Vibration-based condition assessments of cables in cable-supported bridges

Abstract

The study presented in this thesis concerns linear and nonlinear vibration analyses and condition assessments of cables in cable-supported bridges. The linear vibration of large-diameter sagged structural cables is first investigated in this thesis. A three-node curved isoparametric finite element is formulated for dynamic analysis of bridge stay cables by regarding the cable as a combination of an 'ideal cable element' and a fictitious curved beam element in the variational sense. The three-dimensional finite element formulation is suited for both suspended and inclined cables and allows for the consideration of cable flexural rigidity, sag-extensibility, spatial variability of dynamic tension, boundary conditions, lumped masses and intermediate spring and/or intermediate dampers. A case study is eventually provided to compare the measured and computed frequencies of cables in a real bridge. The results show that ignoring bending stiffness gives rise to relative errors of 30% in predicting the natural frequencies of the 19th mode. Another case study reveals stiffness effects of attached dampers on the cable frequencies. The proposed finite element formulation provides a good base line model for accurate identification of cable tension force and other parameters based on measurement of multimode frequencies. Parametric studies are conducted to evaluate the relationship between the modal properties and cable parameters lying in a wide range covering most of the cables in existing cable-supported bridges, and the effect of cable bending stiffness and sag on natural frequencies. The study is then extended to nonlinear oscillation of cables. A hybrid finite element/incremental harmonic balance method is developed for analysis of nonlinear periodically forced vibration of inclined cables with arbitrary sag. The proposed method is an accurate algorithm in the sense that it accommodates multi-harmonic components and no mode-based model reduction is made in the solution process. Both the frequency- and amplitude-controlled algorithms are formulated and are alternatively implemented to obtain complete frequency-response curves including both stable and unstable solutions. The proposed method is also capable of analyzing both super- and sub- harmonic resonances and internal resonances. Case study of applying the proposed method to nonlinear dynamic behaviour analysis of the Tsing Ma Bridge cables is demonstrated. The analysis results show that the side-span free cables of the bridge display distinctly different nonlinear characteristics in the construction and final stages. The super-harmonic and internal resonance characteristics of a viscously damped cable with nearly commensurable natural frequencies are investigated. A suspended cable paradigm under internal resonance condition is studied to demonstrate the capability of the proposed method in analyzing modal coupling and internal resonances. Nonlinear response and modal interaction characteristics of the cable at different frequency regions are identified from analysis of response profiles and harmonic component features. The super-harmonic and internal resonance responses are respectively characterized based on the harmonic distribution. Under an in-plane harmonic excitation, the two-to-one internal resonance between the in-plane and out-of-plane modes and the super-harmonic resonance around the second symmetric in-plane mode are revealed. Strong nonlinear interaction among different modes in the parameter space ranging from primary resonance to super-harmonic resonance is observed. Spatial-temporal response profiles and numerical harmonic components at different parameter ranges are presented to highlight the plentiful nonlinear response behaviours of the cable. Finally, parameter estimation of structural cables is investigated by employing both local and global optimization tools. As an analytical method, the local optimization tools are used to investigate the effects of selection of parameter and weight on the estimation of parameters. Both single- and multiple-parameter estimation procedures are studied. It is noticed in the numerical simulation that single-parameter estimation procedures cannot eliminate the trend in errors between the measured and analytical frequencies. Hence, no prominent procedures or parameters are found. The best estimation is given the multiple-parameter estimation procedures. Methods for cable tension identification are also discussed. Two global optimization tools, i.e the exhaust search and the genetic algorithm (GA) are adopted to discuss further problems in cable parameter estimation. Simulation studies are conducted to show the characteristics of the cost function surfaces under different conditions and to obtain the statistical properties of the cable parameters through the Monte Carlo method. Field vibration data from three real bridges are used to evaluate the condition of corresponding cables. The effects of quantity of modal frequencies and the noise levels on the solution uniqueness and distributions of multiple solutions are investigated. The correlation between the errors of different parameters is obtained through calculating the correlation coefficients.