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 hyperbo...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.展开更多
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 verti...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.展开更多
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 boundar...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.展开更多
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...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.展开更多
The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
Hydroformed parts are widely used in industrial automotive parts because of their higher stiffness and fatigue strength and reduced weight relative to their corresponding cast and welded parts.This paper reports a hyd...Hydroformed parts are widely used in industrial automotive parts because of their higher stiffness and fatigue strength and reduced weight relative to their corresponding cast and welded parts.This paper reports a hydraulicforming experimental platform for rectangular tube fittings that was constructed to conduct an experiment on the hydraulic forming of rectangular tube fittings.A finite element model was established on the basis of the fluid–solid coupling method and simulation analysis.The correctness of the simulation analysis and the feasibility of the fluid–solid coupling method for hydraulic forming simulation analysis were verified by comparing the experimental results with the simulation results.On the basis of the simulation analysis of the hydraulic process of the torsion beam using the fluid–solid coupling method,a sliding mold suitable for the hydroforming of torsion beams was designed for its structural characteristics.The effects of fluid characteristics,shaping pressure,axial feed rate,and friction coefficient on the wall thicknesses of torsions beams during formation were investigated.Fluid movement speed was related to tube deformation.Shaping pressure had a significant effect on rounded corners and straight edges.The axial feed speed was increased,and the uneven distribution of wall thicknesses was effectively improved.Although the friction coefficient had a nonsignificant effect on the wall thickness of the ladder-shaped region,it had a significant influence on a large deformation of wall thickness in the V-shaped area.In this paper,a method of fluid-solid coupling simulation analysis and sliding die is proposed to study the high pressure forming law in torsion beam.展开更多
The meta-heuristic algorithm is a global probabilistic search algorithm for the iterative solution.It has good performance in global optimization fields such as maximization.In this paper,a new adaptive parameter stra...The meta-heuristic algorithm is a global probabilistic search algorithm for the iterative solution.It has good performance in global optimization fields such as maximization.In this paper,a new adaptive parameter strategy and a parallel communication strategy are proposed to further improve the Cuckoo Search(CS)algorithm.This strategy greatly improves the convergence speed and accuracy of the algorithm and strengthens the algorithm’s ability to jump out of the local optimal.This paper compares the optimization performance of Parallel Adaptive Cuckoo Search(PACS)with CS,Parallel Cuckoo Search(PCS),Particle Swarm Optimization(PSO),Sine Cosine Algorithm(SCA),Grey Wolf Optimizer(GWO),Whale Optimization Algorithm(WOA),Differential Evolution(DE)and Artificial Bee Colony(ABC)algorithms by using the CEC-2013 test function.The results show that PACS algorithmoutperforms other algorithms in 20 of 28 test functions.Due to the superior performance of PACS algorithm,this paper uses it to solve the problem of the rectangular layout.Experimental results show that this scheme has a significant effect,and the material utilization rate is improved from89.5%to 97.8%after optimization.展开更多
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 deve...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.展开更多
The present paper presents the sloshing oscillation behaviour and sloshing force in three different tanks of model scales of 1:86,1:57 and 1:43.The rectangular tank is mounted on shake table,to study the scale effect ...The present paper presents the sloshing oscillation behaviour and sloshing force in three different tanks of model scales of 1:86,1:57 and 1:43.The rectangular tank is mounted on shake table,to study the scale effect of sloshing with sway excited motion.The tests are carried out for the aspect ratio(hs/l,where hs liquid depth and l is the length of the tank)of 0.1625,0.325,and 0.4875 which represents 25%,50%and 75%of liquid fill levels,respectively.Seventeen excitation frequencies ranging from 0.4566 Hz to 1.9757 Hz are considered,which covers up to the fifth sloshing mode.The sloshing oscillations occurs in the longitudinal axis when subjected to sway excitations.An experimental setup is designed and devised to measure sloshing force by the concept of ballast mass.The inertia forces are measured by load cells and sloshing oscillation time histories are measured by capacitance probes.It is found that violent sloshing is experienced for 50%filled condition irrespective of scaled tanks,excitation amplitudes and excitation frequencies.The sloshing force is maximum in 1:43 scaled tank than other scaled sloshing tanks irrespective of the excitation frequency and amplitude for 50%fill level.Based on the experimental observations and analysis of results,it is concluded that proportionate volume of water and tank size decides the severity of sloshing in the partially filled tanks.展开更多
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 pl...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.展开更多
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 o...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.展开更多
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 ...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.展开更多
