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This paper examines the dynamic performance of the pantograph passing through an overlap section of the catenary system, using a China's high speed railway with the 4-span overlap as an example. The pantograph and catenary system are simulated as a lumped mass model and finite element model, respectively. The model is verified according to EN50318:2018. The model is also assessed against an experimental study of the contact force and uplift of contact wire at 300 km/h. Then the contact force and uplift of contact wire at the speed of 150–350 km/h are calculated. The research shows that when the pantograph passes through the overlap, the maximum contact force increases beyond 14%, the standard deviation of the contact force increases by more than 26%, and the increase of the vertical displacement exceeds 38%, which becomes more apparent with the increase of speed. Under the influence of aerodynamic force, when the running speed increases from 150 to 350 km/h, the mean contact force in the knuckle-downstream and knuckle-upstream orientation increase by 59.49% and 97.85%, respectively. As a result, the contact force and vertical displacement increase greatly when passing through the overlap section, which could affect the current collection quality. [ABSTRACT FROM AUTHOR]

The railway system is one of the safest, most efficient, and environmentally friendly means of land transport for people and goods. However, as the demand for mobility has increased, the current railway system has shown some weaknesses, requiring an increase in catenary power in order to be able to supply power to longer trains and faster locomotives, as well as to increase rail traffic. This paper proposes a control algorithm to be implemented in a sectioning post-Rail Power Conditioner (sp-RPC). The sp-RPC is connected to the neutral section between two traction power substations (TPS). With the control algorithm, it is possible to minimize the existing unbalance of the active powers of each TPS. In a regenerative braking condition, this surplus energy can be used to assist the traction of another locomotive on the existing overhead line. In this way, it is possible to increase the capacity of the overhead line. The analysis was performed with computer models using a modular multilevel converter (MMC) topology for the sp-RPC. Quantitative results for different consumption events of the locomotives and the analysis of the response to these variations are presented. [ABSTRACT FROM AUTHOR]

The advantage of fractional-order derivative has attracted extensive attention in the field of dynamics. In this paper, we investigated the stability of the fractional-order Mathieu equation under forced excitation, which is based on a model of the pantograph–catenary system. First, we obtained the approximate analytical expressions and periodic solutions of the stability boundaries by the multi-scale method and the perturbation method, and the correctness of these results were verified through numerical analysis by Matlab. In addition, by analyzing the stability of the k'T-periodic solutions in the system, we verified the existence of the unstable k'T-resonance lines through numerical simulation, and visually investigated the effect of the system parameters. The results show that forced excitation with a finite period does not change the position of the stability boundaries, but it can affect the expressions of the periodic solutions. Moreover, by analyzing the properties of the resonant lines, we found that when the points with k'T-periodic solutions were perturbed by the same frequency of forced excitation, these points became unstable due to resonance. Finally, we found that both the damping coefficient and the fractional-order parameters in the system have important influences on the stability boundaries and the resonance lines. [ABSTRACT FROM AUTHOR]

Catenaries are large cable structures which transmit electric current to trains through sliding contact with a pantograph. The finite element method is widely used to model this dynamic interaction problem and obtain the contact force between the pantograph and the catenary. As an alternative, analytical models can also be used to study catenary dynamics, although they require certain simplifications of the features considered in numerical models. In this paper, an analytical model composed of an infinite string and a visco-elastic support is introduced and enhanced by considering a Kelvin-Voigt damping model and the initial height of the contact wire. Considering the finite element (FE) model as a reference, the analytical model parameters are properly adjusted through static and wave propagation analyses to achieve similar behaviour in both the analytical and the FE models. To check the performance of the proposed model, the steady-state response of the pantograph–catenary coupled system is calculated and compared with the results of the FE model. Finally, the analytical model is used to analyse the interference phenomenon produced during two-pantograph operation. [ABSTRACT FROM AUTHOR]

