Limits of Riemann Solutions for Isentropic MHD in a Variable Cross-Section Duct as Magnetic Field Vanishes

The stability for magnetic field to the solution of the Riemann problem for the polytropic fluid in a variable cross-section duct is discussed.By the vanishing magnetic field method,the stable solutions are determined by comparing the limit solutions with the solutions of the Riemann problem for the polytropic fluid in a duct obtained by the entropy rate admissibility criterion.

Analysis of the mass of behind-armor debris generated by RHA subjected to normal penetration of variable cross-section EFP

Analyzing the mass of behind-armor debris (BAD) generated by Rolled Homogeneous Armor (RHA) subjected to normal penetration of variable cross-section Explosively Formed Projectile (EFP) is the purpose of this paper. So theoretical analysis, numerical simulation and experimental data are combined to analyze the influence of variable cross-section characteristic on the time history of crater radius. Moreover the relationships between time history of crater radius (as well as mass of BAD) and the thickness of RHA (from 30mm to 70 mm) and the impact velocity of EFP (1650 m/s to 1860 m/s) are also investigated. The results indicate that: 1) being compared to the variable cross-section characteristic is ignored, the theoretical time history of crater radius is in better agreement with the simulation results when the variable cross-section characteristic is considered;2) being compared to the other three conditions of plug, the theoretical mass of BAD is in the best agreement with the simulation results when the shape of plug is frustum of a cone and the angle between generatrix and bottom is 45- and the axial length of mushroom is considered.

Equivalent bending stiffness of simply supported preflex beam bridge with variable cross-section

In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, preflex beam with alterative web depth and preflex beam with aherative steel flange thickness, are dis- cussed on how to achieve the equivalent moment of inertia and Young＇ s modulus. Additionally, methods of cal- culating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Study of the Bearing Capacity at the Variable Cross-Section of A Riser- Surface Casing Composite Pile

Reducing the cost of offshore platform construction is an urgent issue for marginal oilfield development.The offshore oil well structure includes a riser and a surface casing.The riser,surface casing and oil well cement can be considered special variable cross-section piles.Replacing or partially replacing the steel pipe pile foundation with a variable cross-section pile to provide the required bearing capacity for an offshore oil platform can reduce the cost of foundation construction and improve the economic efficiency of production.In this paper,the finite element analysis method is used to investigate the variable cross-section bearing mode of composite piles composed of a riser and a surface casing in saturated clay under a vertical load.The calculation formula of the bearing capacity at the variable section is derived based on the theory of spherical cavity expansion,the influencing factors of the bearing capacity coefficient N_(c) are revealed,and the calculation method of N_(c) is proposed.By comparing the calculation results with the results of the centrifuge test,the accuracy and applicability of the calculation method are verified.The results show that the riser composite pile has a rigid core in the soil under the variable cross-section,which increases the bearing capacity at the variable cross-section.

The development of real time data driving multi-axis linkage and synergic movement control system of 3D variable cross-section roll forming machine

The three dimensional variable cross-section roll forming is a kind of new metal forming technol- ogy which combines large forming force, multi-axis linkage movement and space synergic movement, and the sequential synergic movement of the ganged roller group is used to complete the metal sheet forming according to the shape of the complicated and variable forming part data. The control system should meet the demands of quick response to the test requirements of the product part. A new kind of real time data driving multi-axis linkage and synergic movement control strategy of 3D roll forming is put forward in the paper. In the new control strategy, the forming data are automatically generated according to the shape of the parts, and the multi-axis linkage movement together with cooperative motion among the six stands of the 3D roll forming machine is driven by the real-time information, and the control nodes are also driven by the forming data. The new control strategy is applied to a 48 axis 3D roll forming machine developed by our research center, and the control servo period is less than 10ms. A forming experiment of variable cross section part is carried out, and the forming preci- sion is better than ＋ 0.5mm by the control strategy. The result of the experiment proves that the control strategy has significant potentiality for the development of 3D roll forming production line with large scale, multi-axis ganged and svner^ic movement

CFD-Based Numerical Analysis of a Variable Cross-Section Cylinder

Using ANSYS-CFX, a general purpose fluid dynamics program, the vortex-induced vibration(VIV) of a variable cross-section cylinder is simulated under uniform current with high Reynolds numbers. Large eddy simulation(LES) is conducted for studying the fluid-structure interaction. The vortex shedding in the wake, the motion trajectories of a cylinder, the variation of drag and lift forces on the cylinder are analyzed. The results show that the vortices of variable cross-section cylinder are chaotic and are varying along the cylinder. In places where cross-sections are changing significantly, the vortices are more irregular. The motion trail of the cylinder is almost the same but irregular. The drag and lift coefficients of the cylinder are varying with the changes of diameters.

