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Sandwich structures with tapered tubes as core:A quasi-static investigation
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作者 Xinmei Xiang Dehua Shao +5 位作者 Xin Zhang Umer Sharif Ngoc San Ha Li Xiang Jing Zhang Jiang Yi 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第3期447-462,共16页
In this article,the experimental and finite element analysis is utilized to investigate the quasi-static compression features of sandwich constructions built with tapered tubes.3D printing technology was utilized to c... In this article,the experimental and finite element analysis is utilized to investigate the quasi-static compression features of sandwich constructions built with tapered tubes.3D printing technology was utilized to create the hollow centers of the tapering tubes,with and without corrugations.The results demonstrate that the energy absorption(EA)and specific energy absorption(SEA)of the single corrugated tapered tube sandwich are 51.6% and 19.8% higher,respectively,than those of the conical tube sandwich.Furthermore,the results demonstrate that energy absorbers can benefit from corrugation in order to increase their efficiency.Additionally,the tapered corrugated tubes'resistance to oblique impacts was studied.Compared to a straight tube,the tapered tube is more resistant to oblique loads and has a lower initial peak crushing force(PCF),according to numerical simulations.After conducting a parametric study,it was discovered that the energy absorption performance of the sandwich construction is significantly affected by the amplitude,number of corrugations,and wall thickness.EA and SEA of DTS with corrugation number of 8 increased by 17.4%and 29.6%,respectively,while PCF decreased by 9.2% compared to DTS with corrugation number of 10. 展开更多
关键词 Sandwich structure Corrugated tube Tapered tube QUASI-STATIC Energy absorption
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A novel slotted helix slow-wave structure for high power Ka-band traveling-wave tubes 被引量:1
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作者 刘鲁伟 魏彦玉 +8 位作者 王少萌 侯艳 殷海荣 赵国庆 段兆云 徐进 宫玉彬 王文祥 杨明华 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第10期593-597,共5页
A novel slotted helix slow-wave structure (SWS) is proposed to develop a high power, wide-bandwidth, and high reliability millimeter-wave traveling-wave tube (TWT). This novel structure, which has higher heat capa... A novel slotted helix slow-wave structure (SWS) is proposed to develop a high power, wide-bandwidth, and high reliability millimeter-wave traveling-wave tube (TWT). This novel structure, which has higher heat capacity than a conven- tional helix SWS, evolves from conventional helix SWS with three parallel rows of rectangular slots made in the outside of the helix tape. In this paper, the electromagnetic characteristics and the beam-wave interaction of this novel structure operating in the Ka-band are investigated. From our calculations, when the designed beam voltage and beam current are set to be 18.45 kV and 0.2 A, respectively, this novel circuit can produce over 700-W average output power in a frequency range from 27.5 GHz to 32.5 GHz, and the corresponding conversion efficiency values vary from 19% to 21.3%, and the maximum output power is 787 W at 30 GHz. 展开更多
关键词 slotted helix slow-wave structure MILLIMETER-WAVE traveling-wave tube beam-wave interaction
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Performance-based global reliability assessment of a high-rise frame-core tube structure subjected to multi-dimensional stochastic earthquakes 被引量:2
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作者 Liu Zhangjun Ruan Xinxin Liu Zixin 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2022年第2期395-415,共21页
When evaluating the seismic safety and reliability of complex engineering structures,it is a critical problem to reasonably consider the randomness and multi-dimensional nature of ground motions.To this end,a proposed... When evaluating the seismic safety and reliability of complex engineering structures,it is a critical problem to reasonably consider the randomness and multi-dimensional nature of ground motions.To this end,a proposed modeling strategy of multi-dimensional stochastic earthquakes is addressed in this study.This improved seismic model has several merits that enable it to better provide seismic analyses of structures.Specifically,at first,the ground motion model is compatible with the design response spectrum.Secondly,the evolutionary power spectrum involved in the model and the design response spectrum are constructed accordingly with sufficient consideration of the correlation between different seismic components.Thirdly,the random function-based dimension-reduction representation is applied,by which seismic modeling is established,with three elementary random variables.Numerical simulations of multi-dimensional stochastic ground motions in a specific design scenario indicate the effectiveness of the proposed modeling strategy.Moreover,the multi-dimensional seismic response and the global reliability of a high-rise frame-core tube structure is discussed in detail to further illustrate the engineering applicability of the proposed method.The analytical investigations demonstrate that the suggested stochastic model of multi-dimensional ground motion is available for accurate seismic response analysis and dynamic reliability assessment of complex engineering structures for performance-based seismic resistance design. 展开更多
