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28 December 2025, Volume 51 Issue 6 Previous Issue    Next Issue

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Materials Science and Engineering

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First-principle on adsorption of SF6/N2 decomposition components on the TiO2/Graphene LI Ning-rui, LIU Bing-bing, GOU Yan, SUN Wei, BAO Yan-yan, LI Xiao-qiang 2025, 51 (6):  1-8.  Abstract ( 119 )   PDF (4622KB) ( 170 )   Save SF6/N2 mixture gas has become one of the green and stable alternative gases of SF6 making the accurate detection and analysis of their characteristic decomposition components highly significant for practical applications. TiO2 with excellent performance was combined with graphene (GE) to construct a stable TiO2/GE composite structure based on the first-principle. The adsorption properties of SF6/N2 decomposition gases (H2S, SO2, SOF2, SO2F2 and NO2) by TiO2/GE were investigated. The variation rule and influencing mechanism of adsorption energy, electrostatic properties, LUMO and HOMO orbitals, electronic properties, and work function of the adsorption systems were systematically analyzed. The results showed that there is charge transfer between TiO2 and graphene, and the adsorption of TiO2/GE for SO2, SOF2, SO2F2, and NO2 is relatively strong. The LUMO-HOMO band gaps of different adsorption systems are different. The gases can be detected and analyzed by the chemical variables generated according to the degree of desorption difficulty. Moreover, TiO2/GE has strong electron orbital overlap with gas molecules, and the work function of each adsorption system are different, which can be applied to field-effect sensors with adjustable gate voltage. References | Related Articles | Metrics

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The influence of Titanium on the mechanical properties of hot-dip Al-Zn plated coating on steel sheet TANG Xing-chang, LI Kun-yu, LIU Xiao-hua, XU Xue-ming, ZHANG Zhi-jian 2025, 51 (6):  9-17.  Abstract ( 68 )   PDF (9619KB) ( 131 )   Save The mechanical properties of the coating are the key to the service life of coated products. The effect of grain refinement caused by the addition of titanium on the mechanical properties of the coating was investigated by taking the aluminum-zinc-plated steel plate coating as the research object. The mechanical properties of the two coatings was tested with the help of nanoindentation meter, abrasion meter and in-situ test bench. The results showed that the addition of Ti to the plating solution can form TiAl-phase fine particles as heterogeneous nucleation points in the plating layer, which promotes grain refinement and makes the titanium-containing plating layer to show more excellent hardness, stiffness, toughness, roughness, wear resistance and bonding force. References | Related Articles | Metrics

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Study on the uniaxial compression mechanical properties of rocks with pre-existing fracture under acid corrosion SHENG Jie, LEI Rong, TANG Xing-chang, ZOU Ren, WU Yun-peng, GAO Qi-dong 2025, 51 (6):  18-28.  Abstract ( 52 )   PDF (9121KB) ( 116 )   Save To investigate the effect of prefabricated fracture inclination angle on the uniaxial compression performance of sandstone containing fractures under acid corrosion, dipping experiments in pH=2, uniaxial compression test, and crack propagation were simulated using Weibull distribution finite element model. The results indicated that the mechanical properties of specimens with low-angle cracks (0° and 30°) significantly deteriorate after acid corrosion, and the failure mode change from single tensile failure to shear tensile mixed failure. The dissolution of the cement lead to the weakening of the internal structure. In contrast, specimens of high-angle cracks (45°, 60°) exhibit non-monotonic response in compressive strength enhancement due to passivation of crack tips and formation of shear crack networks. The numerical simulation is consistent with the experimental results, revealing that acid corrosion regulates the failure process through mineral dissolution, stress field redistribution, and crack closure effects. An increase in Poisson’s ratio indicates a decrease in rock brittleness. References | Related Articles | Metrics

