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28 February 2023, Volume 49 Issue 1 Previous Issue    Next Issue

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Materials Science and Engineering

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Effect of homogenization treatment on the microstructure and mechanical properties of Fe-based medium entropy alloys ZHAO Yan-chun, SHI Zi-qiang, ZHANG Lin-hao, ZHANG Min-ya, KOU Sheng-zhong 2023, 49 (1):  1-6.  Abstract ( 440 )   PDF (4541KB) ( 422 )   Save The (Fe63.3Mn14Si9.1Cr9.8C3.8)98.5Y1.5(Y=Cu、Ag)、(Fe63.3Mn14Si9.1Cr9.8C3.8)97Cu1.5Ag1.5 were prepared by water-cooled copper crucible magnetic levitation melting-copper mold negative pressure suction casting method.The effect of homogenization temperature and time on mechanical properties was studied by establishing the uniformization kinetic equation.(Fe63.3Mn14Si9.1Cr9.8C3.8)98.5Y1.5(Y=Cu、Ag) and (Fe63.3Mn14Si9.1Cr9.8C3.8)97Cu1.5Ag1.5 medium entropy alloys were homogenized at 873, 973, 1 073, 1 173, 1 273 K, respectively. The relationshipwas investigatedbetween its organizational structure and compression performance. The results showed that the uniform distribution of alloying elements is applied and the segregation is significantly reduced, The homogenization alloy is phase stable and still has an fcc structure at 1 173 K, and the compressive mechanical properties of the entropy alloy of (Fe63.3Mn14Si9.1Cr9.8C3.8)97Cu1.5Ag1.5 is the best at 1 173 K, and the compressive strength and plastic strain were 3 992.4 MPa and 35.75%, respectively, and the experimental results were consistent with the calculational prediction of the equation of homogenization diffusion kinetics. References | Related Articles | Metrics

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Effect of cryogenic treatment on Microstructure and mechanical properties of Inconel 617 alloy ZHAO Xiao-long, LUO Xiao-yang, YU Li-dan, WANG Yan-jiang, JIA Zhi 2023, 49 (1):  7-11.  Abstract ( 203 )   PDF (5600KB) ( 265 )   Save Cryogenic treatment is widely used at present because of its simple operation, low price, and obvious improvement of material properties. Inconel 617 alloy was tested under different times and numbers using Cryogenic treatment. The microstructure of Inconel 617 alloy was investigated by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM), and the tensile test was carried out at room temperature by the universal tensile testing machine. The results show that the grain size of Inconel 617 alloy is refined after cryogenic treatment. After single cryogenic treatment for 12, 24 h, the fraction of low-angle grain boundaries increases, which is helpful to improve the tensile strength and ductility of the alloy. However, after cryogenic treatment, a large number of carbides are precipitated in the alloy, which reduces its strength. References | Related Articles | Metrics

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Arc behavior of deep penetration GMAW of weathering steel Q450NQR1 ZHANG Ming-hua, ZHANG Qian-chao, HUANG Xiu-pei, YI Ran FENG Cun-yi, HONG Bo 2023, 49 (1):  12-21.  Abstract ( 159 )   PDF (6866KB) ( 133 )   Save The weathering steel Q450NQR1 was welded separately by using the deep penetration GMAW and pulse MAG. The welding current, voltage and the corresponding arc image during the welding was collected. The relationship between the dynamic behavior of the welding arc and the weld formation was analyzed by processing arc image. At the same time, the influence of the different welding current and welding speed under the deep penetration GMAW on the arc behavior and the weld formation was researched. The results showed that compared with pulsed MAG, deep penetration GMAW has more concentrated arc energy, lower heat source position, increased weld penetration, and good weld geometric symmetry; during deep penetration welding, as the welding current increases and the welding speed decreases, the arc area decreases, the arc edge perimeter becomes shorter, the arc centroid position drops, and the penetration depth of the weld increases; When the welding current is 315 A and welding speed is 650 mm/min, the welding arc is the most stable, and the weld seam forming quality is also the best. The single-side welding and double-side forming ofQ450NQR1 steel sheet with 12 mm thickness is completed by the optimized welding process, the weld is well formed, and there is no softening and embrittlement in each area of the joints. References | Related Articles | Metrics

