| Summary: |
During the last few decades, vibration-based techniques have become widely used in the assessment of the force installed in cables. While the original application of the so-called vibrating chord theory to the identification of the tensile force was verified as accurate for high and relatively long cables [1], the need to inspect cables with other characteristics(low tension, short or uncertain length) has led to extend such methods beyond their limit of application. To improve the quality of force estimation, different authors proposed the implementation of different regression or optimization techniques [2,3,4], which may lead to improved estimates of the free cable length, the moment of inertia of the cross-section and the force. However, these methods still rely on the knowledge of the end conditions of the cable, not to mention that the ill-conditioned nature of the optimization method, with very different sensitivities of the various involved parameters, may result in the estimation of sets of parameters that are local minima and not the real solutions of the problem. The present project aims at developing and validating a new method for the identification of cable force and mechanical properties of a tensioned cable experimentally. This method isbased on the direct measurement of the velocity of propagation of transverse waves and employs dispersion relations to deduce the mechanical properties, namely the bendingstiffness and the shear coefficient of the cross-section. In parallel, the use of this propagating velocity in the vibrating chord formula enables the estimation of the cable force withoutthe need of specifying boundary conditions. This is particularly interesting in cables of cable-stayed bridges where dampers are employed, changing the cable mode shapes, or else when short cables need to be assessed where the uncertainty in the length definition would result in low accuracy of the estimated force. In combining a local measurement of the velocity  |
Summary
During the last few decades, vibration-based techniques have become widely used in the assessment of the force installed in cables. While the original application of the so-called vibrating chord theory to the identification of the tensile force was verified as accurate for high and relatively long cables [1], the need to inspect cables with other characteristics(low tension, short or uncertain length) has led to extend such methods beyond their limit of application. To improve the quality of force estimation, different authors proposed the implementation of different regression or optimization techniques [2,3,4], which may lead to improved estimates of the free cable length, the moment of inertia of the cross-section and the force. However, these methods still rely on the knowledge of the end conditions of the cable, not to mention that the ill-conditioned nature of the optimization method, with very different sensitivities of the various involved parameters, may result in the estimation of sets of parameters that are local minima and not the real solutions of the problem. The present project aims at developing and validating a new method for the identification of cable force and mechanical properties of a tensioned cable experimentally. This method isbased on the direct measurement of the velocity of propagation of transverse waves and employs dispersion relations to deduce the mechanical properties, namely the bendingstiffness and the shear coefficient of the cross-section. In parallel, the use of this propagating velocity in the vibrating chord formula enables the estimation of the cable force withoutthe need of specifying boundary conditions. This is particularly interesting in cables of cable-stayed bridges where dampers are employed, changing the cable mode shapes, or else when short cables need to be assessed where the uncertainty in the length definition would result in low accuracy of the estimated force. In combining a local measurement of the velocity of propagation of waves with the measurement of global cable frequencies, the method enables the identification of damage along a cable as a result of the variation of the corresponding mechanical properties. The project comprehends the systematization of the already developed formulation and sensitivity test studies to identify ranges of parameters and confidence intervals of the estimates, in particular related to the percentage of damage that is identifiable. In the second stage, a laboratory validation will be accomplished by the test of different types of cables at different levels of tension, with different levels of degradation. Prototype tests will complement the laboratory tests and will be used as proof of concept. The project team is composed of highly experienced researchers in cable dynamics [5], dynamic testing [6], damage assessment [7] and site experience with cable bridges and special structures [8, 9]. In particular, the PI obtained a PhD in Cable Dynamics and has done research on the topic for the last 20 years, being involved at the consultancy level in numerous studies related to the characterization of cable force, such as the suspended roof for the London Olympic Stadium in 2012 [10]. In the present proposal, she is responsible for the formulation regarding the identification of force and damage as a function of the velocity of transverse generated waves, which is being developed together with João Rodrigues in the context of his PhD research. The PI and all the members of the team have a wide experimental background which will be necessary both for the laboratory validation and the prototype tests. The co-PI has a PhD in Dynamics and Control of Vibrations and has been highly active in the development of sensors and setups for dynamic tests of different nature. In this project, he will be fundamental in the development of laboratory test setups. The proposed method constitutes an entirely new approach by comparison with other existing vibration-based assessment methods, with the great advantage of the easiness of application and expected high accuracy due to the non-required knowledge of the cable length in the assessment of cable force and properties. At the international level, the validation and demonstration of the proposed method may constitute an important step in both the assessment of cable force and damage, contributing to improving the safety and eventually extending the lifetime of important infrastructures that presently exist throughout Europe and are reaching their end of life. It is further expected that, in the future, this method will be implemented automatically by means of a robot that will run along a suspension cable, for example, to locally detect damage. |