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Preparation and properties of polyhydrazide-based high-strength epoxy adhesives ZHANG Hang, DAI Xiao-yu, LI Yan-zhen, ZHANG Ding-jun, ZENG Jia, HE Zi-rong 2025, 51 (6):  29-34.  Abstract ( 58 )   PDF (1085KB) ( 138 )   Save A polyhydrazide precursor was pre-synthesized via the reaction of hydrazine hydrate and dimethyl terephthalate at 80 ℃. Subsequently, a novel epoxy adhesive was fabricated using epoxy resin E-51 as the matrix and hydroxyethyl ethylenediamine as the curing agent. The influence of polyhydrazide content on the adhesive performance was systematically investigated, and physical properties of the reinforced adhesive, including bonding strength, hardness (Shore D), wettability, and water absorption, were comprehensively evaluated. The debonding behavior of the adhesive in acidic aqueous solutions (35% acetic acid) under simulated service conditions (80 ℃) was characterized to assess environmental resistance.Experimental results demonstrated that the bonding strength of the polyhydrazide-modified epoxy adhesive initially is increased and then decreased with rising polyhydrazide content, while the hardness exhibit a gradual enhancement followed by stabilization. Optimal comprehensive performance is achieved at 7 wt.% polyhydrazide loading, yielding a hardness of 100 HD, bonding strength of 9.13 MPa, and tensile strength of 82.24 MPa. Notably, the adhesive display prolonged debonding resistance in aggressive environments, with a boiling debonding time of 10.4 h in 35% acetic acid at 80 ℃. References | Related Articles | Metrics

Mechanical Engineering and Power Engineering

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Research on hydraulic characteristics and optimal design of small flow labyrinth channel emitters for drip irrigation system CHEN Guo-xue, JI Hong, ZHANG Jian-jun, CHEN Ji-qing, LI Ya-ping, DU Bin 2025, 51 (6):  35-41.  Abstract ( 68 )   PDF (3360KB) ( 116 )   Save As one of the core components of the drip irrigation system, the hydraulic performance of the emitters directly determines the irrigation efficiency of the drip irrigation system. In practical applications, the labyrinth type emitters of the flow rate is too large, which leads to serious water and fertilizer loss, easy to clog the problem. To address these issues, numerical simulation methods were used here to study the flow field characteristics of the complex internal flow channel of the emitters. The influence of the structural parameters such as the height of the flow channel teeth, the angle of the teeth, the depth, the length of the cells, and the clearance at the top of the teeth on the hydraulic characteristics of the emitters was analyzed. A test rig was built to test the hydraulic characteristics of the emitters, and the accuracy of the numerical calculation was verified by comparing the test results with the simulation results. The results indicate that tooth height and tooth angle have minimal influence on flow rate, whereas reducing flow-channel depth and unit length effectively decreases discharge. The small-flow double channels emitter structure that takes into account clogging resistance, improves the clogging resistance by 97.1% and reduces the flow rate by 37.5% compared with the pre-improvement one. References | Related Articles | Metrics

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Fault diagnosis of gearbox cracks based on variance contribution rate GUO Jun-feng, CHEN Da-peng, WANG Miao-sheng, WANG Er-hua 2025, 51 (6):  42-48.  Abstract ( 45 )   PDF (3847KB) ( 139 )   Save The gearbox is the core component of the wind turbine, which is prone to mechanical failure under the interference of internal and external multi-excitation. Aiming at the problem of low fault diagnosis accuracy caused by insufficient data information generated by the single sensor test in the fault diagnosis of the gearbox in the fault diagnosis, a gearbox crack fault diagnosis method based on the original vibration signal fusion of the dual sensor using the variance contribution rate is proposed. Firstly, the acceleration sensor is used to obtain the vibration signals of different measurement points of the gearbox. These signals are then fused using a variance contribution rate-based method, and the fused data are transformed into wavelets to obtain time-frequency images. Secondly, the deep learning model of convolutional neural networks (CNN) is established and trained using the time-frequency images derived from the wavelet transform. Finally, fault diagnosis experiments are conducted using a test dataset.. The results show that compared to the method using unfused data, the proposed method accurately identify crack faults of different lengths of gearbox. References | Related Articles | Metrics

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The classification method of small sample tower surface defects based on improved relational network ZHENG Yu-qiao, JIANG Dong-yu, DONG Fu-gang, ZHANG He-yu 2025, 51 (6):  49-54.  Abstract ( 51 )   PDF (3354KB) ( 131 )   Save To implement the intelligent detection of surface defects on wind turbine tower, a small-sample tower surface defect classification method based on an improved relational network is proposed. The method integrates a residual network with a relation network, where the increased network depth enhances the model’s feature representation capability. An infinite-order continuous, non-monotonic activation function is used in the nonlinear transformation phase, and a general adaptive robust loss function is used in the training phase. The model is tested and validated on a real image dataset of wind turbine tower surface, achieving a classification accuracy of 90.26%, which is 4.57% better than the original model. The accuracy and reliability of the proposed network model meet the current requirements of wind turbine tower condition monitoring and operation, and maintenance. References | Related Articles | Metrics