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Life prediction model of cement-based composite cored wallboard based on Wiener degradation under dry-wet cycles LI Hong-wei, MA Li-na, ZHANG Yan-hui, LI Bo-sheng 2023, 49 (1):  22-29.  Abstract ( 121 )   PDF (3437KB) ( 99 )   Save Most areas in the west are dry and rainless, the temperature difference between day and night is obvious. When the thermal insulation wall panel is in a harsh environment, local stress concentration will occur, which will lead to cracks and shorten its service life. The wet-dry cycle accelerated test was designed, the mechanical properties were tested, the internal structure evolution was observed, and the relative mass and relative dynamic elastic modulus was measured for radar analysis and numerical regression. Finally, based on Wiener model, the reliability of samples was predicted, and the performance degradation law of cement-based composite cored wallboard under wet-dry cycle accelerated was comprehensively analyzed. The resultsshowed thatthe strength increases with the continuous acceleration test of wet-dry cycle, and the compressive strength reaches 42.5 MPa and the flexural strength reaches 9.5 MPa. The internal reaction of microstructure produces more precipitated CaCO3, and gradually develops from denser to looser. The evaluation parameters initial increase from 1 and then decrease , but the overall change state is a decreasing trend, and the mass loss rate has a low sensitivity and a high correlation degree relative to the dynamic modulus. Through regression model analysis, the evaluation index meets the changing law of polynomial function, and the working life mass loss and dynamic elastic modulus by reliability analysis is4 500 d and 3 500 d, respectively. References | Related Articles | Metrics

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Material optimization of polyphosphoric acid modified asphalt based on decision analysis ZHANG Hai-hong, LIU Gui-yong, YANG Yan-hua, YANG Xiao-long 2023, 49 (1):  30-35.  Abstract ( 150 )   PDF (602KB) ( 155 )   Save PPA modified asphalt has the advantages of low price, good storage and high-temperature stability, and has a good application prospect, however, the complex compatibility between PPA and asphalt is an important reason that hinders the application of PPA modified asphalt. To select the best modification effect of PPA modified asphalt materials,PPA modified asphalt materials comprehensive optimization model is established on the basis ofthe analytic hierarchy process (AHP) and fuzzy mathematics method to optimize the best compatibility of the matrix asphalt and PPA raw materials, considering the high temperature properties, rheological properties and low-temperature performance of asphalt.The test results of the selected macro performanceof modified asphalt materials were taken into the model to calculate the superiority of each PPA modified asphalt mixing scheme. The results showed that the compatibility of Shell 90# base asphalt with 115% PPA is the best. References | Related Articles | Metrics

Mechanical Engineering and Power Engineering

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Design of virtual and real interactive monitoring system for CNC machine tools based on digital twins HUANG Hua, LI Jia-ran, LI Dian-lun 2023, 49 (1):  36-43.  Abstract ( 464 )   PDF (5660KB) ( 648 )   Save Aiming at the problem that the actual operating status of CNC machine tools is not directly reflected by traditional monitoring technology and virtual simulation technology, a virtual-real interactive monitoring system for CNC machine tools based on digital twins technology is designed by combining the new generation of information technology and the concept of digital twins. In addition, taking a CNC machine tool as example, the system architecture and related functions are first designed through Portal software. Based on that, the information collected by the sensor is transmitted to the system through PLC and Ethernet for analog conversion; and the digital twins data in the system is connected with the digital twins to realize the reception and transmission of information, then the combination of virtual and real are completed through OPC-DA. Finally, this method is used to monitor the vibration signal of the machine tool in real time and design a remote control panel. The experimental results show that the system using the virtual-real interactive monitoring system and digital twins of the CNC machine tool to double monitor the machining process can reflect the actual operating status of the machine tool more effectively and intuitively. Meanwhile the digital twins is virtually controlled by the virtual-real interactive monitoring system, and the application field of digital twins technology is further expanded. References | Related Articles | Metrics

