Vibrations of beams prestressed by internal frictionless cables

A greased cable is positioned along a generic curve in the interior of a be am and is anchored to the beam at its extreme points. The absence of fricti on permits a relative slipping between the cable and beam at intermediate p oints and this makes the cable strain dependent on the global deformation o f 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 cond itions describing the infinitesimal motions in the neighbourhood of a known balanced static configuration in order to evaluate the effect due to the p resence: of the stretched cable on the motion and free vibrations of the sy stem. The kinematical model adopted for the beam permits a sufficiently acc urate description of the behavior of thin walled beams and the cable strain is obtained as a functional of global deformation. Some qualitative aspect s concerning the problem formulation and the dynamical behavior are stated. An applicative example referring to a case of interest shows that the stat e of stress obtained by stretching the cable notably influences only a redu ced set of vibration modes, determined by the path geometry and cable force . Such aspects of the problem can be of interest in structural identificati on. (C) 1999 Academic Press.