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Data augmentation of rolling bearing faults based on SDP and W-DCGAN SONG Hui-xian, DENG Lin-feng, ZHENG Yu-qiao 2025, 51 (6):  55-64.  Abstract ( 45 )   PDF (3687KB) ( 127 )   Save When the traditional generative adversarial network is used to solve the fault diagnosis of rolling bearing with small samples, low quality of generated samples and unstable training process are the main defects of the network. Therefore, a new method combining symmetrized dot pattern (SDP) and Wasserstein-distance deep convolutional generative adversarial network (W-DCGAN) is proposed to augment the bearing data with small samples. First, the SDP with optimized parameters is used to transform the one-dimensional time-domain signal to the two-dimensional image suitable for inputting into W-DCGAN. Then, the controlled variable method is used to optimize the hyperparameters of the generator and discriminator to determine the basic structure of the W-DCGAN. Meantime, in order to enhance the stability of training process of W-DCGAN, spectral normalization is added into discriminator to improve the quality of generated samples. The performance of the method is verified by an open rolling bearing dataset. The results show that the quality of the generated samples of the proposed method is significantly improved. The structural similarity and peak signal-to-noise ratio of the generated samples relative to the original samples increase by 10.12% and 12.46%, respectively. For the rolling bearing fault identification, the proposed method has the highest accuracy of fault identification, reaching 99.47%, indicating its effectiveness in small sample data augmentation andpattern recognition for rolling bearing fault. References | Related Articles | Metrics

Chemical Industry and Light Industry

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Research on heat generation and thermoelectric coupling characteristics of cylindrical lithium-ion batteries ZHANG Tao, ZHAO Ya-bing, MA Li-qun 2025, 51 (6):  65-71.  Abstract ( 52 )   PDF (3776KB) ( 138 )   Save Lithium iron phosphate (LFP) batteries and nickel-cobalt-manganese (NCM) ternary batteries, the two exhibit different characteristics due to the differences in their cathode materials. Batteries with the same type of electrode material may also display diverse electrochemical and thermal behaviors due to different electrode constructions. The study explored the impact of discharge rates, operating temperatures and other factors on the electrochemical and thermal properties of the batteries, and comparatively analyzed the performance differences between LFP batteries and NCM batteries as well as batteries with varying electrode thicknesses. The results indicated that NCM batteries have superior high-rate discharge characteristics and better performance at low operating temperatures than LFP batteries. The heat generation characteristics of LFP and NCM batteries exhibit different sensitivities to ambient temperature, with LFP batteries showing an increase in heat generation as environmental temperature rises compared to NCM batteries. Batteries with thicker electrodes have a faster temperature rise rate than those with thinner electrodes. However, batteries with thinner electrodes exhibit better rate capability, with a smaller voltage drop after discharge rate increase compared to the batteries with thicker electrodes. References | Related Articles | Metrics

Automation Technique and Computer Technology

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Research on self-maintenance strategy of stage multi-axis synchronous system based on health perception feedback adjustment LI Wei, DING Hai-feng, MAO Hai-jie 2025, 51 (6):  72-81.  Abstract ( 49 )   PDF (2998KB) ( 156 )   Save To solve the problem that the performance of the stage multi-axis synchronous system is degraded due to the hidden degradation of the actuator and the system cannot meet the time limit of the control task, this paper proposes an autonomous maintenance strategy based on the system health perception feedback adjustment. Firstly, implementing a novel PdM module, the PdM framework of the stage multi-axis synchronous system was built. Second, considering the impact of maintenance actions and measurement noise on the actuator degradation process, the Kalman filter and EM algorithm were used to estimate the degradation state in real-time and update the parameters of the Wiener degradation model adaptively, enabling accurate prediction of theRUL of the system. Furthermore, the local terminal constraint of rolling change was incorporated into MPC in the manner of “breaking the whole into parts” through integrating the degradation state, RUL, maintenance target, and prediction step. The constraint matrix Q and R parameters were adaptively adjusted based on holographic feedback of system health information. Finally, it is demonstrated that the suggested technique can maintain the system in a long-term healthy operating condition by real-time health observation and adaptive feedback control of predictive maintenance through the simulation experiment. References | Related Articles | Metrics

