Vibrations of beams prestressed by internal frictionless cables

A greased cable is positioned along a generic curve in the interior of a beam and is anchored to the beam at its extreme points. The absence of friction permits a relative slipping between the cable and beam at intermediate points and this makes the cable strain dependent on the global deformation of the beam. Such a system permits controlling the beam state of stress and strain by assigning a predetermined traction force on the cable. This paper proposes a formulation of the system dynamics by defining the balance conditions describing the infinitesimal motions in the neighbourhood of a known balanced static configuration in order to evaluate the effect due to the presence of the stretched cable on the motion and free vibrations of the system. The kinematical model adopted for the beam permits a sufficiently accurate description of the behavior of thin walled beams and the cable strain is obtained as a functional of global deformation. Some qualitative aspects concerning the problem formulation and the dynamical behavior are stated. An applicative example referring to a case of interest shows that the state of stress obtained by stretching the cable notably influences only a reduced set of vibration modes, determined by the path geometry and cable force. Such aspects of the problem can be of interest in structural identification.