A novel floating-array-buoys wave energy converter (FABWEC) system integrating multi-point absorption wave energy capturing technology and single-point catenary mooring technology is proposed in this study. The research contents of this paper mainly focus on the stability and survivability of the proposed FABWEC system under the rated sea conditions. Numerical simulation and experimental validation are developed, and the comparisons of system performances between experimental and simulated results are performed. The results show that the maximum mooring tension occurs when the inclination angle of anchor chain is 30° under the environment loads of 180°. Under an extreme environmental condition, the safety factor of maximum mooring force is 9.49 which meets the internationally recognized safety requirement for the mooring system, and the maximum displacement of the wave power platform occurs in surge is 14.03 m and the maximum angle occurs in pitch is −6.99°. The experimental motion curves are basically consistent with the simulated results, and the power platform ultimately reaches a stable position during the experiments. According to the simulated and experimental investigation, the stability and survivability of the FABWEC system are effectively confirmed. Significantly, this study provides a beneficial experience for the practical application and stable operation of WECs. • A floating-array-buoys wave energy converter for power generation is presented. • The FABWEC integrates multi-point absorption and single-point mooring technology. • Simulated and experimental performances of the FABWEC are analyzed and compared. • Good stability and survivability of the FABWEC are confirmed. [ABSTRACT FROM AUTHOR]

The numerical tools can be used to facilitate the design of the railway pantograph-catenary system. The validation of the current numerical results is mostly performed at a speed slower than 350 km/h. This paper aims at the validation and analysis of the numerical results at a super-high-speed. The catenary model is constructed based on a nonlinear finite element approach employing the absolute nodal coordinate formulation. A multibody dynamics model is adopted to represent the pantograph. The measurement data are collected by an inspection vehicle equipped with an instrumented pantograph operating at 378 km/h in Chengdu-Chongqing high-speed line. Comparing the numerical simulation and the field test shows that the present pantograph-catenary model can provide reliable numerical results at 378 km/h. The numerical analysis of pantograph-catenary interaction at super-high-speed shows that the trailing pantograph performance does not comply with the assessment standard at 378 km/h. The adjustment of double-pantograph interval and messenger wire tension can effectively improve the trailing pantograph performance. [ABSTRACT FROM AUTHOR]

This paper presents analysis of the influence parameters and the procedure for determining kinematic quantities of person traveling along zipline. Zipline is consisted of tightened rope by which the person is carried by high speed travelling trolley with aim of causing increased excitement. At first sight it is a very simple system, where in the case of small lengths the problem is solved by connecting the rope ends to the pylon (e.g. existing trees) and adjusting the inclination and motion parameters on the spot. But, for quality design and safe usage of longer zipline, it is necessary to perform a detailed analysis of persons kinematic parameters dependence from a range of influential sizes such as person's weight, tensile rope force, inclination angle, position during lowering, wheel resistance, wind, etc. This is especially important in case of long span and extreme inclination angle. The calculation itself is based on the catenary theory, while the analysis are made by computer simulations for concrete conditions of zipline whose installation was planned on Fruška Gora, Serbia. The size of above mentioned significant parameters were varied and the analysis results are given through diagrams that shows the person's speed characteristics. [ABSTRACT FROM AUTHOR]

Dropper is the key component of catenary in high-speed railways. The prediction of the fatigue life of dropper is accomplished using alternating load characteristics. Simulation method for obtaining the dynamic internal load of the dropper in previous studies was insufficient for accurate requirements in predicting dropper life. According to realistic working conditions in the simulation environment, this study proposed a simulation method considering horizontal vibration behaviour for the dropper. The horizontal vibration phenomenon of a dropper was determined on the basis of observing and measuring a real high-speed railway. Moreover, a test for the reappearance of horizontal vibration in the laboratory was performed. The dropper was modelled with multibody dynamics. Finally, the horizontal vibration behaviour of the dropper on-site was reproduced in a laboratory test and computer simulation. Results demonstrated that the coefficient of association between the virtual sensor load in a simulation environment and the real sensor load in a laboratory test is 0.9578. The proposed method provides an accurate approach to simulating the load of the droppers under real working conditions. (Received in July 2019, accepted in November 2019. This paper was with the authors 1 month for 2 revisions.) [ABSTRACT FROM AUTHOR]

