The Effects of the Longitudinal Axis of Loading upon Bending, Shear and Torsion of a Thin-Walled Cantilever Channel Beam

Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section.

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

A Non-Stationary Beam-Enabled Stochastic Channel Model and Characterization over Non-Reciprocal Beam Patterns

The multiple-input multiple-output(MIMO)-enabled beamforming technology offers great data rate and channel quality for next-generation communication.In this paper,we propose a beam channel model and enable it with time-varying simulation capability by adopting the stochastic geometry theory.First,clusters are generated located within transceivers'beam ranges based on the Mate?rn hardcore Poisson cluster process.The line-of-sight,singlebounce,and double-bounce components are calculated when generating the complex channel impulse response.Furthermore,we elaborate on the expressions of channel links based on the propagation-graph theory.A birth-death process consisting of the effects of beams and cluster velocities is also formulated.Numerical simulation results prove that the proposed model can capture the channel non-stationarity.Besides,the non-reciprocal beam patterns yield severe channel dispersion compared to the reciprocal patterns.

Monitoring of Real-Time Complex Deformed Shapes of Thin-Walled Channel Beam Structures Subject to the Coupling Between Bi-Axial Bending and Warping Torsion

Structural health monitoring(SHM)is a research focus involving a large category of techniques performing in-situ identification of structural damage,stress,external loads,vibration signatures,etc.Among various SHM techniques,those able to monitoring structural deformed shapes are considered as an important category.A novel method of deformed shape reconstruction for thinwalled beam structures was recently proposed by Xu et al.[1],which is capable of decoupling complex beam deformations subject to the combination of different loading cases,including tension/compression,bending and warping torsion,and also able to reconstruct the full-field displacement distributions.However,this method was demonstrated only under a relatively simple loading coupling cases,involving uni-axial bending and warping torsion.The effectiveness of the method under more complex loading cases needs to be thoroughly investigated.In this study,more complex deformations under the coupling between bi-axial bending and warping torsion was decoupled using the method.The set of equations for deformation decoupling was established,and the reconstruction algorithm for bending and torsion deformation were utilized.The effectiveness and accuracy of the method was examined using a thin-walled channel beam,relying on analysis results of finite element analysis(FEA).In the analysis,the influence of the positions of the measurement of surface strain distributions on the reconstruction accuracy was discussed.Moreover,different levels of measurement noise were added to the axial strain values based on numerical method,and the noise resistance ability of the deformation reconstruction method was investigated systematically.According to the FEA results,the effectiveness and precision of the method in complex deformation decoupling and reconstruction were demonstrated.Moreover,the immunity of the method to measurement noise was proven to be considerably strong.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Modeling and Free Vibration Behavior of Rotating Composite Thin-walled Closed-section Beams with SMA Fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy（SMA） fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton＇s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin＇s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.

Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section

A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of fiexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

Elastic buckling analysis and optimization of thin-walled bamboo-like pipe beam subjected to pure bending

In this paper,a stiffening design imitating the bamboo node is proposed for weight reduction of the long composite pipe beam subjected to bending load.The distribution of bamboo nodes can efficiently suppress the ovalization of the section,thus significantly improving the bending resistance of the bamboo.Based on this principle,ring stiffeners are proposed to be fixed to the pipe beam,making the long beam equivalent to the combination of a series of short pipes that suffered less section ovalization.A database of the optimal laminate orientations for different normalized lengths is obtained through optimizations,where the discreteness of the ply count is considered.Based on this database,weight optimizations are conducted,and the optimal designs of beams with and without stiffeners are obtained and compared.The comparison results show that the proposed bamboo-like stiffened beam not only regains a near-linear load–displacement relationship,but also reduces the weight by up to 16%under the same buckling load.In addition,it is found that for the pipe beams with radius-to-thickness ratios of more than 18,increasing the radius leads to a decrease in elastic buckling resistance when the weight remains a constant,which is opposite to the design for strength and stiffness.The model and database developed in this paper can provide a reference for weight reduction design and weight estimation for composite pipe beams.

Spot beam handover trigger and channel allocation scheme in GEO mobile satellite communication

An effective spot beam handover trigger and channel allocation scheme is proposed for GEO mobile satellite communication based on its characteristic and application. By using both signal strength and terminal location information, necessary handover is triggered promptly and accurately to reduce the negative effect of long signaling delay. Then handover decision is made with the handover queuing and channel allocation strategy. An adaptive channel resource allocation scheme is considered to optimize resource utilization with guarantee of emergency communication, which is significant for emergency rescue and disaster relief. Simulation results show that the proposed scheme prevents unnecessary handover effectively and has favorable adaptability to emergent requirement of satellite communication.

