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.

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.

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.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.

Optimization of a Dual-Baffled Rectangular Tank Against the Sloshing Phenomenon

A dual-baffled rectangular tank with different configurations is proposed to reduce the sloshing effect,and design optimization is conducted through numerical simulations with open-source software,namely OpenFOAM,based on the computational fluid dynamic model.A series of physical experiments in the dual-baffled rectangular tank is performed for model validation and design optimization with the measured water surface elevation distributions along the tank.The optimization uses the calculated maximum horizontal force exerted on the tank and entropy generation(EG)as the criterion.Results show that the dual-baffle configuration positioned at the tank center is more effective in reducing the sloshing than that of the single baffle when the relative baffle height and initial water depth ratio(Hb/Hw,where Hb and Hw represent baffle height and static water depth,respectively)are larger than 0.5.However,such an effect then diminishes when the ratio is larger than 0.75.The effect of the dual-baffle configuration on the sway motion under the condition of different motion amplitudes and frequencies is also evaluated.The results show that the reduction in the maximum horizontal force is almost the same for dual-and single-baffled configurations and reaches the minimum when the sway motion amplitude is near 0.03 m.The dual-baffled configuration for the angular frequency of the sway motion is more effective than the single-baffled in reducing the sloshing at the low angular frequencies but is only less effective at high angular frequencies.Furthermore,the optimal baffle inclination angle is 85°when the inclined straight and curved baffles are used,and curved baffles can successfully decrease the horizontal force exerted on the tank and EG.

WAVE TRANSFORMATION AND BREAKING OVER A RECTANGULAR STEP

An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.

Robot coverage algorithm under rectangular decomposition environment

The environment modeling algorithm named rectangular decomposition, which is composed of cellular nodes and interleaving networks, is proposed. The principle of environment modeling is to divide the environment into individual square sub-areas. Each sub-area is orientated by the central point of the sub-areas called a node. The rectangular map based on the square map can enlarge the square area side size to increase the coverage efficiency in the case of there being an adjacent obstacle. Based on this algorithm, a new coverage algorithm, which includes global path planning and local path planning, is introduced. In the global path planning, uncovered subspaces are found by using a special rule. A one-dimensional array P, which is used to obtain the searching priority of node in every direction, is defined as the search rule. The array P includes the condition of coverage towards the adjacent cells, the condition of connectivity and the priorities defined by the user in all eight directions. In the local path planning, every sub-area is covered by using template models according to the shape of the environment. The simulation experiments show that the coverage algorithm is simple, efficient and adapted for complex two- dimensional environments.

Laser Doppler Vibrometer Without Directional Ambiguity Using Rectangular Phase Grating

The two-phase detection method for directional discrimination in laser Doppler measurements is discussed.The diffraction efficiency of a sin- gle period rectangular phase grating is analysed and a kind of back-scattered laser Doppler vibrometer without directional ambiguity using the single peri- od rectangular phase grating as the beam-combiner described.The principles of this kind of vibrometer are explained in detail,and some experimental re- sults are given.In this kind of vibrometer,the rectangular phase grating, without the zero diffracted order and even orders,is used to eliminate use- less stray light and to combine the useful signal light.Differential electronics is employed to reject signal noise.Therefore,the signal-to-noise ratio of Doppler signals and the measurement accuracy of the instrument are im- proved and the range of application is expanded.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.

Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field

Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.

Effects of Perforated Baffle on Reducing Sloshing in Rectangular Tank:Experimental and Numerical Study

A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional （3D） rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.

Study on Failure Mechanism and Bearing Capacity of Three-Dimensional Rectangular Footing Subjected to Combined Loading

