Sensitivity Analysis of Cable Parameters on Tension of a Suspended Cable under Combination Resonances

Abstract

This paper studies the vibration of a suspended cable with small sag excited by a second excitation (normal) mode causing combination resonance in the three modes, i.e. tangent, normal and bi-normal modes. The displacement response spectra in the time domain and phase portraits are provided as evidence of the transition from the unstable steady-state motion to the stable one for nonlinear cable oscillation. A nondimensional equation for the cable tension is established with its variation evaluated for the unstable zone. The half-normalized sensitivity analysis of cable parameters, such as damping coefficient, excitation amplitude, arc length parameter and initial conditions, for their influence on cable tension is conducted in the time domain by a direct integration method. Also, the characteristics of the dynamic sensitivity of cable tension to the parameters are discussed. As a result, a sensitivity ranking chart is prepared based on the sensitivity analyses for the parameters considered. It is clearly revealed that cable tension is very sensitive to tangent and normal initial displacements in spite of their small values, whereas the same is not true for the arc length parameter and bi-normal damping coefficient. To verify the sensitivity analysis algorithm, a forced Rayleigh oscillator is introduced. A feasibility study using the oscillator shows that the numerical results obtained are in good qualitative agreement with the analytical predictions, implying that the associated algorithm works well.