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Observer-based security control of cyber-physical system under hybrid cyber attacks ZHU Chao-qun, LIU Cheng-fa 2025, 51 (6):  82-89.  Abstract ( 43 )   PDF (1496KB) ( 137 )   Save This paper investigates the security control problem for a class of cyber-physical systems under hybrid cyber-attacks. Firstly, considering the influence of hybrid cyber attacks and signal quantization error, a closed-loop model of cyber-physical systems is established by utilizing a dynamic observer-based feedback control method. Secondly, by means of Lyapunov stability theory and stochastic system theory, sufficient conditions are derived for the robust stability of cyber-physical systems. The robust controller satisfying H∞ performance is obtained by linear matrix inequality technology and singular value decomposition method. Finally, a simulation example is given to verify the correctness and effectiveness of the proposed control method. References | Related Articles | Metrics

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Decentralized robust control strategy of islanded DC-MG based on convex polytopic model WANG Xiao-lan, ZHANG Liang-liang, GUO Tong-ji 2025, 51 (6):  90-98.  Abstract ( 45 )   PDF (2138KB) ( 136 )   Save In an isolated DC microgrid with a general topology composed of multiple distributed generation units, distributed generation unit plug and play, sudden load changes, and topology changes will affect the stable operation of the system. To solve the problem, various uncertainties in the islanded DC microgrid are described using a convex polytope mode. The asymptotic stability conditions of the distributed generation unit subsystem and microgrid system are obtained based on the extended linear matrix inequality constraints, and the dynamic performance of the distributed generation unit is improved by closed-loop pole position constraints. On this basis, the convex optimization problem of distributed generation units is solved, and a decentralized robust controller for isolated DC microgrids based on a convex polyhedron model is obtained. The simulation results show that compared with the performance of a decentralized Robust control system based on a parameter deterministic model, the proposed method can effectively restrain the voltage fluctuation of the DC microgrid system, thus improving the stability of the DC microgrid system. References | Related Articles | Metrics

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Nonlinear extended object tracking method based on multiplicative noise CHEN Hui, LIU Yu, LIAN Feng 2025, 51 (6):  99-106.  Abstract ( 46 )   PDF (2683KB) ( 148 )   Save Aiming at the nonlinear extended object tracking problem, a nonlinear extended object tracking method based on multiplicative noise is proposed. First, the Doppler range rate is included in the radar nonlinear measurement equation. Through measurement conversion, the direction and diameter distance are converted into the Cartesian coordinate system, and pseudo range rate processing is used to handle the distance in the polar coordinate, followed by the removal of the conversion deviation. Then, a matched linearization approach is applied to deduce the optimal linearized equation under the minimum mean square error, retaining the extended information in the original nonlinear quantitative measurement of the second-order central distance. This ensures that the linearized measurement has the same second-order central moment as the original measurement. The updated closed form solution was obtained by Kalman filter formula. Furthermore, the Gaussian Wasserstein distance is used to evaluate the performance of extended object tracking. Finally, the effectiveness of the proposed algorithm is verified by the extended object tracking and group object tracking experiments. References | Related Articles | Metrics

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A dual-branch global-local attention network for insulator defect detection JIAO Liang, WANG Zhong-shun, WANG Si-run, LI Ce 2025, 51 (6):  107-115.  Abstract ( 67 )   PDF (5575KB) ( 153 )   Save Surface defects of insulators can severely deteriorate their performance and may even lead to power failures. Therefore, accurate identification and precise localization of surface defects on insulators are essential for ensuring the safe operation of the power system. The focus of insulator defect detection is the accurate identification and localization of defects in its materials. However, conventional deep learning-based methods face limitations such as poor detection rates when identifying small defects. To address this issue, this paper proposes aglobal and local dual-branch attention module (GLDA). Firstly, the global branch utilizes a traditional attention mechanism but applies downsampling to K and V to reduce computational load, capturing low-frequency global information. The local branch effectively integrates shared weights and context-aware weights to aggregate high-frequency local information. Secondly, an Adaptive Spatial Feature Fusion (ASFF) module is used to extract multi-scale information of defects, enhancing detection accuracy. Lastly, the CIoU algorithm is introduced to optimize the training loss of the baseline model. Experimental results show that the proposed method achieves accuracy, recall, and mAP of 93.2%, 92.9%, and 95.2%, respectively. References | Related Articles | Metrics