Wave growth rate in a cylindrical metal waveguide with ion-channel guiding of a relativistic electron beam

This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide. To derive the dispersion equations of the beam-wave interaction, it solves relativistic Lorentz equation and Maxwell＇s equations for appropriate boundary conditions. It has been found in this waveguide structure that the TM0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes. The interaction of the dispersion curves of the electromagnetic TM0m modes and the upper betatron modes is studied. The growth rates of the wave are obtained, and the effects of the beam radius, the beam energy, the plasma frequency, and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.

Focusing characteristics of the relativistic electron beam transmitting in ion channel

Based on the beam-plasma system model established in this paper,the trajectory of the electron beam in the ion channel is studied quantitatively through the envelope equation.Under different initial system parameters,the focusing transmission conditions of the beam in the ion channel are discussed.Then,a series of particle-in-cell simulations are performed,which generally versifies the theoretical results and shows some further details of the focusing behavior of the beam.It is found that the deceleration of some electrons around the focusing point or the beam-plasma interaction at the ion channel boundary will result in the generation of the residual electrons,which forms the electron return current that leads to the new instabilities influencing the focusing characteristics of the beam.

The propagation dynamics and stability of an intense laser beam in a radial power-law plasma channel

By containing ponderomotive self-channeling,the propagation behavior of an intense laser beam and the physical conditions are obtained theoretically in a radial power-law plasma channel.It is found that ponderomotive self-channeling results in the emergence of a solitary wave and catastrophic focusing,which apparently decreases the region for stable propagation in a parameter space of laser power and the ratio of the initial laser spot radius to the channel radius(RLC).Direct numerical simulation confirms the theory of constant propagation,periodic defocusing and focusing oscillations in the parameter space,and reveals a radial instability which prevents the formation of bright and dark solitary waves.The corresponding unstable critical curve is added in the parameter space numerically and the induced unstable region above the unstable critical curve covers that of catastrophic focusing,which shrinks the stable region for laser beams.For the expected constant propagation,the results reveal the need for a low RLC.Further study illustrates that the channel power-law exponent has an obvious effect on the final stable region and laser propagation,for example increasing this exponent can enlarge the stable region significantly,which is beneficial for guiding of the laser and increases the lowest RLC for constant propagation.Our results also show that the initial laser amplitude has an apparent influence on the propagation behavior.

Estimation of the Temperature in the Weld Penetration Channel in Electron Beam Welding

In this paper, the method of experimental estimation of the temperature in a penetration channel in electron beam welding is described on the basis of chemical elements concentration in the vapors above welding zone. The temperature of a vapor-gas phase in the penetration channel is determined when equating calculated and experimental concentrations of the elements.

A nonlinear explicit dynamic GBT formulation for modeling impact response of thin-walled steel members

A nonlinear explicit dynamic finite element formulation based on the generalized beam theory(GBT)is proposed and developed to simulate the dynamic responses of prismatic thin-walled steel members under transverse impulsive loads.Considering the rate strengthening and thermal softening effects on member impact behavior,a modified Cowper-Symonds model for constructional steels is utilized.The element displacement field is built upon the superposition of GBT cross-section deformation modes,so arbitrary deformations such as cross-section distortions,local buckling and warping shear can all be involved by the proposed model.The amplitude function of each cross-section deformation mode is approximated by the cubic non-uniform B-spline basis functions.The Kirchhoff s thin-plate assumption is utilized in the construction of the bending related displacements.The Green-Lagrange strain tensor and the second Piola-Kirchhoff(PK2)stress tensor are employed to measure deformations and stresses at any material point,where stresses are assumed to be in plane-stress state.In order to verify the effectiveness of the proposed GBT model,three numerical cases involving impulsive loading of the thin-walled parts are given.The GBT results are compared with those of the Ls-Dyna shell finite element.It is shown that the proposed model and the shell finite element analysis has equivalent accuracy in displacement and stress.Moreover,the proposed model is much more computationally efficient and structurally clearer than the shell finite elements.