In-Plane Impact Dynamics Analysis of Re-Entrant Honeycomb with Variable Cross-Section

Due to the unique deformation characteristics of auxetic materials(Poisson’s ratioμ<0),they have better shock resistance and energy absorption properties than traditional materials.Inspired by the concept of variable crosssection design,a new auxetic re-entrant honeycomb structure is designed in this study.The detailed design method of re-entrant honeycomb with variable cross-section(VCRH)is provided,and five VCRH structures with the same relative density and different cross-section change rates are proposed.The in-plane impact resistance and energy absorption abilities of VCRH under constant velocity are investigated by ABAQUS/EXPLICIT.The results show that the introduction of variable cross-section design can effectively improve the impact resistance and energy absorption abilities of auxetic re-entrant honeycombs.The VCRH structure has better Young’s modulus,plateau stress,and specific energy absorption(SEA)than traditional re-entrant honeycomb(RH).The influence of microstructure parameters(such as cross-section change rateα)on the dynamic impact performance of VCRH is also studied.Results show that,with the increase in impact velocity andα,the plateau stress and SEA of VCRH increase.A positive correlation is also found between the energy absorption efficiency,impact load uniformity andαunder both medium and high impact speeds.These results can provide a reference for designing improved auxetic re-entrant honeycomb structures.

Dynamic symmetry breaking and structure-preserving analysis on thelongitudinal wave in an elastic rod with a variable cross-section

The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background,in which the longitudinal wave dissipation determines some important performances of the slender structure.To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section,a structure-preserving approach is developed based on the dynamic symmetry breaking theory.For the dynamic model controlling the longitudinal wave propagating in the elastic rod with the variable cross-section,the approximate multi-symplectic form is deduced based on the multi-symplectic method,and the expression of the local energy dissipation for the longitudinal wave propagating in the rod is presented,referring to the dynamic symmetry breaking theory.A structure-preserving method focusing on the residual of the multi-symplectic structure and the local energy dissipation of the dynamic model is constructed by using the midpoint difference discrete method.The longitudinal wave propagating in an elastic rod fixed at one end is simulated,and the local/total energy dissipations of the longitudinal wave are investigated by the constructed structure-preserving scheme in two typical cases in detail.

Numerical Analysis of Flow-Induced Vibration and Noise Generation in a Variable Cross-Section Channel

Flow channels with a variable cross-section are important components of piping system and are widely used in variousfields of engineering.Using afinite element method and modal analysis theory,flow-induced noise,mode shapes,and structure-borne noise in such systems are investigated in this study.The results demonstrate that the maximum displacement and equivalent stress are located in the part with variable cross-sectional area.The aver-age excitation force on theflow channel wall increases with theflow velocity.The maximum excitation force occurs in the range of 0–20 Hz,and then it decreases gradually in the range of 20–1000 Hz.Additionally,as theflow velocity rises from 1 to 3 m/s,the overall sound pressure level associated with theflow-induced noise grows from 49.37 to 66.37 dB.Similarly,the overall sound pressure level associated with the structure-borne noise rises from 40.27 to 72.20 dB.When theflow velocity is increased,the increment of the structure-borne noise is higher than that of theflow-induced noise.

THE APPROXIMATE ANALYTICAL SOLUTION FOR THE BUCKLING LOADS OF A THIN-WALLED BOX COLUMN WITH VARIABLE CROSS-SECTION

For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.

Simulation of Variable Air Volume System with Different Duct Layout

The duct static pressure reset (DSPR) control method is a popular modern control method widely applied to variable air volume (VAV) systems of commercial buildings. In this paper, a VAV system simulation program was used to predict the system performance and zone air temperature of two kinds of layouts that were applied to a typical floor of an existing building office in Hong Kong. The position where the static pressure sensor was placed should affect the zones temperature and energy consumption. The comparison of predictions of the two kinds of layouts indicates that with the same DSPR control method the layout of the air duct might influence the fan control result and energy savings.

