OSCILLATIONS OF A RIGID-BODY CONTAINING AN ELASTIC ELEMENT WITH DISTRIBUTED PARAMETERS

The motions of a hybrid (discrete-continual) system, consisting of a c arrier rigid body and an elastic element with distributed parameters f astened to it are investigated. Two types of fastening are considered: (1) both ends are clamped, and (2) one of the ends is clamped while t he other is free. A closed system of integro-differential equations is obtained which describes the state of the system under arbitrary init ial conditions and forces applied to the rigid body. The perturbed mot ion of the rigid body in the case of a quasi-linear restoring force is investigated using asymptotic methods. The motions are studied both w hen there is internal resonance between the oscillations of the rigid body and the natural oscillations of the element, and when there are n o such resonances. Qualitative effects are found.