Eddy current damping has been widely applied in mechanical engineering; however, its adaptation for civil engineering applications remains rather limited due to its low density of energy dissipation. This study presents the development of a new type of eddy current damper and theoretical and experimental characterization of its damping properties. In addition to rectangular permanent magnets and conductive plate, both primary back iron and secondary back iron are considered in the proposed eddy current damper, which represents an improved design over previous configurations. The analytical method based on the charge model of permanent magnets is extended to simulate the extra damping effect of the primary back iron and secondary back iron, and the magnet field and damping properties of the dampers are evaluated analytically. The use of a back iron in the proposed damper is shown to increase the damping coefficients by a factor of up to 5. The analytical results are compared with those obtained with the finite-element analysis in terms of accuracy in magnetic field distributions, eddy current distributions, and damping coefficients. The linear assumption, which implies the damping force is linearly proportional to velocity in the analytical model, is also examined for different motional velocities and relative permeability of the permanent magnet. It is shown that the linear damping assumption in the analytical model is only valid for a limited range of low velocity, and this velocity range can be increased by reducing the thickness or conductivity of the conductive plate. In addition, a modification is needed for the analytical model if the relative permeability of the permanent magnet significantly deviates from the assumed value of 1.0. Finally, the accuracy of the analytical model and the finite-element model is verified by experiment of a prototype damper mounted in a laboratory steel frame.

The main structure of the transmission tower consists of the tower body and the cross arm, which serve as vertical support and transverse extension, respectively. Compared with the tower body, due to the difference between the transverse and longitudinal projected areas of the cross-arm, the wind load distribution of the cross-arm is more complicated and requires more in-depth research. In this paper, wind tunnel force tests under skew wind were carried out on the 1:20 scaled rigid models of the tubular and the tubular-angle combined cross-arms. The tests consider four solidity ratios (0.2, 0.3, 0.4, and 0.5) under three wind speeds and 19 yaw angles. The aerodynamic force coefficients Ci, the skewed wind load factor Kθ, the transversal and longitudinal wind load distribution factor nX and nY, and the angle α between the transversal aerodynamic force coefficient (CX) and the resultant wind force coefficient (CR) were obtained and analyzed. It was found that the wind load coefficients decrease with increasing solidity ratio. The tested drag coefficient of the tubular cross-arm is larger than the combined cross-arm under the same solidity ratio. The nX of the tubular and combined cross-arm reaches the maximum range of 0.33–0.47 and 0.22–0.23 at 30° <θ < 45° and 30° < θ < 35°, respectively. The nY curves were ordered from large to small as follows: EN 50341-1, the tested tubular cross-arm, the tested combined cross-arm, and JEC-127-1979. At 55° < θ < 65°, the difference of α and θ for the tested tubular and combined cross-arm reaches the maximum of 10°–18° and 29°–32°, respectively, indicating that the lift force cannot be ignored and the assumption α = θ is not applicable. Reasonable nonlinear fitting functions are proposed to accurately calculate the wind load of the two types of cross-arms.

The recognition of the road surface unevenness can provide an important support for optimizing the maintenance and management strategies of local intelligent transportation networks. This study proposes a BiGRU-Transformer model optimized with Beluga Whale Optimization (BWO) and combined with the Cubature Kalman Filter (CKF) for road surface unevenness recognition in intelligent transportation systems. The model addresses the limitations of existing methods in time series data processing and nonlinear state estimation. It uses BiGRU to model short-term vehicle vibration dependencies and incorporates the Transformer’s self-attention mechanism to capture long-term and global dynamics. BWO optimizes the global hyperparameters of the model, avoiding local optima and improving accuracy. CKF updates the noise matrix in real-time, enhancing prediction and generalization through recursive nonlinear state estimation. Experimental results demonstrate significant improvements in performance, including recognition accuracy, noise immunity, and convergence speed, when applied to real road datasets. The proposed model outperforms existing methods, offering enhanced road condition identification and providing effective real-time decision support for intelligent transportation systems, thereby improving management efficiency and responsiveness.

This study derives a theoretical formula for calculating the damping force of the electromagnetic source eddy current damper (ES-ECD) based on the magnetic vector potential form of Maxwell’s equations and layer theory. The accuracy of the formula is validated through finite element modeling (FEM) and a static magnetic field test, with a maximum error of less than 3% in the damping force–velocity curve. A comparison with the permanent-magnet source eddy current damper (PS-ECD) reveals the electromagnetic evolution mechanism underlying the damping force–velocity relationship of the ES-ECD. The results indicate that the ES-ECD exhibits a lower critical velocity and enhanced nonlinearity in the damping force beyond the critical point, attributed to the intensified opposing magnetic field generated in the time-varying field. The axial pole-pitch ratio, $\alpha $ , significantly influences the nonlinear characteristics of the ES-ECD, with the damping force per unit ampere-turn reaching its maximum at $\alpha =0.65$ . The nonlinear characteristics of the ES-ECD make the damping coefficient more sensitive to variations in conductor thickness and air gap. At low velocities, the higher nonlinear damping coefficient broadens the optimal parameter range of traditional eddy current dampers (ECDs), offering enhanced versatility. Through numerical simulation of the dynamic response characteristics of the impact buffering system for the falling mass block, it has been verified that the ES-ECD can achieve up to a 20.6% improvement in buffering performance compared to the PS-ECD, effectively absorbing the system’s impact energy and achieving swift vibration attenuation.