Structural dynamics of steel cables under non-linear elastic deformation conditions
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This study develops and validates a multiscale numerical model, conceived as a computational experimentation framework, that enables the evaluation of the mechanical behavior of steel cables subjected to axial, torsional, and fl exural loads. The model was validated through two complementary approaches: on one hand, using experimental results obtained in the laboratory, and on the other, using dynamic records from the Second Severn Crossing cable-stayed bridge. Although the case of the bridge served as a reference for modal calibration, the methodology is applicable to any geometric confi guration or type of structural cable. At the global scale, a fi nite element model calibrates stiff ness based on natural frequencies measured in the fi eld, achieving frequency discrepancies of less than 1.2% and damping alignment within two to three cycles. At the local scale, a contact submodel resolves Hertzian pressures and stick–slip cycles, reproducing the stress–strain curve with secant modulus deviations of less than or equal to 3.1% and peak load errors below 5.5%. The integration of both scales through an energy-conserving projection feedback algorithm enables tracking of a quasi-logarithmic stiff ness loss, from an initial 8% drop after pretensioning to a 27% plateau governed by plasticity in the outer wires. Ambient vibration tests, combined with a high-precision laser scanner that captures the actual curvature of the cable axis, confi rm that modal variations faithfully refl ect the evolution of internal damage: frequency shifts greater than or equal to 10% and a twofold increase in high-frequency vibrational energy mark critical fatigue thresholds. Furthermore, input signals with equal mean energy but diff erent kurtosis produce divergent dynamic responses, challenging classical Gaussian models in predictive maintenance. In general, the methodology identifi es zones of critical damage accumulation at early stages, reduces the root mean square error of the energy to less than 6.5%, and establishes robust dynamic indicators for the management of bridges and prestressed cable systems. Building on these foundations, this doctoral dissertation delivers a physically grounded multiscale framework that, for the fi rst time, couples Hertzian contact mechanics, elastoplastic fatigue kinetics, and full-scale structural dynamics to quantify and monitor degradation in steel cables. The proposed formulation enables the defi nition of modal and energetic indicators with a physical basis, bridges the gap between modal response and the actual internal damage state, and defi nes predictive maintenance criteria transferable to various structural confi gurations.
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