Architectural Sciences

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Damage identification of footbridge based on computer vision CUI De-peng, WANG Cui-yun, ZHU Qian-kun 2025, 51 (6):  116-124.  Abstract ( 37 )   PDF (5370KB) ( 154 )   Save A noncontact damage identification scheme for footbridges based on computer vision is established to solve the problems of low-efficiency of the existing bridge vibration damage identification system and poor identification effect of small vibration. The phase-based motion magnification technique and the segmented optical flow method are combined with the additional mass method for structural damage identification to identify structural damage. The feasibility of the proposed method for structural vibration identification is verified by the experiments under three different working conditions on the laboratory footbridge model. The system can judge whether the structure is damaged and the location of damage by the change of modal MAC values and mode shapes. The results show that the modal information of the footbridge in the vibration time-history is more complete and accurate than that of the HS optical flow method under the three conditions, and successfully identifies both the presence and location of structural damage, which can reach the second level of damage quality evaluation of engineering structures. The scheme has a wide application prospect for its robustness and economics. References | Related Articles | Metrics

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Rheological properties and viscoplastic model of asphalt in miscible recycling asphalt mixture WANG Meng, LI Ping, LIU Bin, DING Pang, ZHAI Xiao-cheng 2025, 51 (6):  125-132.  Abstract ( 35 )   PDF (4211KB) ( 128 )   Save The rheological properties of blended original and aged asphalt with the recycled agent miscible affect the performance of large-mix recycled asphalt mixtures directly. Fourier infrared spectroscopy (FTIR), dynamic shear rheometry (DSR), and multi-stress creep recovery test (MSCR) were used to study the changes of characteristic functional groups, complex modulus, and irrecoverable creep flexibility after miscibility of different proportions of original asphalt, aging asphalt and regenerant. The mechanical response of asphalt is predicted based on the results of the multi-stress creep recovery test and viscoplastic strain model (VP model). A comparative analysis of the road performance of large-dose hot recycled asphalt mixtures was conducted. The results show that the carbonyl index is poorly correlated with the conventional asphalt indices. The regeneration effect of miscible hot recycled asphalt can be effectively controlled by using a range of folded sulfoxide group and aromatic characteristic functional group area index. The VP visco-plastic strain model accurately captures the strain response of rejuvenated asphalt under repeatedcreep-recovery loading. It is recommended that, during mixture design, original and aged asphalt be blended first, followed by the determination of the optimal rejuvenator dosage to ensure desirable rheological properties of the rejuvenated binder. References | Related Articles | Metrics

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Research on sand resistance performance of comprehensive protection facilitiesfor desert hinterland highways under strong wind environment ZHENG Zhong-yuan, DU Mu-qing 2025, 51 (6):  133-138.  Abstract ( 34 )   PDF (4206KB) ( 127 )   Save Based on field testing in the desert hinterland, combined with the numerical simulation of Fluent wind-sand two-phase flow, the sand resistance performances of comprehensive protection in the desert hinterland under strong wind environment are investigated. The transient wind speed and wind direction around the comprehensive protection facility are measured by two 3D ultrasonic anemometers on the highway in the desert hinterland, and the initial wind speed of the sand flow is provided for the numerical simulation boundary. Numerical models of a high vertical sand barrier, a grass grid sand barrier, and a roadbed are established by Fluent. Based on Euler two-fluid model and porous media theory, the sand movement around comprehensive protective facilities and subgrade is numerically simulated. The study found that on the leeward side of the high vertical sand barrier, the wind speed quickly decreases to the range of 0~3 m/s, and the large sand particles are mainly deposited on the windward side of the high vertical sand barrier. The wind speed near the ground by the grass-checkered sand barrier is further decreased. The grass square forms a stable concave surface to generate backflow, which can ensure that the sand surface does not sand itself in a strong wind environment, and can also make sand carried in the airflow accumulate around the groove of the grass square. References | Related Articles | Metrics