Optimal Cross-Sectional Shape of Gas/Air Ducts

In industrial plants, ships, and buildings, a large amount of gas and air ducts are applied for equipment connection, HVAC, medium transport, and exhaust, etc. These ducts can be designed in varied cross-sectional shapes, such as round or rectangle. The author reveals through geometric calculation of the duct cross-sectional shapes and engineering experiences that the round cross-section is an optimal shape in the duct system. The round duct has the shorter perimeter than the other cross-sectional shape ducts and the stronger structure in the same working condition. The material saving of the round duct due to the shorter perimeter is quantitatively determined. In the pater, it is shown that the round duct is economically attractive. The economic analysis for the material cost saving is illustrated by an example. For a long duct system, the material and material cost savings are significant. It is suggested that the round duct in the gas and air duct system should have priority as long as the field conditions are allowed. In the paper, the material cost saving is also converted to PW, AW, and FW used for LCC economic analysis.

Failure analysis and control technology of intersections of large‑scale variable cross‑section roadways in deep soft rock

In deep underground mining,achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge.Owing to the coupling action of multiple factors such as deep high stress,adjacent faults,cross-layer design,weak lithology,broken surrounding rock,variable cross-sections,wide sections up to 9.9 m,and clusters of nearby chambers,there was severe deformation and breakdown in the No.10 intersection of the roadway of large-scale variable cross-section at the−760 m level in a coal mine.As there are insufcient examples in engineering methods pertaining to the geological environment described above,the numerical calculation model was oversimplifed and support theory underdeveloped;therefore,it is imperative to develop an efective support system for the stability and sustenance of deep roadways.In this study,a quantitative analysis of the geological environment of the roadway through feld observations,borehole-scoping,and ground stress testing is carried out to establish the FLAC 3D variable cross-section crossing roadway model.This model is combined with the strain softening constitutive(surrounding rock)and Mohr–Coulomb constitutive(other deep rock formations)models to construct a compression arch mechanical model for deep soft rock,based on the quadratic parabolic Mohr criterion.An integrated control technology of bolting and grouting that is mainly composed of a high-strength hollow grouting cable bolt equipped with modifed cement grouting materials and a high-elongation cable bolt is developed by analyzing the strengthening properties of the surrounding rock before and after bolting,based on the Heok-Brown criterion.As a result of on-site practice,the following conclusions are drawn:(1)The plastic zone of the roof of the cross roadway is approximately 6 m deep in this environment,the tectonic stress is nearly 30 MPa,and the surrounding rock is severely fractured.(2)The deformation of the roadway progressively increases from small to large cross-sections,almost doubling at the largest cross-section.The plastic zone is concentrated at the top plate and shoulder and decreases progressively from the two sides to the bottom corner.The range of stress concentration at the sides of the intersection roadway close to the passageway is wider and higher.(3)The 7 m-thick reinforced compression arch constructed under the strengthening support scheme has a bearing capacity enhanced by 1.8 to 2.3 times and increase in thickness of the bearing structure by 1.76 times as compared to the original scheme.(4)The increase in the mechanical parameters c andφof the surrounding rock after anchoring causes a signifcant increase inσt;the pulling force of the cable bolt beneath the new grouting material is more than twice that of ordinary cement grout,and according to the test,the supporting stress feld shows that the 7.24 m surrounding rock is compacted and strengthened in addition to providing a strong foundation for the bolt(cable).On-site monitoring shows that the 60-days convergence is less than 30 mm,indicating that the stability control of the roadway is successful.

Research of Elastic and Elastic-Plastic Deformation on Bending Problems of Variable Stiffness Beams

A novel variable stiffness model was proposed for analyzing elastic-plastic bending problems with arbitrary variable stiffness in detail.First,it was assumed that the material of a rectangular beam is an ideal isotropic elastic-plastic material,whose elastic modulus,yield strength,and section height are functions of the axial coordinates of the beam respectively.Considering the effect of shear on the deformation of the beam,the elastic and elastic-plastic bending problems of the axially variable stiffness beam were studied.Then,the analytical solutions of the elastic and elastic-plastic deformation of the beam were derived when the cross-section height and the elastic modulus of the material were varied by special function along the length of the beam respectively.The elastic and elastic-plastic analysis of the variable stiffness beam was carried out using Differential Quadrature Method(DQM)when the bending stiffness varied arbitrarily.The influence of the axial variation of the bending stiffness on the elastic and elastic-plastic deformation of the beam was analyzed by numerical simulation,DQM,and finite element method(FEM).Simulation results verified the practicability of the proposed mechanical model,and the comparison between the results of the solutions of DQM and FEM showed that DQM is accurate and effective in elastic and elastic-plastic analysis of variable stiffness beams.

