Cable modal parameter identification. I: Theory

Cable modal parameters (natural frequencies and damping ratios) that represent the cable inherent dynamic characteristics play an important role in the construction, vibration control, condition assessment, and long-term health monitoring of cable-supported structures. The existing options to identify cable modal parameters through vibration measurements are somewhat limited. For this purpose, a cable dynamic stiffness based method is presented to effectively identify the cable modal parameters. In the first part of this two-part paper, the cable dynamic stiffness is analytically discussed for a viscously damped, uniform, inclined sagging cable supported at the lower end and subjected to a harmonically varying arbitrary angle displacement excitation in an arbitrary angle at the upper end when the cable is assumed to have a parabolic profile at its position of static equilibrium. Special attention is paid to the physical meaning and significance of every part of the frequency-dependent closed-form cable dynamic stiffness. Comprehensive numerical analyses have been carried out and a simplified cable dynamic stiffness is proposed for the purpose of identifying the cable modal parameters with a good accuracy over a wide range of frequencies.