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Multiaxial fatigue life prediction of crane beams considering stress concentration LI Bin, LI Wei-dun, LANG Shan-shan, LI Ya-nan 2023, 49 (1):  44-48.  Abstract ( 218 )   PDF (1624KB) ( 330 )   Save Steel structure crane beams have been widely used in industrial buildings. Due to the existence of stress concentration, parts of crane beams with geometric discontinuity are in service under multiaxial stress. In this paper, finite element method is used to analyze the stress and strain state of crane beam, determine the position of dangerous point, and extract its stress and strain component. Taking the plane with the highest energy density as the critical plane, a method to determine the critical plane based on energy criterion is proposed. Given that the crane beam works under asymmetric load, with the help of Goodman equation of mean stress correction, the fatigue life of crane beam is calculated by combining the approximate S-N curve of Q355D steel. The proposed method considers the effect of the multiaxial stress near the region of stress concentration on the fatigue damage and provides a new method for fatigue life evaluation of steel members with geometric discontinuous under complicated stress. References | Related Articles | Metrics

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Bionics design of wind turbine tower based on bamboo structure WEI Tai, DONG Fu-gang 2023, 49 (1):  49-54.  Abstract ( 205 )   PDF (1178KB) ( 377 )   Save To address the stability problem of the towering structure of wind turbine tower, the bamboo vascular bundles were introduced into the tower structure according to the bionic structure design theory. The method of improving the stability of the tower is studied through the design of a bamboo structure. Taking the 2 MW wind turbine tower as theobject of study, the Analytic Hierarchy Procedure (AHP) is applied to calculate the similarity between the bamboo and the tower to verify the rationality of the biological selection. By studying the relationship between the characteristics of bamboo vascular bundles and the stability of the bamboo, a bionic bamboo tower with four stiffening ribs was designed. Finite element analysis is employed to comparatively investigate the performance of the bionic bamboo tower and the original tower in the static and dynamic. Through the investigation, it is suggested that the maximum deformation and maximum stress can be reduced by 2.27% and 13.48% of the bionic bamboo tower, respectively. This approach results in 1.31% and 1.58% increase respectively in the first and second natural frequencies. Moreover, the overall stability of the bionic bamboo tower structure is improved by 1.4%. The feasibility of the bionic design of 2MW wind turbine towers is verified here, and a new method for the design of subsequent tower structures is provided. References | Related Articles | Metrics

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Theoretical modeling and calculation of critical position of internal circulation air flow in a plunging-type dropshaft WEI Jia-fang, LU San-qiang, ZHAO Wen-ju, NAN Jun-hu LONG Li-li, ZENG Yong-liang 2023, 49 (1):  55-60.  Abstract ( 156 )   PDF (825KB) ( 117 )   Save The installation of an internal air circulationflow system in the plunging-type dropshaft can effectively slow down the air pressure and air accumulation in downstream drainage pipelines. In order to determine the critical position where the air in the internal air circulation flow system can form a circulation loop, the theoretical calculation method was used to explore the pressure distribution in the wet shaft and the air shaft in the plunging-type dropshaft with an internal air circulation system. The results showed that the system played an effective role only when the air-circulated route was above the critical position (corresponding to the critical pressure). The calculated air pressure distributions in both shafts through the theoretical calculation method agree with the measurements well. For the plunging-type dropshaft with a drop height of H = 7.72 m, the critical position was about 0.65H ~ 0.84H. Moreover, the critical position was closer to the bottom of the dropshaft with the increase of the water flow rate. References | Related Articles | Metrics

