Analytical and Experimental Research on Wave Scattering by an Open-Type Rectangular Breakwater with Horizontal Perforated Plates

This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The hydrodynamic characteristics of this breakwater are analyzed through analytical potential solutions and experimental tests.The quadratic pressure drop conditions are exerted on the horizontal perforated plates to facilitate assessing the effect of wave height on the dissipated wave energy of breakwater through the analytical solution.The hydrodynamic quantities of the breakwater,including the reflection,transmission,and energyloss coefficients,together with vertical and horizontal wave forces,are calculated using the velocity potential decomposition method as well as an iterative algorithm.Furthermore,the reflection and transmission coefficients of the breakwater are measured by conducting experimental tests at various wave periods,wave heights,and both porosities and widths of the horizontal perforated plates.The analytical predicted results demonstrate good agreement with the iterative boundary element method solution and measured data.The influences of variable incident waves and structure parameters on the hydrodynamic characteristics of the breakwater are investigated through further calculations based on analytical solutions.Results indicate that horizontal perforated plates placed on the water surface for both sides of the rectangular breakwater can enhance the wave dissipation ability of the breakwater while effectively decreasing the transmission and reflection coefficients.

Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

Rectangular tunnel heading stability in three dimensions and its predictive machine learning models

Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization.Nevertheless,it is possible to study the stability of tunnels in three dimensions(3D)with a rectangular shape using finite element limit analysis(FELA)and a nonlinear programming technique.This paper employs 3D FELA to generate rigorous solutions for stability numbers,failure mechanisms,and safety factors for rectangular-shaped tunnels.To further explore the usefulness of the produced results,multivariate adaptive regression spline(MARS)is used for machine learning of big dataset and development of design equations for practical design applications.The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.

Numerical simulation of sedimentation of rectangular particle in Newtonian fluid

The sedimentation of a rectangular particle falling in a two-dimensional channel filled with Newtonian fluid was simulated with finite element arbitrary Lagrangian-Eulerian domain method. The numerical procedure was validated by comparison of the simulation results with existing numerical work. Morea over, good agreement was obtained between the simulation results and experimental measurements performed in the current study. The equilibrium position, stable orientation and drag coefficient ofa rect- angular particle for different particle Reynolds numbers （Rep） were studied. The results show that there is a critical particle Reynolds number for the preferred orientation of a rectangular particle falling in a Newtonian fluid. When Rep is smaller than the critical value, the particle fails with its long side parallel to gravity; otherwise the particle fails with its long side perpendicular to gravity. The critical particle Reynolds number is a decreasing function of the blockage ratio and aspect ratio. The distributions of pressure and shear stress on rectangular particle surface were analyzed. Moreover, the drag coefficient of the rectangular particle decreases as Rep or the blockage ratio increases; however, it appears to be independent of aspect ratio.

Subwavelength rectangular cavity partially filled with left-handed materials

In this paper, we present the electromagnetic analysis of a rectangular cavity partially filled with a left-handed material slab. Our theoretical investigation shows that there exist novel resonant modes in the cavity, and such a cavity becomes a subwavelength cavity. The eigenvalue equation of the cavity is derived and the resonant frequencies of the novel modes are calculated by using numerical simulation. We also discuss the stability of the novel resonant modes and show the best condition under which a useful rectangular cavity of subwavelength dimensions with tolerable stability is obtained.

Influence of Axial Feeding on Hydroforming of Aluminum Alloy Tubular Part with Rectangular Section

The hydroforming experiment of aluminum tubular part with rectangular section was carried out to investigate influence of axial feeding on thickness distribution and calibration pressure of the corner.Thickness distribution and relation between corner radius and internal pressure were analyzed.The influence of lubricant was discussed.Microstructure and hardness of different region were observed.It is shown that thickness reduction in the transition region between the corner and center region is the biggest.Friction condition has influence both on the thickness distribution and calibration pressure of the corner.As the increase of the axial feeding,the calibration pressure is decreased.There is only little change for the microstructure,but the hardness is increased by 23.3% for the transition region.

