Tension Estimation Method for Cable With Damper Using Natural Frequencies and Two-Point Mode Shapes With Uncertain Modal Order

Abstract

In the maintenance of cable structures, such as cable-stayed bridges, cable safety is assessed based on the cable tension. In Japan, the cable tension is generally estimated from the cable’s natural frequencies using the higher-order vibration method. In recent years, dampers have been installed onto cables to suppress aerodynamic vibrations. Because the damper changes the cable’s natural frequencies, the damper is removed to measure the natural frequencies and estimate the cable tension without a damper, and the damper is then reinstalled. To avoid damper removal and reinstallation, the authors previously proposed Method 2F for estimating the tension of a cable with a damper from the natural frequencies without removing the damper. Because the tension estimation error of the higher-order vibration method for a cable without a damper has been reported as 5%, the authors set the target tension estimation error within 5%. However, the tension estimation error of Method 2F exceeded 5% in the experimental verification. Furthermore, although Method 2F estimates the tension and bending stiffness of the cable and the damper parameters simultaneously from the natural frequencies, the accuracy of the bending stiffness and damper parameters is unsatisfactory. In this paper, the new Method 2FM is proposed to estimate the tension and bending stiffness of the cable and damper parameters using the natural frequencies and two-point mode shapes. With the addition of mode shapes, Method 2FM attempts to improve the accuracy of estimating the tension and other parameters. The validity of Method 2FM was confirmed by numerical simulations and experiments. The numerical verification confirmed that Method 2FM is superior to Method 2F in estimating the cable tension and damper parameters. The experimental verification confirmed that the tension estimation accuracy of Method 2FM is higher than that of Method 2F, and the estimation error is lower than 5%. However, the damper parameters estimated by Method 2FM are different to the design values. The reason for this is the modeling error of the damper, as found by conducting an element test on the damper.

Method for estimating tension of two Nielsen–Lohse bridge cables with intersection clamp connection and unknown boundary conditions

“…Ma (2017) and Yan et al (2019) modeled arbitrary boundaries using rotational springs. Furukawa et al (2021Furukawa et al ( , 2022aFurukawa et al ( , 2022bFurukawa et al ( , 2023 proposed methods for estimating the tension of a cable with a damper installed near the cable boundary from the natural frequencies and mode shapes. A damper is directly modeled with complex stiffness, and a formula has been proposed to estimate the tension, bending stiffness, and damper parameters simultaneously from the natural frequencies.…”

Estimating Natural Vibration Characteristics of Bridge Cables Based on N4sid Subspace Method

“…The natural frequency is generally estimated by reading the dominant frequency of the acceleration Fourier spectrum. In the maintenance of cable bridges, such as cable-stayed bridges [3][4] [5] [6] and Nielsen-Lohse bridges [7][8] [9], cable tension is estimated from the natural frequencies of the cable. The cable tension is sensitive to the lower mode natural frequencies, while the bending stiffness of the cable is sensitive to the higher mode natural frequencies.…”

“…Estimated mode shape includes errors due to calculation measurement errors [13]. In cable maintenance, it was found that the mode shapes can be expected to improve the estimation accuracy of the cable tension and bending stiffness, and damper parameters [5].…”