Comparison of cable tension force prediction using effective length with linear regression and two-mode combination method

The development of vibration-based tension determination has increased in recent years. The effective vibration length concept is one of the most robust methods in dealing with various end-rotational support stiffness. Recently, a two-mode combination approach by compelling multiple frequencies and effective lengths has been developed to replace the bending rigidity from the cable relationship so the tension can be solved explicitly. This paper aims to compare the tension prediction using the effective length concept with two existing methods: linear regression and the two-mode combination. Three cases of cable support: hinged-hinged (Case 1), hinged-fixed (Case 2), and fixed-fixed (Case 3), are studied through numerical simulation. The cable is vibrated under random excitation, and its dynamical properties are extracted through the SSI method. Equivalent frequencies and equivalent-effective lengths are computed to perform the two-mode approach. The study shows that linear regression produces more minor errors than the two-mode combination method, either for Cases 1, 2, or 3. The theoretical results are presented to figure out the cause of errors. However, linear regression and the two-mode method both produce promising results in calculating the cable tension in these three cases. Similar results are also shown in the study using experimental laboratory test data.