In this paper Substrate Integrated Waveguide-basedfiltenna operating at Ku band is proposed.The model is designed on a low loss dielectric substrate having a thickness of 0.508 mm and comprises of shorting vias along ...In this paper Substrate Integrated Waveguide-basedfiltenna operating at Ku band is proposed.The model is designed on a low loss dielectric substrate having a thickness of 0.508 mm and comprises of shorting vias along two edges of the substrate walls.To realize a bandpassfilter,secondary shorting vias are placed close to primary shorting vias.The dimension and position of the vias are carefully analyzed for Ku band frequencies.The model is fabricated on Roger RT/duroid 5880 and the performance characteristics are measured.The proposed model achieves significant impedance characteristics with wider bandwidth in the Ku band.The model also achieves a maximum gain of 7.46 dBi in the operating band thus making it suitable for Ku-band applications.Substrate Integrated Waveguide(SIW)Structures possess most of the advantages over conventional radiofrequency waveguides since they have high power management capacity with self-consistent electrical shielding.The most noteworthy advantage of SIW,it can able to integrate all the components on the same substrate,both passive and active components.展开更多
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 Men...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.展开更多
Antennas are an indispensable element in wireless networks. For long-distance wireless communication, antenna gains need to be very strong (highly directive) because the signal from the antenna loses a lot of str...Antennas are an indispensable element in wireless networks. For long-distance wireless communication, antenna gains need to be very strong (highly directive) because the signal from the antenna loses a lot of strength as it travels over long distances. This is true in the military with missile, radar, and satellite systems, etc. Antenna arrays are commonly employed to focus electromagnetic waves in a certain direction that cannot be achieved perfectly with a single-element antenna. The goal of this study is to design a rectangular microstrip high-gain 2 × 1 array antenna using ADS Momentum. This microstrip patch array design makes use of the RT-DUROID 5880 as a substrate with a dielectric constant of 2.2, substrate height of 1.588 mm, and tangent loss of 0.001. To achieve efficient gain and return loss characteristics for the proposed array antenna, RT-Duroid is a good choice of dielectric material. The designed array antenna is made up of two rectangular patches, which have a resonance frequency of 3.3 GHz. These rectangular patches are excited by microstrip feed lines with 13 mm lengths and 4.8 mm widths. The impedance of the patches is perfectly matched by these transmission lines, which helps to get better antenna characteristics. At a resonance frequency of 3.3 GHz, the suggested antenna array has a directivity of 10.50 dB and a maximum gain of 9.90 dB in the S-band. The S parameters, 3D radiation pattern, directivity, gain, and efficiency of the constructed array antenna are all available in ADS Momentum.展开更多
The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and nea...The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.展开更多
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 ...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.展开更多
A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform(RT) method, a probl...A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform(RT) method, a problem that has never been resolved before, for the Green's function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.展开更多
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 expe...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.展开更多
The aim of this study is to apply process mineralogy as a practical tool for further understanding and predicting the flotation kinetics of the copper sulfide minerals. The minerals' composition and association, g...The aim of this study is to apply process mineralogy as a practical tool for further understanding and predicting the flotation kinetics of the copper sulfide minerals. The minerals' composition and association, grain distribution, and liberation within the ore samples were analyzed in the feed, concentrate, and the tailings of the flotation processes with two pulp densities of 25 wt% and 30 wt%. The major copper-bearing minerals identified by microscopic analysis of the concentrate samples included chalcopyrite(56.2 wt%), chalcocite(29.1 wt%),covellite(6.4 wt%), and bornite(4.7 wt%). Pyrite was the main sulfide gangue mineral(3.6 wt%) in the concentrates. A 95% degree of liberation with d_(80) > 80 μm was obtained for chalcopyrite as the main copper mineral in the ore sample. The recovery rate and the grade in the concentrates were enhanced with increasing chalcopyrite particle size. Chalcopyrite particles with a d_(80) of approximately 100 μm were recovered at the early stages of the flotation process. The kinetic studies showed that the kinetic second-order rectangular distribution model perfectly fit the flotation test data. Characterization of the kinetic parameters indicated that the optimum granulation distribution range for achieving a maximum flotation rate for chalcopyrite particles was between the sizes 50 and 55 μm.展开更多
基金supported by the National Natural Science Foundation of China(21972131)。
文摘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.
基金funded jointly by the National Nature Science Funds of China(No.42274010)the Fundamental Research Funds for the Central Universities(Nos.2023000540,2023000407).
文摘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.
基金Project supported by the National Natural Science Foundation of China (No. 12002195)the National Science Fund for Distinguished Young Scholars (No. 12025204)the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)。
文摘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.
基金Project supported by the Natural Science Foundation of Inner Mongolia of China(Grant No.2021BS01008)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2323)the Scientific Research Funding Project for introduced high level talents of IMNU(Grant No.2020YJRC014)。
文摘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.
