Vibrations of a rigid body containing elastic element with distributed parameters

Motions are studied of a hybrid (discrete - continual) system consisting of a carrying solid body and attached to it an elastic element with distributed parameters. Two types of fasteners are considered: two ends are squeezed and one end is squeezed and other one is free. A closed set is obtained of integro-differential equations describing the object state at arbitrary initial conditions and forces applied to the body. Perturbed motion of the solid body is investigated by asymptotical methods in the case of a quasi-linear returning force. Motions are studied both in the presence of the internal resonance between oscillations and natural oscillations of the element and when the resonance is absent.