关键词 multi-dimensional stochastic ground motion dimension-reduction representation frame-core tube structure global dynamic reliability performance-based seismic design
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Nonlinear seismic response analysis of reinforced concrete tube in tube structure 被引量:1
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作者 WANG Hai-bo SHEN Pu-sheng 《Journal of Central South University of Technology》 2005年第z1期183-188,共6页
Super-highly reinforced concrete tube in tube structure is a developing structure system of high-rise building. The more reasonable derivation process of the multi-vertical-line-element model stiffness matrix is given... Super-highly reinforced concrete tube in tube structure is a developing structure system of high-rise building. The more reasonable derivation process of the multi-vertical-line-element model stiffness matrix is given.On the premise of pointing out the problems of present multi-spring element model, combined with present multivertical-line-element model for analyzing on shear wall, the model is expanded to spatial one, and the stiffness matrix of which is derived. Combined with hysteretic axial model and hysteretic shear model, it is suitable for columns,wall limbs and beams with all kinds of section form. Some examples are calculated and compared with test results,which shows that the models have relatively good accuracy. On the base of the experimental phenomenon and failure mechanism for tube in tube structure specimen, nonlinear seismic responses analysis program on the basis of the advantaged element model for tube in tube structure is developed. Calculation results are in good agreement with those of the pseudo-dynamic tests and the failure mechanism can be well reflected. 展开更多
关键词 tube in tube structure of reinforced concrete SEISMIC responses nonlinear analysis multi-vertical-lineelement model multi-spring element PSEUDO-DYNAMIC test
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THEORETICAL STUDY ON THE BIFURCATION OF VORTEXES STRUCTURE FOR FLOW IN CURVED TUBE
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作者 吴望一 谭文长 +1 位作者 李娟 谢文俊 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第12期1345-1358,共14页
The number and distribution of the singular points of streamlines in the cross-section of steady flow through a curved tube ate discussed by using the method of topological structure analysis. And a theoretical criter... The number and distribution of the singular points of streamlines in the cross-section of steady flow through a curved tube ate discussed by using the method of topological structure analysis. And a theoretical criterion is obtained for the bifurcation of flow vortexes for the secondary flow turning from two-vortex structure into four-vortex structure. Furthermore, the critical Dean number for bifurcation and the semi-analytical expressions of stream function and axial velocity are given by using Galerkin technique. The result of calculation is consistent with the theoretical criterion. 展开更多
关键词 curved tube steady flow BIFURCATION topological structure Galerkin technique
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Seismic behavior of concrete filled steel tubular arch structures 被引量:4
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作者 熊峰 Sashi K Kunnath 刘浩吾 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2005年第1期107-115,共9页
Shaking table tests of a 1:10 scale arch model performed to investigate the seismic behavior and resistance of concrete filled steel tubular (CFT) arch structures are described in this paper. The El-Centro record and ... Shaking table tests of a 1:10 scale arch model performed to investigate the seismic behavior and resistance of concrete filled steel tubular (CFT) arch structures are described in this paper. The El-Centro record and Shanghai artificial wave were adopted as the input excitation. The entire test process can be divided into three stages depending on the lateral brace configurations, i.e., fully (five) braced, two braces removed, and all braces removed. A total of 46 tests, starting from the elastic state to failure condition, have been conducted. The natural vibration frequencies, responses of acceleration, displacement and strain were measured. From the test results, it is demonstrated that the CFT arch structures are capable of resisting severe ground motions and that CFT arches offer a credible alternative to reinforced concrete arches, especially in regions of high seismic intensity. 展开更多
