Effect of cable flexibility on transient response of a beam–pendulum system

The effect on beam–pendulum response of cable flexibility is studied. The system is forced at its base by a prescribed damped periodic oscillation. Response from cable tension is estimated at a delayed time step from known variables computed at a previous time step in a linear modal analysis. The effects of base excitation and force from cable flexibility are included adopting the static–dynamic superposition method. Two distinct non-dimensional parameters κo and μr, control the linear modal response of beam and pendulum. Unlike periodic excitation where the pendulum may be used as an absorber of energy, in transient response the conditions leading to absorption do not apply. Even for large pendulum swings, cable flexibility has a negligible effect on flexural response considering that cable tension dominated by high frequencies is larger than the shear force QxxL it transmits at the beam-free end. Contrary to its effect on flexure, cable flexibility induces a high-frequency axial force comparable to QxxL.