Bridges with external post-tensioned tendons are considered to be more durable than bridges with internal tendons (tendons within the webs and flanges), because external tendons are easier to inspect. In addition, in the event that extensive corrosion damage is detected, it is possible to replace an external tendon. However, an appropriate inspection for detecting damage needs to be determined for external tendons. This investigation focuses on the vibration technique, which uses the dynamic properties of the external tendon to infer the effective prestress force. Four large-scale external tendons, designed to simulate one section of an external tendon between two deviators in a post-tensioned bridge, were tested. In the study, damage to the tendons was induced in a quantifiable fashion at a specific location and the tensile force was measured directly. In addition, free-vibration tests were conducted periodically. This provided a direct means of measuring the sensitivity of measured natural frequencies and measured tensile force to local damage. The measured data were correlated with an approximation of the stiff string vibration model. In addition to the laboratory specimens, field testing was conducted on a bridge with external post-tensioned tendons. The findings from the study show that a loss in tensile force was not linear with a loss in the cross-sectional area of the strand, which results from stress redistribution within the tendon. Also, the natural frequencies were much less sensitive to the level of induced damage than the tensile force. While the measured data from the laboratory data compared very well with the analytical model, the field measurements exhibited a much greater deviation from the model. Due to several factors, the difference between the laboratory specimens and the bridge tendons are believed to be caused by larger levels of inherent error in the model. The findings from the investigation support the notion that vibration testing is most appropriately used in comparing relative differences between peer tendons. / text

Most modern product development utilizes computational models. With increasing demands on reducing the product development lead-time, it becomes more important to improve the accuracy and efficiency of simulations. In addition, to improve product performance, a lot of products are designed to be lighter and more flexible, thus more prone to nonlinear behaviour. Linear finite element (FE) models, which still form the basis of numerical models used to represent mechanical structures, may not be able to predict structural behaviour with necessary accuracy when nonlinear effects are significant. Nonlinearities are often localized to joints or boundary conditions. Including nonlinear behaviour in FE-models introduces more sources of uncertainty and it is often necessary to calibrate the models with the use of experimental data. This research work presents a model calibration method that is suitable for mechanical systems with structural nonlinearities. The methodology concerns pre-test planning, parameterization, simulation methods, vibrational testing and optimization. The selection of parameters for the calibration requires physical insights together with analyses of the structure; the latter can be achieved by use of simulations. Traditional simulation methods may be computationally expensive when dealing with nonlinear systems; therefore an efficient fixed-step state-space based simulation method was developed. To gain knowledge of the accuracy of different simulation methods, the bias errors for the proposed method as well as other widespread simulation methods were studied and compared. The proposed method performs well in comparison to other simulation methods. To obtain precise estimates of the parameters, the test data should be informative of the parameters chosen and the parameters should be identifiable. Test data informativeness and parameter identifiability are coupled and they can be assessed by the Fisher information matrix (FIM). To optimize the informativeness of test data, a FIM based pre-test planning method was developed and a multi-sinusoidal excitation was designed. The steady-state responses at the side harmonics were shown to contain valuable information for model calibration of FE-models representing mechanical systems with structural nonlinearities. In this work, model calibration was made by minimizing the difference between predicted and measured multi-harmonic frequency response functions using an efficient optimization routine. The steady-state responses were calculated using the extended multi-harmonic balance method. When the parameters were calibrated, a k-fold cross validation was used to obtain parameter uncertainty. The proposed model calibration method was validated using two test-rigs, one with a geometrical nonlinearity and one with a clearance type of nonlinearity. To attain high quality data efficiently, the amplitude of the forcing harmonics was controlled at each frequency step by an off-line force feedback algorithm. The applied force was then measured and used in the numerical simulations of the responses. It was shown in the validation results that the predictions from the calibrated models agree well with the experimental results. In summary, the presented methodology concerns both theoretical and experimental aspects as it includes methods for pre-test planning, simulations, testing, calibration and validation. As such, this research work offers a complete framework and contributes to more effective and efficient analyses on mechanical systems with structural nonlinearities.