Steel beams with web openings are frequently used as floor and roof beams in building construction to achieve attractive, flexible and optimised design solutions for passage of services. In practical construction, such beams may be axially restrained by the surrounding structure. The presence of axial restraint can drastically change the behaviour of such beams in fire, but the behaviour of axially restrained steel beams with web opening has received little attention. This paper investigates the effects of openings on axially restrained steel beams at elevated temperatures through extensive numerical simulations. The examined parameters include opening shape, opening size and opening position, load ratio, level of axial restraint and cross-section temperature distribution profile. The results of this numerical investigation identify the key stages and quantities that should be evaluated in fire resistance design of axially restrained perforated steel beams. The simulation results show that axially restrained steel beam with web opening may enter catenary action at a much lower temperature than the commonly accepted critical temperature of the beam calculated assuming no axial restraint. This happens when the opening is slender (long and deep) and when it is placed at high bending moment regions of the beam. The effect is more severe as the level of end axial restraints increases. An important implication of this finding is that additional tensile forces may exist in such beams at the critical temperatures calculated without considering axial restraint. The results of this paper also indicate that when the maximum axial tension in the beam is reached, the top tee-section has almost zero axial force. At the same temperature, the bottom tee-section (in tension) has reached its maximum tensile capacity. Hence the maximum axial force in the beam is the same as the tensile capacity of the bottom tee-section. This finding can be used to determine the maximum tensile force against which the connections. The companion paper presents an analytical solution. [ABSTRACT FROM AUTHOR]

This paper describes the methods for the numerical simulation of pantograph–catenary interaction developed at Politecnico di Milano and implemented in the simulation software PCaDA (Pantograph–Catenary Dynamic Analysis). The paper also describes how these methods were applied in the pantograph–catenary interaction benchmark treated in this special issue and provides some evaluation of the results obtained using PCaDA in this benchmark. [ABSTRACT FROM AUTHOR]

Dynamic simulations of pantograph–catenary interaction are nowadays essential for improving the performance of railway locomotives, by achieving better current collection at higher speeds and lower wear of the collecting parts. The first step in performing these simulations is to compute the static equilibrium of the overhead line. The initial dropper lengths play an important role in hanging the contact wire at an appropriate height. From a classical point of view, if one wants to obtain the static equilibrium configuration of the system for different combinations of dropper lengths, one static problem must be solved for each combination of lengths, which involves a prohibitive computational cost. In this paper we propose a parametric model of the catenary, including the undeformed dropper lengths as extra-coordinates of the problem. This multidimensional problem is efficiently solved by means of the Proper Generalized Decomposition (PGD) technique, avoiding the curse of dimensionality issue. The capabilities and performance of the proposed method are shown by numerical examples. [ABSTRACT FROM AUTHOR]

In a column-removal scenario for a building structure, the catenary action will play an essential role for the frame in resisting a progressive collapse. This paper investigates the catenary behaviour of welded unreinforced flange-bolted web connections (i.e. WUF-B connection) in plane frames by means of full-scale testing and numerical simulation. Two different layouts of bolts at the beam web were considered, with four bolts arranged in one row or two rows in the two specimens, respectively. The results demonstrate that both specimens of the WUF-B moment connection were able to develop an effective catenary action via the bolted web following the primary flexural phase. The failure modes of the bolted web vary with different bolt arrangements under the catenary action. When all (four) bolts were arranged in one row, the lowest bolt bearing area on the web tends to be compressed to fracture before bolt tear-out failure occurs near the weld access hole. When the bolts were arranged in two rows, however, the shear tab cracked at the section across the bolt holes. The former failure mode is deemed to be more robust than the latter under a column removal scenario. [ABSTRACT FROM AUTHOR]