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Micro-vibration test and analysis of reactor key system workshop site LI Xin, ZHOU Yu, SUN Kai, GAN Lu-yi, ZHANG Hai-yun, LIN Jian 2025, 51 (6):  139-144.  Abstract ( 54 )   PDF (2244KB) ( 121 )   Save To investigate the dynamic response of fusion reactor key system structures and their sites under environmental micro-vibration excitation, a representative key system building of a fusion reactor was selected as the study object. Field measurements were conducted to capture the time-domain responses of both the building structure and the underlying site under environmental and vehicle-induced excitations. Using the power spectral density method and the least squares complex exponential method with multiple reference points, dynamic characteristic parameters were extracted to identify the micro-vibration response characteristics of the structure and site under different excitations. The micro-vibration performance of the structure was then evaluated based on general vibration criteria for sensitive equipment. The results indicate that, under environmental excitation, the peak structural velocity remains below the criterion threshold, demonstrating satisfactory vibration isolation performance. However, under vehicle-induced excitation, large-amplitude vibrations generated by vehicle operations are transmitted through the column bases to the site, resulting in peak ground velocities within the building exceeding the allowable limits. This suggests that the current vibration isolation measures are insufficient, and additional vibration mitigation strategies for sensitive equipment within the structure are necessary. References | Related Articles | Metrics

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Seismic response analysis of frame structure with liquefiable interlayer site based on probability density evolution method YANG Jia-zhi, LI Rui, WANG Jun-cheng 2025, 51 (6):  145-151.  Abstract ( 32 )   PDF (3043KB) ( 131 )   Save Based on FLAC3D finite difference software, a numerical model for coupling analysis of foundation and frame structure is established to analyse the influence of different buried depths and thickness of liquefied interlayer on the seismic response of frame structure, and to study the variation law of inter-story displacement angle and settlement of structure. On this basis, the random seismic response of the structure is further studied by probability density evolution theory. The results show that the maximum inter-story displacement angle and the overall settlement of the building decrease with the increase of the buried depth of the liquefied interlayer, and the location of the most dangerous floor moves downward with the increase of the buried depth of the liquefied interlayer. Moreover, with the increase of the thickness of the liquefied interlayer, the maximum inter-story displacement angle and the overall settlement of the building increase. Based on the deterministic calculation results, the seismic reliability of the structure is 0.492, which indicates that it is necessary to consider the random characteristics of the ground motion in the seismic analysis of the structure. References | Related Articles | Metrics

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Damage evolution analysis of CFRP-strengthened seismic-damaged exterior joints in composite frame consisting of CFSST columns and steel beams XU Cheng-xiang, NI Meng-jie 2025, 51 (6):  152-156.  Abstract ( 42 )   PDF (2074KB) ( 168 )   Save In order to study the damage evolution process of concrete-filled square steel tubular frame exterior joints strengthened with carbon fiber sheet under earthquake, based on the destructive tests of four groups of concrete-filled square steel tubular frame exterior joints strengthened with carbon fiber sheet under low cyclic loading, the influence of seismic damage was considered by the method of material performance reduction. The finite element software ABAQUS was used to simulate the seismic damage of concrete-filled square steel tubular frame exterior joints strengthened with carbon fiber sheet. The improved two-parameter seismic damage model was used to calculate the damage index and to examine the damage evolution characteristics of the specimens. The results show that the method of simulating seismic damage by reducing material properties is reasonable and effective. The selected seismic damage model can quantitatively analyze the damage index of the structure at each stage. The obtained damage evolution curve proves that the carbon fiber sheet can effectively reduce the seismic damage degree of the concrete-filled square steel tubular frame edge joints. Compared with the unreinforced joint specimens, the seismic capacity of the joint specimens strengthened by a carbon fiber sheet is stronger, and the seismic capacity of the earthquake-damaged reinforced joints is also significantly restored. References | Related Articles | Metrics

Scientific

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Dynamic analysis of a time-delayed SIS model with saturation incidence YUAN Hai-long, FAN Yu, WANG Wei-ming 2025, 51 (6):  157-166.  Abstract ( 47 )   PDF (2348KB) ( 124 )   Save Taking the time delay as the bifurcation parameter, a time-delayed SIS model with saturation incidence is studied. The stability of the equilibrium is analyzed, and the Turing instability of the model and the existence of the Hopf bifurcation are discussed. The direction and stability of the Hopf bifurcation are determined by the correlation bifurcation theory, and numerical simulations are also presented. References | Related Articles | Metrics

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On a half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function WANG Ai-zhen, YANG Bi-cheng 2025, 51 (6):  167-172.  Abstract ( 40 )   PDF (415KB) ( 127 )   Save By means of the weight functions, Hermite-Hadamard’s inequality, and the method of real analysis, a new and more accurate half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function is given. As applications, the equivalent conditions of the best possible constant factor related to a few parameters in the new inequality and some particular inequalities for taking special parameter values are further explored and demonstrated. References | Related Articles | Metrics