Non-linear dynamic response of a cable system with a tuned mass damper to stochastic base excitation via equivalent linearization technique

Abstract: Non-linear dynamic model of a cable–mass system with a transverse tuned mass damper is considered. The system is moving in a vertical host structure therefore the cable length varies slowly over time. Under the time-dependent external loads the sway of host structure with low frequencies and high amplitudes can be observed. That yields the base excitation which in turn results in the excitation of a cable system. The original model is governed by a system of non-linear partial differential equations with corresponding boundary conditions defined in a slowly time-variant space domain. To discretise the continuous model the Galerkin method is used. The assumption of the analysis is that the lateral displacements of the cable are coupled with its longitudinal elastic stretching. This brings the quadratic couplings between the longitudinal and transverse modes and cubic nonlinear terms due to the couplings between the transverse modes. To mitigate the dynamic response of the cable in the resonance region the tuned mass damper is applied. The stochastic base excitation, assumed as a narrow-band process mean-square equivalent to the harmonic process, is idealized with the aid of two linear filters: one second-order and one first-order. To determine the stochastic response the equivalent linearization technique is used. Mean values and variances of particular random state variable have been calculated numerically under various operational conditions. The stochastic results have been compared with the deterministic response to a harmonic process base excitation

Repair of reinforced concrete bridge columns subjected to chloride-induced corrosion with ultra-high performance fiber reinforced concrete

The rehabilitation of reinforced concrete (RC) bridge columns subjected to chloride-induced corrosion is addressed in the present paper. The proposed strategy is based on the replacement of the original external layer made of normal-strength concrete (NSC) with ultra-high performance fiber reinforced concrete (UHPFRC), and it additionally involves the substitution of the existing corroded longitudinal reinforcement with new machined steel rebars. This repair technique aims at restoring strength, stiffness, and ductility of the original column in a short time without altering its cross-section dimensions. Because of the high compactness of the UHPFRC, it also serves at improving its durability. The main contribution of the present work is a numerical investigation carried out in order to identify how the design decisions about the repair strategy influence the behavior of the restored column. The parametric investigation reveals that the length of the zone in which NSC is replaced by UHPFRC as well as the machined index (i.e., ratio between turned and original rebar cross-section area) must be properly selected to make the intervention effective. Numerical results also highlight that the main design issue to deal with is the relocation of the plastic hinge from the repaired zone towards the weak unrepaired part of the column. Practical design recommendations are finally formulated