Nonlinear semi-analytical modeling of liquid sloshing in rectangular container with horizontal baffles

A nonlinear semi-analytical scheme is proposed for investigating the finiteamplitude nonlinear sloshing in a horizontally baffled rectangular liquid container under the seismic excitation.The sub-domain method is developed to analytically derive the modal behaviors of the baffled linear sloshing.The viscosity dissipation effects from the interior liquid and boundary layers are considered.With the introduction of the generalized time-dependent coordinates,the surface wave elevation and velocity potential are represented by a series of linear modal eigenfunctions.The infinite-dimensional modal system of the nonlinear sloshing is formulated based on the Bateman-Luke variational principle,which is further reduced to the finite-dimensional modal system by using the NarimanovMoiseev asymptotic ordering.The base force and overturning moment induced by the nonlinear sloshing are derived as the functions of the generalized time-dependent coordinates.The present results match well with the available analytical,numerical,and experimental results.The paper examines the surface wave elevation,base force,and overturning moment versus the baffle parameters and excitation amplitude in detail.

Chaotic Motion Analysis for a Coupled Magnetic-Flow-Mechanical Model of the Rectangular Conductive Thin Plate

The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.

Spontaneous emission of a moving atom in a waveguide of rectangular cross section

We study the spontaneous emission(SE) of an excited nonrelativistic two-level system(TLS) interacting with the vacuum in a waveguide of rectangular cross section. All TLS’s transitions and the center-of-mass motion of the TLS are taken into account. The SE rate and the carried frequency of the emitted photon for the TLS initially being at rest are obtained, it is found that in the first order of the mass M, the frequency of the emitted photon is smaller than the transition frequency of the TLS and the SE rate is smaller than the SE rate Γfof the TLS fixed in the same waveguide. The SE rate for the TLS initially being moving is obtained in the second order of the mass M. The SE rate is smaller than Γfbut it is dependent not only on the atomic mass but also on the initial momentum. The carried frequency of the emitted photon is decreased when it travels along the direction of the initial momentum, whereas it is increased when it travels in the opposite direction of the initial momentum.

Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.

Study of Rectangular Underexpanded Microjets

The underexpanded microjet emerging from a rectangular convergent nozzle with a high aspect ratio at the nozzle exit is investigated numerically using the Reynolds-averaged Navier-Stokes (RANS) simulation with the Menter’s shear stress transport (SST) k-ω turbulence model. The simulation is performed at the nozzle pressure ratio of 5.0 to produce a strong shock and it is validated by a comparison with a rainbow schlieren picture of the microjet. The three-dimensional structure of the shock-containing rectangular microjet is demonstrated using the isopycnic surface and bright-field schlieren representations.

多块排样方式的二维板材下料优化模型与算法

针对矩形件二维板材剪切下料问题,提出一种多块排样方式的二维板材下料优化模型与求解算法。为了均衡考虑排样方式的计算复杂度和板材利用率,将多块排样方式的块数定为八块。通过3次一分为二剪切操作将板材分割成八个矩形块,并将每个块剪切成方向相同的同种矩形件。构造八块排样的优化模型及算法是按照排样价值最大原则来确定所有可能尺寸的块中矩形件的最优布局和板材的最优八块划分。提出的列生成算法迭代调用上述八块排样算法生成一系列下料方案,选择耗费板材最少的一个下料方案作为最终解。通过采用文献基准例题和实际生产实例验证了本文算法,实验结果表明:八块排样算法的排样价值高于3种文献排样算法,并且,八块排样方式的下料算法板材利用率高于已有文献给出的下料算法。本文给出算法计算时间可满足实际应用需要。

Unified Solution Method of Rectangular Plate Elastic Bending

The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...

Sensitivity of springback and section deformation to process parameters in rotary draw bending of thin-walled rectangular H96 brass tube

In order to study the effects of the process parameters on springback and section deformation, a sensitivity analysis model was established based on the combination use of the multi-parameter sensitivity analysis method and the springback/section deformation prediction finite element model, and by using this model the sensitivities of the springback and the section deformation to process parameters were analyzed and compared. The results show that the most sensitive process conditions for springback angle are the boost speed and the pressure of pressure die, and the most sensitive process condition for section deformation is the number of cores. When the clamp force, the boost speed and the pressure of pressure die are utilized to control section deformation, the effect of these process parameters on springback should be considered. When the process parameters are mainly used to control springback, the effect of these process parameters on the section deformation should be always considered.

