Analytical free vibration analysis of planar taut two-span cables

Abstract

Abstract This study presents an extension to the theory for analytically analyzing the eigenfunctions and frequency equation of a taut cable with an intermediate point support. The equations of motion for the free vibration of the two-span cable, along with the corresponding boundary and continuity conditions, are established to define the eigenvalue problem and derive simple analytical expressions for the modal properties. Examination of the obtained spectrum reveals “localized modes”—in which only one span exhibits significant vibration amplitudes—“global modes”—in which the vibration of the cable extends across both spans—and “degenerate modes”—where there is more than one independent eigenfunction for a natural frequency. In a numerical example, the analytical results are confirmed by a comparison with finite element solutions obtained with computation endowed with commercial software (ABAQUS).