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Influence of blade wrap angle on performance of constant head pump CHENG Xiao-rui, TIAN Long, LI Tian-peng, YANG Deng-feng 2023, 49 (1):  61-68.  Abstract ( 331 )   PDF (6240KB) ( 391 )   Save In order to study the influence of blade wrap angle on the performance of constant head pump, six impeller schemes with different blade wrap angle had been designed. Based on the Reynolds time-average N-S equation and the RNG k-ε turbulence model, the steady numerical calculation had been carried out, following the calculated results verified by experiments. The results show that before the cut-off flow, pump head decreases with the increase of the wrap angle. When the wrap angle of pump is 0 degree, the pump head is the largest. Under the schemes of 15 degrees, 30 degrees, and 45 degrees, the head of the pump is almost equal. When the wrap angle of pump is 60 degrees, pump has the smallest head, and the pump head decreases linearly with the increase of flow when the wrap angle is 75 degrees. The blade wrap angle has a significant influence on the efficiency of the pump. The pump efficiency in any scheme first increases and then decreases with the increase of flow, while the efficiency reaches its maximum value near the cut-off flow. Under the condition before the cut-off flow, the pump efficiency increases with the increase of the wrap angle, while after the cut-off flow, the larger the wrap angle is, the faster the efficiency decreases with the increase of the flow. References | Related Articles | Metrics

Chemical Industry and Light Industry

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Self-propagation combustion preparation and properties of neodymium ion-doped lithium manganate nanoparticles ZHANG Qing-tang, ZHU Yong-fang, HU Xiao-jun 2023, 49 (1):  69-73.  Abstract ( 194 )   PDF (2936KB) ( 150 )   Save A neodymium ion-doped lithium manganate(LiMn1.99Nd0.01O4) nanoparticle was prepared using the self-propagation combustion method. The crystal structure, microscopic morphology, and electrochemical performance of the material were characterized by XRD, SEM, and CV. The results show that neodymium ion doping does not affect the crystal structure, but can reduce the particle size of LiMn2O4 particles, thereby improving its electrochemical performance. The discharge specific capacity at 0.2C is as high as 125.6 mAh·g－1. The initial discharge capacity at 1C is 118.4 mAh·g－1, and the discharge-specific capacity after 100 cycles is 110.4 mAh·g－1. The capacity retention rate is 93.2%. References | Related Articles | Metrics

Automation Technique and Computer Technology

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Dynamic output feedback control of cyber-physical systems under false data injection attacks ZHU Chao-qun, ZHU Yi-rong 2023, 49 (1):  74-82.  Abstract ( 279 )   PDF (1259KB) ( 711 )   Save In this paper, an H-infinity dynamic output feedback control strategy with attack defense ability is investigated to deal with the problem of security control of cyber-physical system (CPS) under false data injection (FDI) attacks, which is taken as a special kind of external disturbance. Firstly, the effect of FDI attacks in the measurement channel and random time-delay on the communication network is considered, and a closed-loop system model with FDI attack, random time-delay, and external disturbance is established. Secondly, the sufficient conditions for the asymptotic stability of the closed-loop system under FDI attacks are derived based on the Lyapunov stability theory, and then the design scheme of H-infinity dynamic output feedback controller by utilizing linear matrix inequality technology is presented. Finally, a simulation example is given to demonstrate the feasibility and effectiveness of the proposed method. References | Related Articles | Metrics

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Design of second-order state-tuned filter using simulated inductance LI Yong-an, HOU Jing-qiang 2023, 49 (1):  83-86.  Abstract ( 264 )   PDF (1642KB) ( 229 )   Save Based on the dominant-pole model of the integrated operational amplifier (Op Amp), the equivalent admittance expression of the simulated inductance using grounded capacitors and dual op amps is first derived, which shows that only under ideal op amp conditions, the circuit can be equivalent to an inductor with a value of CR2. Based on that and combined with the classic passive second-order band-pass filter topology, a second-order state-tuned filter is designed by the component replacement method, which can not only realize band-pass filtering but also realize low-pass filtering. With the circuit using only two Op Amps and two grounded capacitors, the circuit is suitable for integration. The computer simulation result shows that the circuit can run up to 10 MHz, and Q can be as high as 100. In addition, the reason for Q enhancement and fo weakening under high-frequency conditions is correctly explained. References | Related Articles | Metrics