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
基金Natural Science Foundation of China(Grant No.81960332)Guangxi Provincial Innovation driven Development Project(Grant No.GKAA17204062)+1 种基金Guangxi Provincial Natural Science Foundation(Grant No.2016GXNSFAA380211)Liuzhou Municipal Scientific Research and Technology Development Plan(Grant No.2016C050203)。
文摘Hydroformed parts are widely used in industrial automotive parts because of their higher stiffness and fatigue strength and reduced weight relative to their corresponding cast and welded parts.This paper reports a hydraulicforming experimental platform for rectangular tube fittings that was constructed to conduct an experiment on the hydraulic forming of rectangular tube fittings.A finite element model was established on the basis of the fluid–solid coupling method and simulation analysis.The correctness of the simulation analysis and the feasibility of the fluid–solid coupling method for hydraulic forming simulation analysis were verified by comparing the experimental results with the simulation results.On the basis of the simulation analysis of the hydraulic process of the torsion beam using the fluid–solid coupling method,a sliding mold suitable for the hydroforming of torsion beams was designed for its structural characteristics.The effects of fluid characteristics,shaping pressure,axial feed rate,and friction coefficient on the wall thicknesses of torsions beams during formation were investigated.Fluid movement speed was related to tube deformation.Shaping pressure had a significant effect on rounded corners and straight edges.The axial feed speed was increased,and the uneven distribution of wall thicknesses was effectively improved.Although the friction coefficient had a nonsignificant effect on the wall thickness of the ladder-shaped region,it had a significant influence on a large deformation of wall thickness in the V-shaped area.In this paper,a method of fluid-solid coupling simulation analysis and sliding die is proposed to study the high pressure forming law in torsion beam.
基金funded by the NationalKey Research and Development Program of China under Grant No.11974373.
文摘The meta-heuristic algorithm is a global probabilistic search algorithm for the iterative solution.It has good performance in global optimization fields such as maximization.In this paper,a new adaptive parameter strategy and a parallel communication strategy are proposed to further improve the Cuckoo Search(CS)algorithm.This strategy greatly improves the convergence speed and accuracy of the algorithm and strengthens the algorithm’s ability to jump out of the local optimal.This paper compares the optimization performance of Parallel Adaptive Cuckoo Search(PACS)with CS,Parallel Cuckoo Search(PCS),Particle Swarm Optimization(PSO),Sine Cosine Algorithm(SCA),Grey Wolf Optimizer(GWO),Whale Optimization Algorithm(WOA),Differential Evolution(DE)and Artificial Bee Colony(ABC)algorithms by using the CEC-2013 test function.The results show that PACS algorithmoutperforms other algorithms in 20 of 28 test functions.Due to the superior performance of PACS algorithm,this paper uses it to solve the problem of the rectangular layout.Experimental results show that this scheme has a significant effect,and the material utilization rate is improved from89.5%to 97.8%after optimization.
基金Project supported by the National Natural Science Foundation of China(Nos.51978336 and11702117)。
文摘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.
基金The Science and Engineering Research Board(SERB)and Department of Science and Technology(DST),Government of India under the project“Optimal Damping of Porous Screen in TLDStructure Interaction”(ECR/2015/000176).
文摘The present paper presents the sloshing oscillation behaviour and sloshing force in three different tanks of model scales of 1:86,1:57 and 1:43.The rectangular tank is mounted on shake table,to study the scale effect of sloshing with sway excited motion.The tests are carried out for the aspect ratio(hs/l,where hs liquid depth and l is the length of the tank)of 0.1625,0.325,and 0.4875 which represents 25%,50%and 75%of liquid fill levels,respectively.Seventeen excitation frequencies ranging from 0.4566 Hz to 1.9757 Hz are considered,which covers up to the fifth sloshing mode.The sloshing oscillations occurs in the longitudinal axis when subjected to sway excitations.An experimental setup is designed and devised to measure sloshing force by the concept of ballast mass.The inertia forces are measured by load cells and sloshing oscillation time histories are measured by capacitance probes.It is found that violent sloshing is experienced for 50%filled condition irrespective of scaled tanks,excitation amplitudes and excitation frequencies.The sloshing force is maximum in 1:43 scaled tank than other scaled sloshing tanks irrespective of the excitation frequency and amplitude for 50%fill level.Based on the experimental observations and analysis of results,it is concluded that proportionate volume of water and tank size decides the severity of sloshing in the partially filled tanks.
基金funded by the Anhui Provincial Natural Science Foundation(Grant No.2008085QE245)the Natural Science Research Project of Higher Education Institutions in Anhui Province(2022AH040045)the Project of Science and Technology Plan of Department of Housing and Urban-Rural Development of Anhui Province(2021-YF22).