“Buckets effect”in the kinetics of electrocatalytic reactions

In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbolic relationship,i.e.,the ORR current excluding the effect of other variables increases with proton concentration and then tends to a constant value.We consider that this is caused by the limitation of ORR kinetics by the trace oxygen concentration in the solution,which determines the upper limit of ORR kinetics.A model of effective concentration is further proposed for rectangular hyperbolic relationships:when the reactant concentration is high enough to reach a critical saturation concentration,the effective reactant concentration will become a constant value.This could be due to the limited concentration of a certain reactant for reactions involving more than one reactant or the limited number of active sites available on the catalyst.Our study provides new insights into the kinetics of electrocatalytic reactions,and it is important for the proper evaluation of catalyst activity and the study of structureperformance relationships.

EXPERIMENTAL RESEARCH AND NONLINEAR FINITE ELEMENT ANALYSIS ON NEW TYPE JOINT BETWEEN COLUMN AND STEEL BEAM OF CONCRETE-FILLED RECTANGULAR STEEL TUBULAR

Experimental results of new type joints between the column and the. steel beam of concrete-filled rectangular steel tubular （CFRT） under reversed cyclic loads are presented. The earthquake resistant capacity of the joint is influenced by infilled concrete, stiffener length and relative dimensions of column and beam. It is found that the hysteresis curves obtained in the experiment are full and the joints have a good energy dissipation capacity. The nonlinear finite element models are also used to analyze the hysteresis behavior of the joints under reversed cyclic loads using ANSYS 8.0. The influences of the stiffener length and the infilled concrete are analyzed. Analytical results show that the stiffener length and the infilled concrete are critical for the joints. Furthermore, the skeleton curves of the finite element models are in good agreement with those of experiments.

Yield Modeling of Rectangular Defect Outline

In integrated circuits, the defects associated with photolithography are assumed to be in the shape of circular discs in order to perform the estimation of yield and fault analysis. However,real defects exhibit a great variety of shapes. In this paper,a novel yield model is presented and the critical area model of short circuit is correspondingly provided. In comparison with the circular model corrently available, the new model takes the similarity shape to an original defect, the two-dimensional distributional characteristic of defects, the feature of a layout routing and the character of yield estimation into account. As for the aspect of prediction of yield, the experimental results show that the new model may predict the yield caused by real defects more accurately than the circular model does. It is significant that the yield is accurately estimated and improved using the proposed model.

Predicting bathymetry based on vertical gravity gradient anomaly and analyses for various influential factors

The prediction of bathymetry has advanced significantly with the development of satellite altimetry.However,the majority of its data originate from marine gravity anomaly.In this study,based on the expression of vertical gravity gradient(VGG)of a rectangular prism,the governing equations for determining sea depths to invert bathymetry.The governing equation is solved by linearization through an iterative process,and numerical simulations verify its algorithm and its stability.We also study the processing methods of different interference errors.The regularization method improves the stability of the inversion process for errors.A piecewise bilinear interpolation function roughly replaces the low-frequency error,and numerical simulations show that the accuracy can be improved by 41.2%after this treatment.For variable ocean crust density,simulation simulations verify that the root-mean-square(RMS)error of prediction is approximately 5 m for the sea depth of 6 km if density is chosen as the average one.Finally,two test regions in the South China Sea are predicted and compared with ship soundings data,RMS errors of predictions are 71.1 m and 91.4 m,respectively.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

多约束下矩形件排样问题的混合求解算法研究

针对板材和玻璃下料过程中存在的矩形件排样问题,提出了一种基于分割匹配算法与改进蚁群算法的混合算法进行求解。建立了以最大化均方利用率和剩余加工时间为目标的排样优化模型;利用蚁群算法作为排样顺序算法确定部分零件的排样顺序以满足零件的加工时间限制,为了提高蚁群算法搜索效率,提出了自适应信息素更新策略,引入基于遗传变异和2-opt变异的混合变异策略来增强局部搜索能力。针对于零件在毛坯上位置的排布问题,为提高毛坯的均方利用率同时又满足一刀切约束条件,提出分割匹配算法进行矩形件排布优化。将改后的算法与其他优化算法用国际标准测试案例和企业实际案例进行对比分析,验证了所提混合算法的有效性。