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Design of automobile remote monitoring system based on cloud platform ZHAO Geng-yun, WANG Jia, LI Wan-min, LIU Xiao-bin 2023, 49 (1):  87-93.  Abstract ( 370 )   PDF (6550KB) ( 441 )   Save In order to realize the real-time monitoring of vehicle status and position, query the vehicle historical data and track, and get rid of regional restrictions, a remote monitoring system for vehicles based on a cloud platform is designed. The system includes vehicle terminal and cloud service platform, which the former is responsible for collecting vehicle status data and GPS longitude and latitude, and uploading them to the cloud through 4G network. The cloud service platform includes visual monitoring center, database, and web server. The system administrator carries out real-time remote monitoring and data query on the vehicle through the cloud monitoring center, and the ordinary users monitor vehicles through the web browser, forming a two-level supervision mode. The results of long-term operation show that the system is stable and reliable, and can realize remote monitoring in different places. The monitoring data is rich, and the data refresh frequency is about 0.62 Hz. Therefore, the system has good real-time performance and can query the historical data and historical track of vehicles. References | Related Articles | Metrics

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Collaborative filtering algorithm based on graph neural network cross-feature WANG Yan, ZHAO Ni-ni, FAN Lin 2023, 49 (1):  94-102.  Abstract ( 204 )   PDF (3762KB) ( 253 )   Save Learning effective vector representations of users and items are the core goal of the recommendation system. Most of the existing recommendation models use deep neural networks or specially designed feature crossing to learn the feature crossing between users and projects to generate user (item) vector representations, but the cross information between user (item) features is not coded into the embedding vector to make full use of the feature cross information, and multiple feature cross information has different effects on the generation of the final user (item) vector representation. Based on this, two graph neural network modules are constructed to learn the intersection information between user (item) features and the feature intersection information between user and item, following the feature cross information weighted by calculating the attention score to obtain the user (item) feature information. Then the original feature information and the feature cross information learned from the network layer are aggregated through the gated recurrent neural network (GRU) to obtain the final user (item) vector expression. Finally, the final recommendation result is obtained through the element product of user vector and item vector. The validity of the model is verified on the datasets MovieLens 1M, Book-Crossing, and Taobao. References | Related Articles | Metrics

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Multi-label text classification based on word-label probability ZHAO Hong, ZHENG Hou-ze, GUO Lan 2023, 49 (1):  103-109.  Abstract ( 193 )   PDF (1801KB) ( 324 )   Save Multi-label text classification is one of the important tasks in the field of natural language processing, the goal of which is to find the label subset associated with the text from a given label set. Aiming at the problem of how to effectively extract text features and obtain the potential correlation between labels in processing multi-label text classification, a model of convolutional neural networks (CNN) combined with bi-directional long short-term memory (Bi-LSTM) is proposed to process multi-label text classification. Firstly, text features are extracted through the CNN network and max pooling. Then, the trained Labeled Latent Dirichlet Allocation (labeled LDA) model is used to obtain the word-label probability information of all words and labels. In addition, the Bi-LSTM network and CNN network are used to extract the word-label information feature of each word in the current prediction text. Finally, combined with the extracted text features, the label set associated with the text is predicted. The experimental results show that the F1 value of the model can be effectively improved by using the word-label probability to get the correlation information between the words and labels in the text. References | Related Articles | Metrics