Dynamic compression of risers can play an important role in the structural stability of submerged pipes in catenary-like configuration. In this paper, the analytical formulation for the buckling critical load, developed in the early 2000's, is revisited and extended to cover a wider range of practical cases. A purely algebraic expression for the critical load is provided, eliminating the original formulation requirement related to solving transcendental equations, for both free and anchored risers. The analytic formulations and respective algebraic approximations are compared with numerical simulations, presenting a fairly good agreement. A discussion on the differences and similarities of each formulation ends this paper, highlighting their range of validity. Also, from the comparison, the analytical formulation developed in this work was more suitable for precise and fast determination of the critical buckling load for both riser types, rigid and flexible, and for most typical operating conditions. The proposed algebraic expressions were highly accurate and may substitute the previous analytical formulations for critical load prediction. • Risers may experience buckling due to dynamic compression at small top-end angles. • Prior formulation is improved for an algebraic way to get the buckling critical load. • The buckling critical load can be accurately predicted with just a few parameters. • The algebraic formulation obtains more accurate results, especially in severe cases. • Analytical results confirmed that risers have two mechanisms of load accommodation. [ABSTRACT FROM AUTHOR]

In this paper, a bilayer ultrathin (≈ 0. 153 λ) metalens is presented by exploring the advantage of the metasurface with catenary shape and symmetry transformation. The simulation results show that the proposed metalens has high polarization conversion efficiency (>90% even when the incidence angle is 60°), and the wide-angle beam steering ability is beyond ± 70°. Compared with the previous beam steering lens with transmitted array, the metalens in this paper exhibits obvious advantages. Moreover, the longitudinal local catenary fields existing in this metalens can ensure the wide-angle operation for this structure. • The metalenses with catenary have become a promising alternative to traditional bulky components. • We propose a novel large field of view structure based on the catenary shape. • The polarization conversion ratio (PCR) for proposed structure has been optimized over 90% by arranging the catenary elements. • When the incident angle is 60°, the maximum conversion rate can still exceed 90%. • The wide-angle beam steering ability is beyond ± 70°for proposed structure. [ABSTRACT FROM AUTHOR]

In global responses analysis for an innovative deep draft multi-spar platform, three different types of the mooring system are considered, namely a catenary, a semi-taut and a taut mooring system. These three types of mooring systems have the same arrangements with similar static restoring force characteristics. In this paper, the platform motions and mooring responses in three different water depths ranging from 500 m to 1500 m are analyzed. The coupling effects between the spar platform and its mooring lines are investigated through a numerical simulation method. Free-decay and three hours simulations under certain sea state conditions in the South China Sea are executed. The specific numerical results and analysis conclusions would be helpful for mooring system selection and motion performance study in the preliminary design. [ABSTRACT FROM AUTHOR]

• A catenary Finite Element model is enhanced by considering double cantilevers and tensioning devices. • The pantograph-catenary dynamic interaction in overlap sections is studied in a wide range of scenarios. • The effect of the tensioning devices' efficiency is analysed. • The geometry of an entire catenary section is optimised by means of Bayesian Optimisation techniques. The transition between catenary tensioning sections is accomplished smoothly by overlapping a number of spans in each catenary section. This work presents an analysis of the overlap section in a high-speed railway catenary based on numerical simulations. The paper studies the influence on the system's dynamic behaviour of features such as double cantilevers and tensioning devices efficiency. Four and five-span overlaps are compared and the effect of train speed and overlap contact wire geometry are also analysed. Finally, an entire catenary section is optimised by Bayesian Optimisation techniques, leading to a catenary configuration with an interaction force with a standard deviation notably lower than that provided by the nominal catenary design. [ABSTRACT FROM AUTHOR]