The consistency of magnetic flux density of damping gap (CMDG) represents the balancing magnetic flux density in each damping gap of magnetorheological (MR) dampers. It can make influences on the performances of MR dampers and the accuracy of relevant objective functions. In order to improve the mechanical performances of the MR damper with a two-stage coil, the function for calculating CMDG needs to be found. By establishing an equivalent magnetic circuit model of the MR damper, the CMDG function is derived. Then, the multiobjective optimization function and the working flow of optimal design are presented by combining the parallel-plate model of the MR damper with the function posed before. Taking the damping force, the dynamic range, the response time, and the CMDG as the optimization objective, and the external geometric dimensions of the SG-MRD60 damper as the bound variable, this paper optimizes the internal geometric dimensions of MR damper by using a NSGA-III algorithm on the PlatEMO platform. The results show that the obtained scheme in Pareto-optimal solutions has existed with better performance than that of SG-MRD60 scheme. According to the results of the finite element analysis, the multiobjective optimization design including the CMDG function can improve the uniformity of magnetic flux density of the MR damper in damping gap, which meets the requirements of manufacture and application.
Vibration-based (VB) method and elasto-magnetic (EM) method are usually used to measure cable forces of cable-supported bridges. For the VB method, it is difficult to accurately identify each order natural frequency of the cable disturbed by random excitations, and there are also no precise selection criteria between the taut string model and the hinged beam model. For the EM method, it is not convenient to calibrate EM sensors on bridges in service due to unknown cable forces. To address these issues, a vibration-based elasto-magnetic (VBEM) method is proposed. In this method, a numerical model describing the tie between each order natural frequency and induced voltage was constructed first, and then, a new cable force formula with nominal flexural stiffness was derived. To verify the VBEM method, a steel strand experimental platform was built and the load applied to the steel strand was achieved by a jack. At 18 °C, the first three order natural frequencies of the steel strand and corresponding induced voltage were recorded for each load. According to the obtained experimental data, the VBEM method is tested and analyzed. The results show that the VBEM method exhibits the ability to identify each order natural frequency of the steel strand with high precision; the introduction of nominal flexural stiffness makes the hinged beam model cover the taut string model, resulting in tension force measurement with satisfactory accuracy; the constructed models do not contain tension forces, and this will make it very beneficial to calibration of EM sensors on bridges in service.
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