关键词 concrete filled steel tube arch structures shaking table test seismic behavior lateral braces
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Crashworthiness Design and Multi-Objective Optimization for Bio-Inspired Hierarchical Thin-Walled Structures 被引量:5
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作者 Shaoqiang Xu Weiwei Li +2 位作者 Lin Li Tao Li Chicheng Ma 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第5期929-947,共19页
Thin-walled structures have been used in many fields due to their superior mechanical properties.In this paper,two types of hierarchical multi-cell tubes,inspired by the self-similarity of Pinus sylvestris,are propose... Thin-walled structures have been used in many fields due to their superior mechanical properties.In this paper,two types of hierarchical multi-cell tubes,inspired by the self-similarity of Pinus sylvestris,are proposed to enhance structural energy absorption performance.The finite element models of the hierarchical structures are established to validate the crashworthiness performance under axial dynamic load.The theoreticalmodel of themean crushing force is also derived based on the simplified super folded element theory.The finite element results demonstrate that the energy absorption characteristics and deformation mode of the bionic hierarchical thin-walled tubes are further improved with the increase of hierarchical sub-structures.It can be also obtained that the energy absorption performance of corner self-similar tubes is better than edge self-similar tubes.Furthermore,multiobjective optimization of the hierarchical tubes is constructed by employing the response surface method and genetic algorithm,and the corresponding Pareto front diagram is obtained.This research provides a new idea for the crashworthiness design of thin-walled structures. 展开更多
关键词 Bionic structure crashworthiness design hierarchical tube multi-objective optimization
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Thermal Structure of Glass Fiber Reinforce Plastic Support Structure 被引量:2
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作者 刘康 汪荣顺 +1 位作者 石玉美 顾安忠 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第3期370-374,共5页
The assembled form of thick-wall glass fiber reinforced plastics (GFRP) tube and 0Cr18Ni9 austenitic stainless steel pipes was designed as the radius thermal-insulating and load-supporting structure in cryogenic vesse... The assembled form of thick-wall glass fiber reinforced plastics (GFRP) tube and 0Cr18Ni9 austenitic stainless steel pipes was designed as the radius thermal-insulating and load-supporting structure in cryogenic vessels. In order to study the thermal leakage and gap changes on the support structure, as well as radius temperature and stress distribution on GFRP tube, an experimental investigation has been taken. The results indicate that the support structure is proved to fit well as thermal-insulating and load-supporting part in cryo-genic vessels, furthermore has high security during cryogenic applications. 展开更多
关键词 glass fiber reinforced plastics (GFRP) tube support structure CRYOGENIC temperature stress
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STRESS ANALYSIS OF RING STIFFENED TUBULAR JOINTS FOR OFFSHORE STRUCTURES——REVIEW OF STUDIES IN CHINA
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作者 Chen, Bozhen 《China Ocean Engineering》 SCIE EI 1990年第1期1-12,共12页
In China, the stress analysis of tubular joints for offshore structures was started at the end of 1970's. In addition to simple joints, the ring stiffened tubular joint have been analyzed recently. In this paper, ... In China, the stress analysis of tubular joints for offshore structures was started at the end of 1970's. In addition to simple joints, the ring stiffened tubular joint have been analyzed recently. In this paper, the author reviews the research work of stress analysis of ring stiffened joints, including brief introduction to the methods used, stress concentration behaviour, effects of ring stiffeners' number, location, dimension, type and stress distribution of ring stiffeners. Emperical formulae for predicting SCF of ring stiffened joints are also presented. 展开更多
关键词 Offshore structures Stresses ANALYSIS tubeS Stresses
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Application of color structured light pattern to measurement of large out-of-plane deformation