Architectural Sciences

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Seismic performance analysis of PC base-isolated double-tower structure with a large base floor under extremely rare earthquake DU Yong-feng, ZHOU Dong-lei, LI Hu, CHI Pei-hong 2023, 49 (1):  110-118.  Abstract ( 184 )   PDF (6581KB) ( 169 )   Save In order to study the seismic performance of PC base-isolated double-tower structure with a large base-floor under extremely rare earthquakes, the software ANSYS was used to carry out the finite element analysis of PC and RC base-isolated double-tower structure with a large base-floor. The floor displacement, base-floor stress distribution, other dynamic responses, and energy dissipation of the above two structures under rare and extremely rare earthquakes were compared and analyzed.The results show that compared with the RC structure, the natural vibration period and floor displacement response of the PC structure increase, while the top floor acceleration decreases. The plastic energy dissipation of the superstructure increases, and the damage is serious. Under the extremely rare earthquake, the isolation layer deformation of the two structures increases significantly, while the energy dissipation capacity decreases relatively, and the proportion of energy absorbed by the superstructure increases. Therefore, it is suggested that isolation bearing with a larger diameter should be considered in the isolation design as far as this situation is concerned. Under the extremely rare earthquake, the peak stress at the connection position of the two towers and the large base plate significantly increases, so corresponding strengthening measures should be taken in the design of the connection position of the towers. References | Related Articles | Metrics

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Analysis of uplift bearing characteristics and deformation prediction of root pile HUANG Xue-feng, ZHANG Ji-lu, ZHOU Jun-peng, WEI Lin-hui YUAN Jun, WANG Xue-ming 2023, 49 (1):  119-126.  Abstract ( 136 )   PDF (2190KB) ( 134 )   Save The full-scale field test of root pile shows that implantation of roots not only greatly improves the bearing capacity of foundation, but also effectively restrains the displacement of pile attributed to the stable exertion of root resistance. However, due to the limitation of test conditions, the ultimate bearing capacity of root piles has not been measured under various combination modes, and the existing results alone can not systematically predict the ultimate bearing capacity of root piles. Therefore, ABAQUS software is used to simulate and analyze the full-scale test mentioned. By comparing Q-S curves under different root densities and locations, the influence rule of different root combinations on the bearing capacity and the change of the bearing characteristics of the roots are determined. Based on the load transfer theory, a nonlinear deformation calculation method of the root pile considering the influence of the root bond density and the spacing is proposed. The results show that the theoretical prediction highly agrees with the simulation results, which correctly reflect the deformation law of the foundation under different root bond combination modes. References | Related Articles | Metrics

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Experimental study on mechanical properties and freezing resistance of rice husk ash improved saline soil CHOU Ya-ling, HAN Hang-tian 2023, 49 (1):  127-135.  Abstract ( 222 )   PDF (3190KB) ( 322 )   Save Saline soil is widely distributed in the seasonal frozen soil area of Northwest China, which has poor continuity in spatial distribution and extremely unstable engineering properties. Moreover, the mechanical properties of shallow saline soil are in dynamic changes for a long time due to the repeated influence of freezing and thawing, which brings great challenges to engineering design and construction. In view of this, through the consolidation compression test and the unconfined compressive strength test, the improvement effect of rice husk ash on chloride saline soil was studied. The results show that rice husk ash can significantly improve the compressive properties of saline soil and increase its unconfined compressive strength, and there is a negative linear relationship between the compression coefficient and compressive strength of improved soil. With the increase of rice husk ash and curing age, the compression coefficient of the improved saline soil continues to decrease, and the unconfined compressive strength shows an increasing trend, which can be increased by about 4 times. By using the loss rate of unconfined compressive strength as evaluation criteria, the frost resistance of the improved soil was evaluated. It was found that the frost resistance of the improved soil increase first and then decrease with the increase of the amount of ash, and the frost resistance effectis the most significant when the amount of ash was 15%. Relatively speaking, the curing age has little effect on the frost resistance of the improved saline soil. References | Related Articles | Metrics