This paper presents two kinematic failure mechanisms of threc-dimensional rectangular footing resting on homogeneous undrained clay foundation under uniaxial vertical loading and uniaxial moment loading. The failure mechanism under vertical loading comprises a plane strain Prandti-type mechanism over the central part of the longer side, and the size of the mechanism gradually reduces at the ends of the longer side and over the shorter side as the corner of rectangular footing is being approached where the direction of soil motion remains normal to each corresponding side respectively. The failure mechanism under moment loading comprises a plane strain scoop sliding mechanism over the central part of the longer side, and the radius of scoop sliding mechanism increases linearly at the ends of the longer side. On the basis of the kinematic failure mechanisms mentioned above, the vertical ultimate bearing capacity and the ultimate bearing capacity against moment or moment ultimate bearing capacity are obtained by use of upper bound limit analysis theory. At the same time, numerical analysis results, Skempton＇ s results and Salgado et al. ＇s results are compared with this upper bound solution. It shows that the presented failure mechanisms and plastic limit analysis predictions are validated. In order to investigate the behaviors of undrained clay foundation beneath the rectangular footing subjected to the combined loadings, numerical analysis is adopted by virtue of the general-purpose FEM software ABAQUS, where the clay is assumed to obey the Mohr-Coulomb yielding criterion. The failure envelope and the ultimate bearing capacity are achieved by the numerical analysis results with the varying aspect ratios from length L to breadth B of the rectangular footing. The failure mechanisms of rectangular footing which are subjected to the combined vertical loading V and horizontal loading H （Vertical loading V and moment loading M, and horizontal loading H and moment loading M respectively are observed in the finite element analysis. ） is explained by use of the upper bound plasticity limit analysis theory. Finally, the reason of eccentricity of failure envelope in H-M loading space is given in this study, which can not be explained by use of the traditional ＇ swipe test＇.

Measurement and Correlation of Pressure Drop for Gas-Liquid Two-phase Flow in Rectangular Microchannels

The pressure drop of gas-liquid two-phase flow in microchannel is of fundamental importance in heat and mass transfer processes. In this work,the pressure drop of gas-liquid two-phase flow in horizontal rectangular cross-section microchannels was measured by a pressure differential transducer system. Water,ethanol and n-propanol were used as liquid phase to study the effects of capillary number on pressure drop;air was used as the gas phase. Four microchannels with various dimensions of 100 μm× 200 μm,100 μm× 400 μm,100 μm× 800 μm and 100 μm× 2000 μm(depth × width) were used for determining the influence of configuration on the pressure drop. Experimental results showed that in micro-scale,the capillary number also affected the pressure drop remarkably,and in spite of only one-fold difference in aspect ratio,the variation of pressure drop reached up to near three times under the same experimental conditions. Taking the effects of aspect ratio and surface tension into account,a modi-fied correlation for Chisholm parameter C in the Chisholm model was proposed for predicting the frictional multi-plier,and the predicted values by the proposed correlation showed a satisfactory agreement with experimental data.

Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.

Resonance suppression and electromagnetic shielding effectiveness improvement of an apertured rectangular cavity by using wall losses

The cavity-mode resonance effect could result in significant degradation of the shielding effectiveness （SE） of a shielding enclosure around its resonance frequencies. In this paper, the influence of coated wall loss on the suppression of the resonance effect is investigated. For this purpose, an equivalent circuit model is employed to analyze the SE of an apertured rectangular cavity coated with an inside layer of resistive material. The model is developed by extending Robinson＇s equivalent circuit model through incorporating the effect of the wall loss into both the propagation constant and the characteristic impedance of the waveguide. Calculation results show that the wall loss could lead to great improvement on the SE for frequencies near the resonance but almost no effect on the SE for frequencies far away from the resonance.

Numerical Simulation of Bragg Reflection Based on Linear Waves Propagation over A Series of Rectangular Seabed

A numerical model, Evolution Equation of Mild-Slope Equation （EEMSE） developed by Hsu et al. （2003）, was applied to study the Bragg reflection of water waves over a series of rectangular seabed. Three key parameters of the Bragg reflection including the peak coefficient of primary Bragg reflection, its corresponding relative wavelength, and the bandwidth, have shown to be effective in describing the characteristics of the primary Bragg reflection. The characteristics of the Bragg reflection were investigated under the various conditions comprising number, height, and spacing interval of a series of rectangular seabed. The results reveal that the peak of Bragg reflection increases with the increase of rectangular seabed height and number, the bandwidth and the shift value of the Bragg reflection depend on the increase of the rectangular seabed height as well as the decrease of rectangular seabed number, and the relative rectangular seabed spacing in the rang of 3 and 4 could produce higher Bragg reflection. Finally, a correlative and regressive analysis is performed by use of the calculated data. Based on the results of the analysis, empirical equations were established. Our study results can provide an appropriate choice of a series of rectangular seabed field for a practical design.