Coupled Bending, Torsion and Axial Vibrations of a Cable-Harnessed Beam With Periodic Wrapping Pattern

This paper presents an equivalent continuum model to study the bending-torsion-axial coupled vibrations of a cable-harnessed beam. The pre-tensioned cable is wrapped periodically around the beam in a diagonal manner. The host structure is assumed to behave as a Euler-Bernoulli beam. The system is modeled using energy methods. The diagonal wrapping pattern results in variable coefficient strain and kinetic energies. Homogenization technique is used to convert spatially varying coefficients into a constant coefficient one. Coupled partial differential equations representing the bending, torsion and the axial modes are derived using Hamilton’s principle. The free vibration characteristics such as the natural frequencies and the mode shapes of the coupled system are analyzed for a fixed-fixed boundary condition and compared to results from the uncoupled and finite element analysis models.