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作者 Xing Lu Jun-Hong Zhou Dong-Dong Liu Jue Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第6期1098-1104,共7页
Measurement of out-of-plane deformation is significant to understanding of the deflection mechanisms of the plate and tube structures.In this study,a new surface contouring technique with color structured light is app... Measurement of out-of-plane deformation is significant to understanding of the deflection mechanisms of the plate and tube structures.In this study,a new surface contouring technique with color structured light is applied to measure the out-of-plane deformation of structures with one-shot projection.Through color fringe recognizing,decoding and triangulation processing for the captured images corresponding to each deformation state,the feasibility of the method is testified by the measurement of elastic deflections of a flexible square plate,showing good agreement with those from the calibrated displacement driver.The plastic deformation of two alloy aluminum rectangular tubes is measured to show the technique application to surface topographic evaluation of the buckling structures with large displacements. 展开更多
关键词 Out-of-plane deformation Surface contouring Color structured light Plate deflection - Rectangular tube buckling
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Effects of Heat Exchange Tube Structural Parameters on Performance of Vehicle Radiator
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作者 Zeyan Liu Xilei Kong +3 位作者 Xiaobiao Han Hui Liu Quanzhen Wang Zhenling Wang 《Journal of Power and Energy Engineering》 2020年第9期1-7,共7页
In order to improve the performance of vehicle radiators, a two-dimensional heat transfer steady-state model of the radiator was set up. The influence of the structural parameters (axial ratio) of the heat exchange tu... In order to improve the performance of vehicle radiators, a two-dimensional heat transfer steady-state model of the radiator was set up. The influence of the structural parameters (axial ratio) of the heat exchange tube on the windward side on the heat transfer performance of the radiator was studied. With the increase of the axial ratio of the heat exchange tube on the windward side, the heat exchange capacity of the heat exchange tube surface slightly decreases. The heat exchange area increases significantly, which increases the total heat exchange of the radiator and improves the heat transfer performance of the radiator. When the axial ratio increases from 1.0 to 2.0, the average surface heat transfer capacity decreases from 5664.16</span><span style="font-family:""> </span><span style="font-family:Verdana;">W/m<sup>2</sup> to 5623.57</span><span style="font-family:""> </span><span style="font-family:Verdana;">W/m<sup>2</sup>. 展开更多
关键词 Vehicle Radiator Heat Transfer Performance Heat Exchange tube structure Parameters Axial Ratio
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Research on the Characteristic of the Disk-Loaded Waveguide, Rib-Loaded Disk-Loaded Waveguide and Helix Slow-Wave Structures
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作者 ZHANGYong 《Journal of Electronic Science and Technology of China》 2005年第2期188-189,共2页
关键词 traveling wave tube disk-loaded waveguide HELIX slow-wave structure dispersion characteristics interaction impedance plasma filled computer simulation rib-loaded hybrid mode
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预应力拱形管桁架中索的位置对结构的影响分析
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作者 汪可 于文静 《山西建筑》 2025年第2期48-51,76,共5页
在大跨度空间结构中,预应力管桁架是一种常用的结构形式,由于预应力索的引入,能够最大限度优化结构内力,增大结构竖向刚度,减小支座水平推力。而索的位置是否合理,直接影响到结构整体受力的合理性以及用钢量的大小。以重庆某预应力管桁... 在大跨度空间结构中,预应力管桁架是一种常用的结构形式,由于预应力索的引入,能够最大限度优化结构内力,增大结构竖向刚度,减小支座水平推力。而索的位置是否合理,直接影响到结构整体受力的合理性以及用钢量的大小。以重庆某预应力管桁架料场大棚为例,通过在有限范围内调整索的位置,选取多个结构控制指标进行对比,研究计算结果对结构整体的影响,从而确定较为合理的索布置。分析结果表明,以反弯点处为基准,索的位置向上调整,则支座反力和挠度增大,最大杆内力也会相应变大,实际工程中,索的位置建议根据结构的外形,通过单线模型先确定反弯点高度,结合工艺的要求,在此位置上下1至2个节间范围内为宜。 展开更多
关键词 预应力索 管桁架 空间结构 跨中挠度
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A staggered double vane circuit for a W-band traveling-wave tube amplifier 被引量:1
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作者 赖剑强 魏彦玉 +4 位作者 刘洋 黄民智 唐涛 王文祥 宫玉彬 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第6期548-553,共6页
