NONLINEARLY FORCED VIBRATIONS OF ELASTIC-SYSTEMS CARRYING RIGID BODIES

A general theory is derived for forced one-dimensional elastic systems carrying elastically or rigidly mounted rigid bodies by using the Lagrangian approach. The theory is applied for the prototype monopode system with one discrete rotational degree of freedom acted on by the non-linear force of a moving ice floe. The dynamics of the monopode are discussed in terms of the eigenmodes. For the realistic parameter values used the resonance in the first eigenmode causes a large swinging of the rigid top body. The second eigenmode gives the main contribution to the deflection of the beam. The third eigenmode can give a large contribution to the velocity and acceleration of the monopode. © 1994 Academic Press Limited.