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Numerical simulation and optimization of mechanical properties of step surfaces for stepped spillway ZHAO Ting-hong, SHI Yu-xuan 2023, 49 (1):  136-143.  Abstract ( 139 )   PDF (4290KB) ( 215 )   Save With the help of ANSYS finite element analysis software, the stress state of step surface of stepped spillway dam under the action of water flow near the dam body has been concerned, and the attempt to optimize and improve the stepped spillway dam has been carried out, followed by the comprehensive comparison between the original model and optimization scheme. The calculation results show that the stress singularity is easy to appear in the corner of the step, which will endanger the safety of the structure. However, this situation can be improved by adopting the optimization and improvement measures of the fillet in the corner of the step without basically affecting the energy dissipation performance. References | Related Articles | Metrics

Scientific

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Bounds for the spectral radius and energy of a kind of weighted adjacency matrix of graphs LU Peng-li, XUE Xiao-yan 2023, 49 (1):  144-151.  Abstract ( 161 )   PDF (913KB) ( 304 )   Save A kind of weighted adjacency matrix of graph G is denoted by Adb(G)=(adbij)n×n, where $a_{i j}^{d b}=\frac{d_{i}+d_{j}}{d_{i} d_{j}}$ if the vertices vi and vj are adjacent, and adbij=0 otherwise. In this paper, some upper and lower bounds of the weighted spectral radius of graph G are first obtained, and then the Nordhaus-Gaddum-type relation for weighted spectral radius is given. In addition, several upper and lower bounds for the weighted energy are obtained, then, the Nordhaus-Gaddum-type results for the weighted energy are presented. References | Related Articles | Metrics

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Solving reduced biquaternion regulating equation based on semi-tensor product of matrices XI Yi-meng, LI Ying, LIU Zhi-hong, SUN Jian-hua 2023, 49 (1):  152-157.  Abstract ( 133 )   PDF (654KB) ( 215 )   Save Based on the semi-tensor product of matrices and the real vector representation of reduced biquaternion, the problem of reduced biquaternion regulating equations A1X－A2XB=C is transformed into a matrix equation on real number field without constraint, and then the (anti-)Hermitian solution of reduced biquaternion regulating equations is obtained by using real matrix equation. The effectiveness of this method is verified by numerical experiments. Finally, this method is applied to the continuous zeroing dynamics design of time-varying linear systems. References | Related Articles | Metrics

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Error analysis of modified schemes for time-fractional Cable equation WU Xiao-lei, YANG Yan, YAN Yu-bin 2023, 49 (1):  158-163.  Abstract ( 143 )   PDF (811KB) ( 156 )   Save Error analysis of the modified second-order backward difference scheme for the time-fractional Cable equation is carried out. By using continuous Laplace transform and inverse Laplace transform, the exact solution of the equation is obtained, and the finite element semidiscrete solution is obtained similarly. Then Lubich's correction method is used to get the modified form of the fractional differential equation. The discrete solutions of the Cable equation are obtained by means of the discrete Laplace transform and the inverse Laplace transform. Finally, the error estimates under the norm are discussed and the second order of convergence is obtained. Numerical results verification is finally performed to validate the theoretical findings discussed here, which proved that it is better than the first order convergence without modification. References | Related Articles | Metrics

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The invariant Einstein metrics of the full flag manifold Sp(3)/T GAO Ying-ying, WANG Yu 2023, 49 (1):  164-172.  Abstract ( 133 )   PDF (553KB) ( 186 )   Save The invariant Einstein metrics of the full flag manifold Sp(3)/T that was divided into nine isotropy subspaces were studied. First, the value of the non-zero structure constant was calculated, then according to its Einstein equation, sixty-four invariant Einstein metrics (up to a scale) were obtained by the Maple, which included a unique Kähler Einstein metric and three non-Kähler Einstein metrics (up to isometry) in the sense of equidistance. References | Related Articles | Metrics