Based on the combination of a staggered double vane slow wave structure (SWS) and round electron beam, a 200-W W-band traveling-wave tube (TWT) amplifier is studied in this paper. The main advantages of round beam... Based on the combination of a staggered double vane slow wave structure (SWS) and round electron beam, a 200-W W-band traveling-wave tube (TWT) amplifier is studied in this paper. The main advantages of round beam operation over the sheet beam is that the round beam can be formed more easily and the focus requirement can be dramatically reduced. It operates in the fundamental mode at the first spatial harmonic. The geometric parameters are optimized and a transition structure for the slow wave circuit is designed which can well match the signal that enters into and goes out from the tube. Then a TWT model is established and the particle-in-cell (PIC) simulation results show that the tube can provide over 200-W output power in a frequency range of 88 GHz-103 GHz with a maximum power of 289 W at 95 GHz, on the assumption that the input power is 0.1 W and the beam power is 5.155 kW. The corresponding conversion efficiency and gain at 95 GHz are expected to be 5.6% and 34.6 dB, respectively. Such amplifiers can potentially be used in high power microwave-power-modules (MPM) and for other portable applications. 展开更多
关键词 traveling-wave tube staggered double vane slow wave structure W-BAND
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Numerical Simulation and Optimization of Perforated Tube Trolley in Circular Cooler 被引量:1
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作者 Bin Wu Kunrong Huang +1 位作者 Defan Qing Maokui Zhu 《World Journal of Engineering and Technology》 2017年第4期684-695,共12页
Three symmetrically perforated tubes were arranged in the circular cooler trolley as auxiliary cooling inlet to improve the cooling performance of the sintered body during the production process. Fluent 15.0 has been ... Three symmetrically perforated tubes were arranged in the circular cooler trolley as auxiliary cooling inlet to improve the cooling performance of the sintered body during the production process. Fluent 15.0 has been used to simulate the process;the study shows that the perforated tube structure trolley has changed the temperature field within the sintering area, thereby improving the sintering area of the cooling effect and uniformity, also greatly reducing the cooling time. Compared with the traditional trolley, the best structure of the porous tube trolley has reduced 41% cooling time and increased 50% waste heat recovery. 展开更多
关键词 CIRCULAR COOLER Perforated tube structural Optimization COOLING Performance ORTHOGONAL Test
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Formation mechanism of external finned tubes by extrusion-plough method 被引量:4
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作者 汤勇 陆龙生 +2 位作者 潘敏强 刘小康 刘晓晴 《中国有色金属学会会刊:英文版》 CSCD 2006年第A02期283-288,共6页
关键词 挤压-犁切法 外翅管 成型 机理
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Design of a re-entrant double-staggered ladder circuit for V-band coupled-cavity traveling-wave tubes
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作者 刘洋 徐进 +6 位作者 赖剑强 许雄 沈飞 魏彦玉 黄民智 唐涛 宫玉彬 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第7期291-297,共7页
The re-entrant double-staggered ladder slow-wave structure is employed in a high-power V-band coupled-cavity traveling-wave tube. This structure has a wide bandwidth, a moderate interaction impedance, and excellent th... The re-entrant double-staggered ladder slow-wave structure is employed in a high-power V-band coupled-cavity traveling-wave tube. This structure has a wide bandwidth, a moderate interaction impedance, and excellent thermal dissipation properties, as well as easy fabrication. A well-matched waveguide coupler is proposed for the structure. Combining the design of attenuators, a full-scale three-dimensional circuit model for the V-band coupled-cavity traveling- wave tube is constructed. The electromagnetic characteristics and the beam wave interaction of this structure are investigated. The beam current is set to be 100 mA, and the cathode voltage is tuned from 16.8 kV to 15.8 kV. The calculation results show that this tube can produce a saturated average output power over 100 W with an instantaneous bandwidth greater than 1.25 GHz in the frequency ranging from 58 GHz to 62 GHz. The corresponding gain and electronic efficiency can reach over 32 dB and 6.5%, respectively. 展开更多
关键词 coupled-cavity traveling-wave tube V band re-entrant double-staggered ladder slow-wave structure
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An open-styled dielectric-lined azimuthally periodic circular waveguide for a millimeter wave traveling-wave tube
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作者 刘漾 魏彦玉 +4 位作者 徐进 殷海荣 岳玲娜 宫玉彬 王文祥 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第4期597-604,共8页