Effect of Accumulative Strain on Grain Refinement and Strengthening of ZM6 Magnesium Alloy During Continuous Variable Cross-Section Direct Extrusion

In order to study the influence of die combination on continuous variable cross-section direct extrusion （CVCDE） in the extrusion process, the accumulative strain formula is derived, and it can be known that the extrusion ratio of various stages directly determines the size of corresponding stage strain by formula. In this paper, as an example of the two interim dies, three die combinations of different angles and extrusion ratio are designed. Aviation magnesium alloy ZM6 is studied, and the results show that dynamic recrystallization is even more complete when continuous shear deformation occurs, so that the refinement and homogenization of microstructure are obtained. By the use of different die combinations, the accumulative strain increases under the conditions of same total extrusion ratio. Thus, the refined crystalline strengthening effect of extrusion deformation can be further analyzed. Due to the dead-zone defects, the actual accumulative strain decreases significantly and the effect of microstructure and performance improvements also decreases with it. Therefore, the optimal design of die combination is the key to the process and product of CVCDE, which provides a scientific basis for the development of severe plastic deformation.

Monte Carlo simulation of phonon transport in variable cross-section nanowires

A dedicated Monte Carlo (MC) model is proposed to investigate the mechanism of phonon transport in variable cross-section silicon nanowires (NWs). Emphasis is placed on understanding the thermal rectification effect and thermal conduction in tapered cross-section and incremental cross-section NWs. In the simulations, both equal and unequal heat input conditions are discussed. Under the latter condition, the tapered cross-section NW has a more prominent thermal rectification effect. Additionally, the capacity of heat conduction in the tapered cross-section NW is always higher than that of the incremental one. Two reasons may be attributed to these behaviors: one is their different boundary conditions and the other is their different volume distribution. Although boundary scattering plays an important role in nanoscale structures, the results suggest the influence of boundary scattering on heat conduction is less obvious than that of volume distribution in NWs with variable cross-sections.

Microstructural characteristics and deformation of magnesium alloy AZ31 produced by continuous variable cross-section direct extrusion

Magnesium（Mg） alloy AZ31 was produced by continuous variable cross-section direct extrusion（CVCDE）to study its deformation behavior. Metallographic microscopy（OM）, transmission electron microscopy（TEM）, and scanning electron microscopy（SEM） were used to observe the variations in microstructure and fracture morphology of Mg alloy AZ31 as a function of processing methods. The results reveal that grains of Mg alloy AZ31 were refined and their microstructure was homogenized by CVCDE. The recrystallization in Mg alloy AZ31 produced by CVCDE with 2 interim dies was more complete than that produced by conventional extrusion（CE） and CVCDE with 1 interim die, and the grains were finer and more uniform.Plasticity of the AZ31 alloy was improved. Fracture mode was evolved from a combination of ductility and brittleness to a sole ductile form. In summary, a CVCDE mold structure with 2 interim dies can improve microstructure, plasticity, and toughness of Mg alloy AZ31.

Experimental investigation of tubing collar's influence on hydrodynamic behavior of annular duct flow

Tubing collars’influence on hydrodynamic behavior of annular duct flow has been investigated using Particle Image Velocity(PIV)technology.PIV has become an efficient method for complex transient flows visualization.A water flow loop with two replaceable variable cross-sections(VCS),75-90 mm and 90-110 mm,in a 129 mm inner diameter(ID)pipe was used.The whole field of the variable cross-section annulus(VCSA)was visualized,including forward-facing step(FFS),narrow annulus(NA),and backwardfacing step(BFS)flow.The VCSA ratio and Reynolds(Re)number influence on streamline distribution,velocity distribution,and turbulence intensity were discussed.Results showed that the recirculation is easier to form in BFS than FFS flow under the same condition.The VCSA ratio affects the formation of recirculation zones and the location of the reattachment point.Reynolds number mainly affects BFS flow by influencing the main velocity component-axial velocity.The turbulence intensity is relatively high in BFS than FFS flow and is larger at y/h>1.0 than y/h<1.0.Furthermore,the streamwise cohere nt structures reveal that the first two modes are predominant and represent the main characteristics of the flow by proper orthogonal decomposition(POD)method.

固体电蓄热体风道优化模拟研究

对固体电蓄热体圆形风道采用ANSYS软件进行数值模拟,根据模拟云图得到圆形风道的温度分布和出口温度。在圆形风道的基础上进行改变风道的形状,并且对变径风道进行数值模拟计算,变径风道即是适当增大入口直径且减小出口直径的风道。模拟结果显示出变径后的风道比原始的圆形风道在出口温度、出口速度以及总传热效率有部分的提高,放热14h后,变径风道蓄热体平均温度比圆形风道蓄热体平均温度下降80.63K,放热性能提高18.24%,空气总传热速率提高23.90%,使蓄热体的放热性能得到优化。