Spatial Correlation Characteristics Analysis of Multi-Beam Channels of Mobile Satellite System

Due to the influence of scatterers around the receiving antenna, the multipath signal in satellite mobile communication systems is correlated with each other which would influence the system performance. There is no systematic standard on the channel modelling of the wideband satellite channel at present, so the study of the modelling of the wideband satellite channel is of great importance. In this paper, firstly we created a multi-beam model which can figure out the antenna gain of the nth component beam. Secondly, we combined the characteristics of multi-beam satellite channel and the distribution of the scatterers, and set up a three-dimension random channel model. This model is more realistic for satellite communication system since it considers the height of scatterers. According to the channel models, we had the formula of spatial correlation coefficient. We used the formula to calculate the relationship between spatial correlation coefficient and the interval of antennas. The result shows that the spatial correlation exists and cannot be ignored while modeling for mobile satellite system.

深厚冲积层薄基岩条件下沿空留巷支护技术研究

为解决某矿16041工作面原支护方案沿空留巷变形大、破坏严重难题,提出了顶板采用“16#槽钢梁+注浆锚索”、采空区侧采用“36U型钢+注浆锚杆”不对称耦合支护优化方案,基于理论分析研究围岩结构破坏形式,通过单元荷载法计算了留巷顶板与采空区侧围岩应力,最后开展工业性应用,验证优化后方案的合理性。研究表明:优化后支护方案顶板和采空区侧计算单元面荷载分别为351.85 kPa和206.53 kPa;注浆锚索和注浆锚杆承载力分别为263.89 kN和199.08 kN,均小于注浆锚索(锚杆)极限承载力。根据对留巷数据监测,最大顶板下沉量为35.6 mm,较原支护方案减小了1.40倍;采空区侧最大移近量为29.6 mm,与较原支护方案减小了4.13倍;最大注浆锚索承载力为253 kN,与理论计算值误差为4.1%;最大注浆锚杆承载力为174 kN,与理论计算值误差为12.6%。位移量与支护承载力均在工程允许范围内,优化后方案支护效果良好。

装配式槽钢-混凝土组合梁受弯性能研究

为研究采用螺栓连接的装配式槽钢-混凝土组合梁(PSCCB)的受弯性能,制作了7个不同宽跨比、梁高和剪切连接间距的PSCCB试件,对其进行四点弯曲测试。基于ABAQUS软件建立PSCCB有限元模型,通过试验结果验证模型的可靠性,并分析螺栓间距、螺栓预紧力、抗剪连接件间距、剪跨比、宽跨比、槽钢强度和混凝土强度对PSCCB受弯性能的影响。试验结果表明:高强度螺栓能确保PSCCB具有较高的整体性和良好的强度和延性;随着宽跨比增大,PSCCB抗弯承载力和延性分别提高8%~19%和11%~21%;穿孔钢板剪力连接件在槽钢和混凝土板之间提供高效的组合作用,部分抗剪连接与完全抗剪连接PSCCB的延性、强度、刚度差异少于10%;与梁高320 mm的PSCCB相比,梁高400 mm的PSCCB的抗弯承载力提高96%,但延性降低10%。分析结果说明:有限元分析结果与试验结果较吻合,所建立的模型能准确反映PSCCB的受弯性能;随着螺栓间距和预紧力的增大,PSCCB受弯承载力和初始刚度基本保持不变;适当增加抗剪连接程度和宽跨比能有效提升PSCCB的受弯承载力和初始刚度;增加槽钢强度能显著提高PSCCB的受弯承载力,而混凝土强度变化对其受弯承载力影响较小。根据试验和有限元参数分析,提出PSCCB受弯性能设计方法,受弯承载力和跨中挠度计算值与试验及有限元分析结果吻合良好,可为PSCCB的工程设计提供参考。

基于时间调制多波束阵列的单通道全向测向方法

基于多波束阵列的测向方法具有测向精度高的优势,但各波束都需要独立的射频通道,导致其测向系统复杂且成本高,通道之间的幅相不一致也会增大测向误差。本文提出了一种基于时间调制多波束阵列的单通道全向测向方法,通过时间调制技术将多波束阵列测向系统简化为单通道系统,利用接收信号的谐波特征获得不同波束的接收信号强度实现高精度测向,同时降低了系统的复杂度及成本。仿真结果表明在相同条件下,本文提出的方法比基于多波束阵列的多通道测向方法具有更小的测向误差。经实测验证,本文的方法在4~5 GHz频带内的测向误差小于1.3°,低于现有的多波束阵列测向误差。

Application of stiffness matrix of a beam element considering section distortion effect

According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.