An open-styled dielectric-lined azimuthMly periodic circular waveguide (ODLAP-CW) for a millimeter-wave traveling-wave tube (TWT) is proposed, which is a modified form of a dielectric-lined azimuthally periodic ci... An open-styled dielectric-lined azimuthMly periodic circular waveguide (ODLAP-CW) for a millimeter-wave traveling-wave tube (TWT) is proposed, which is a modified form of a dielectric-lined azimuthally periodic circular waveguide (DLAP-CW). The slow-wave characteristics of the open-styled DLAP-CW are studied by using the spatial harmonics method, which includes normalized phase velocity and interaction impedance. The complicated dispersion equations are numerically solved with MATLAB and the results are in good agreement with the simulation results obtained from HFSS. The influence of structural parameters on the RF properties is investigated based on our theory. The numerical results show that the optimal thickness of the metal rod can increase the interaction impedance, with the dielectric constant held fixed. Finally, the slow-wave characteristics and transmission properties of an open-styled structure are compared with those of the DLAP-CW. The results validate that the mode competition is eliminated in the improved structure with only a slight influence on the dispersion characteristics, which may significantly improve the stability of an open-styled DLAP-CW-based TWT, and the interaction efficiency is also improved. 展开更多
关键词 dispersion characteristics slow-wave structure millimeter wave traveling-wave tube spa- tial harmonics method
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A comparative crashworthiness analysis of multi-cell polygonal tubes under axial and oblique loads
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作者 邹翔 高广军 +3 位作者 张洁 周细赛 陈威 关维元 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第9期2198-2208,共11页
In order to investigate the energy absorption characteristics of multi-cell polygonal tubes with different cross-sectional configurations,firstly,the theoretical formulae of the mean crushing force under axial load fo... In order to investigate the energy absorption characteristics of multi-cell polygonal tubes with different cross-sectional configurations,firstly,the theoretical formulae of the mean crushing force under axial load for four multi-cell polygonal tubes were derived by combining the Super Folding Element theory with Zhang’s research results.These formulae can be used to validate the numerical model and quickly evaluate the energy absorption ability of multi-cell polygonal tubes.Furthermore,a comparative study on the energy absorption performance of eight multi-cell polygonal tubes under axial and oblique loads was conducted.The results show that all tubes have a stable mixed deformation mode under axial load.The multi-cell decagon tube has better energy-absorption ability compared with other tubes.Whenθis less than 10°,all the tubes maintain a stable deformation mode,and the multi-cell decagon tube also has the biggest crushing force efficiency and specific energy absorption among these eight tubes;meanwhile compared with the results atθ=0°,the specific energy absorption of all tubes decreases by about 8%-21%,while the crushing force efficiency increases by 20%-56%.However,at large angles 20°and 30°,all of the tubes collapse in bending modes and lose their effectiveness at energy absorption. 展开更多
关键词 multi-cell polygonal tubes thin-walled structure axial load oblique load energy absorption mean crushing force
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Ductility and Ultimate Capacity of Concrete-Filled Lattice Rectangular Steel Tube Columns
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作者 Chengquan Wang Yun Zou +3 位作者 Tianqi Li Jie Ding Xiaoping Feng Tiange Lei 《Structural Durability & Health Monitoring》 EI 2018年第2期99-110,共12页
A kind of concrete-filled lattice rectangular steel tube(CFLRST)column was put forward.The numerical simulation was modeled to analyze the mechanical characteristic of CFLRST column.By comparing the load-deformation c... A kind of concrete-filled lattice rectangular steel tube(CFLRST)column was put forward.The numerical simulation was modeled to analyze the mechanical characteristic of CFLRST column.By comparing the load-deformation curves from the test results,the rationality and reliability of the finite element model has been confirmed,moreover,the change of the section stiffness and stress in the forcing process and the ultimate bearing capacity of the column were analyzed.Based on the model,the comparison of ultimate bearing capacity and ductility between CFLRST column and reinforced concrete(RC)column were also analyzed.The results of the finite element analysis show that the loading process of CFLRST column consists of elastic stage,yield stage and failure stage.The failure modes are mainly strength failure and failure of elastoplastic instability.CFLRST column has higher bearing capacities in comparison with reinforced concrete columns with the same steel ratio.In addition,the stiffness degeneration of CFLRST column is slower than RC column and CFLRST column has good ductility. 展开更多
关键词 Steel-concrete composite structure concrete-filled lattice rectangular steel tube column nonlinear finite element ultimate strength DUCTILITY
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