文摘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.
基金supported by the Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province, China (Grant No. 2020RC4047)the National Natural Science Foundation of China (Grant Nos. 11975095, 12075082, and 11935006)。
文摘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.
基金support of this work by the National Natural Science Foundation of China(No.51405096)the Fundamental Research Funds for the Central Universities(HEUCF210710).
文摘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.
文摘In this paper Substrate Integrated Waveguide-basedfiltenna operating at Ku band is proposed.The model is designed on a low loss dielectric substrate having a thickness of 0.508 mm and comprises of shorting vias along two edges of the substrate walls.To realize a bandpassfilter,secondary shorting vias are placed close to primary shorting vias.The dimension and position of the vias are carefully analyzed for Ku band frequencies.The model is fabricated on Roger RT/duroid 5880 and the performance characteristics are measured.The proposed model achieves significant impedance characteristics with wider bandwidth in the Ku band.The model also achieves a maximum gain of 7.46 dBi in the operating band thus making it suitable for Ku-band applications.Substrate Integrated Waveguide(SIW)Structures possess most of the advantages over conventional radiofrequency waveguides since they have high power management capacity with self-consistent electrical shielding.The most noteworthy advantage of SIW,it can able to integrate all the components on the same substrate,both passive and active components.
文摘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.
文摘Antennas are an indispensable element in wireless networks. For long-distance wireless communication, antenna gains need to be very strong (highly directive) because the signal from the antenna loses a lot of strength as it travels over long distances. This is true in the military with missile, radar, and satellite systems, etc. Antenna arrays are commonly employed to focus electromagnetic waves in a certain direction that cannot be achieved perfectly with a single-element antenna. The goal of this study is to design a rectangular microstrip high-gain 2 × 1 array antenna using ADS Momentum. This microstrip patch array design makes use of the RT-DUROID 5880 as a substrate with a dielectric constant of 2.2, substrate height of 1.588 mm, and tangent loss of 0.001. To achieve efficient gain and return loss characteristics for the proposed array antenna, RT-Duroid is a good choice of dielectric material. The designed array antenna is made up of two rectangular patches, which have a resonance frequency of 3.3 GHz. These rectangular patches are excited by microstrip feed lines with 13 mm lengths and 4.8 mm widths. The impedance of the patches is perfectly matched by these transmission lines, which helps to get better antenna characteristics. At a resonance frequency of 3.3 GHz, the suggested antenna array has a directivity of 10.50 dB and a maximum gain of 9.90 dB in the S-band. The S parameters, 3D radiation pattern, directivity, gain, and efficiency of the constructed array antenna are all available in ADS Momentum.
文摘The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.
基金supported by the Natural Science Foundation of Hebei Province of China(No.E2010001254)
文摘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.
基金Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University,China(Grant No.15ZY16)
文摘A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform(RT) method, a problem that has never been resolved before, for the Green's function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.
基金supported by the China Postdoctoral Science Foundation(Grant No.2012M511192)the National Natural Science Foundation of China(Grant Nos.51209080 and 51061130547+5 种基金Open Fund of State Key Laboratory of Coastaland Off shore Engineering(Grant No.LP1207the Open Fund of State Key Laboratory of Hydraulics and Mountain River Engineering(Grant No.1213)Qing Lan Project and 333 Project of Jiangsu Province(Grant No.BRA2012130)the Fundamental Research Funds for the Central Universities(Hohai University,Grant No.2012B06514the 111 Project(Grant No.B12032)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120181110084)
文摘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.
文摘The aim of this study is to apply process mineralogy as a practical tool for further understanding and predicting the flotation kinetics of the copper sulfide minerals. The minerals' composition and association, grain distribution, and liberation within the ore samples were analyzed in the feed, concentrate, and the tailings of the flotation processes with two pulp densities of 25 wt% and 30 wt%. The major copper-bearing minerals identified by microscopic analysis of the concentrate samples included chalcopyrite(56.2 wt%), chalcocite(29.1 wt%),covellite(6.4 wt%), and bornite(4.7 wt%). Pyrite was the main sulfide gangue mineral(3.6 wt%) in the concentrates. A 95% degree of liberation with d_(80) > 80 μm was obtained for chalcopyrite as the main copper mineral in the ore sample. The recovery rate and the grade in the concentrates were enhanced with increasing chalcopyrite particle size. Chalcopyrite particles with a d_(80) of approximately 100 μm were recovered at the early stages of the flotation process. The kinetic studies showed that the kinetic second-order rectangular distribution model perfectly fit the flotation test data. Characterization of the kinetic parameters indicated that the optimum granulation distribution range for achieving a maximum flotation rate for chalcopyrite particles was between the sizes 50 and 55 μm.