyse the elastic behaviour of the free-free system. In the following sections the relative motion, relative forces will be introduced and a definition of the inertia-relief flexibility matrix [G _f] will be given.