15 April 2026, Volume 45 Issue 7
    

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    VIBRATION THEORY AND INTERDISCIPLINARY RESEARCH
  • A study of high-performance overlapping finite element dynamic model for magneto-electro-elastic coupling problems
    JIANG Zhilong1, 2, ZHANG Feng2, LI Wei1, 3, 4, LI Kaifu5, CHAI Yingbin1, GUI Qiang1
    Journal of Vibration and Shock. 2026, 45(7): 1-8.
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    A coupled magneto-electro-elastic (MEE) overlapping finite element method was developed for MEE structures in dynamics problems.Through free vibration and harmonic response analyses of the MEE structures, the influence of the used basis functions in the overlapping finite element method on its numerical performance, such as computational accuracy, efficiency, and convergence properties, was discussed in detail.Furthermore, the displacement transmission of a typical MEE phononic crystal beam was calculated, and the bandgap characteristics of this beam was accurately predicted using the overlapping finite element method.This work provides an effective numerical approach for the analysis of MEE phononic crystals and contributes to the further development of high-performance coupled MEE-overlapping finite element method dynamic model.

  • Non-uniform discrete modeling and precision optimization of circumferential long arc spring-type vibration damper
    YUAN Xinjian1, LI Shunming2
    Journal of Vibration and Shock. 2026, 45(7): 9-18.
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    Addressing the conflict between modeling accuracy and computational efficiency caused by the “partial operation phenomenon” in the Circumferential Long Arc Spring-Type Vibration Damper (AS-LTD) under high-speed, low-amplitude operating conditions, this paper proposes a non-uniform discretization method based on a folded-back arithmetic sequence and a dynamic multi-contact-pair friction model.Compared with traditional methods that only achieve parameter identification for the hysteresis model of dual-mass flywheels without addressing non-uniform deformation or external load coupling,resulting in an error exceeding 5% for a single contact pair, and relevant studies that consider gap hysteresis but fail to resolve micro-amplitude errors (>3%) or the accuracy-cost trade-off, the innovations of this study are as follows:  Fine segmentation at the ends,with a stiffness of 1/16 of the overall stiffness,combined with coarse segmentation in the middle to adapt to the “partial operation phenomenon”; a multi-contact-pair model that responds in real time to changes in torque and rotational speed; correction of micro-amplitude errors using the friction memory effect.Simulations and experiments demonstrate that under low-amplitude conditions at 3 000 r/min, the friction torque error rate is reduced from 32% to 08%, while the computational cost is reduced by 45% compared to equidistant discretization with nElm=16 elements, under low-amplitude conditions.This provides a “high-accuracy, low-cost” solution for the noise, vibration and harshness optimization of drivelines.
  • Robust sliding mode compensation control of the tendon-sheath transmission system based on feedforward compensation
    YANG Mingxing1, 2, WANG Qi1, 2, ZHANG Xing1, 2, GAO Jiapeng1, 2, WANG Lu1, 2
    Journal of Vibration and Shock. 2026, 45(7): 19-29.
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    The tendon-sheath transmission system is widely utilized across various fields due to its simple structure, agile transmission characteristics,and capability for long-distance power transmission in narrow and curved space.However, the inherent flexibility of the tendon, along with friction between the tendon and the casing during operation, which leads to nonlinear phenomena such as displacement gap, hysteresis and dead-zone within the system.These issues considerably affect the precision of control over the system’s end motion.Firstly, the static model and dynamic model of the tendon-sheath transmission system were established based on the Coulomb friction model and the Lugre friction model theory.In addition, the inverse transmission model of the system was deduced according to the forward static model.Secondly, a sliding mode compensation control strategy based on feedforward compensation was proposed, and the precise control of the system was realized by combining the sliding mode control algorithm with feedforward compensation.Then, the effectiveness of feedforward compensation algorithm was verified in the comparative experiment with or without feedforward compensation control.Finally, performance comparison experiments were conducted on  proportional-integral-differential control and sliding mode compensation control algorithms with/without interference conditions, and the results confirm the feasibility and superiority of the sliding mode compensation control algorithm in the field of tendon-sheath transmission.
  • Dynamic characteristics analysis of rotor system with squeeze film damper considering fluid inertia during maneuvering flight
    WU Feihan1, 2, CHEN Qiang2, DONG Xingjian1
    Journal of Vibration and Shock. 2026, 45(7): 30-38.
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    This paper focuses on the rotor system of micro turbojet engines under conditions of high squeeze film damper (SFD) Reynolds number and heavy maneuver load. The oil film force of the SFD with fluid inertia was obtained by energy approximation method. A finite element model was established for the rotor system during steady hovering. The dynamic response was solved by numerical method. The results show that the dynamic characteristics vary from different levels of mass unbalance. With normal unbalance excitation, the amplitude frequency response remains stable even under large maneuvering conditions. The influence of fluid inertia on the radius of the precession orbit, the maximum eccentricity, and the external force decreases as the maneuver load increases. However, with extreme unbalance excitation, the system exhibits bistable response. Due to the effect of fluid inertia, the radius of the orbit at the amplitude mutation point is significantly reduced, and the suppression of the bistable speed range is enhanced.
  • Dynamic response analysis of saturated soil under multi-field coupling of thermo-hydro-mechanical
    MA Jianjun, FAN Qingfeng, LIU Fengjun, GUO Ying
    Journal of Vibration and Shock. 2026, 45(7): 39-49.
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    The coupled interactions among ground water, ground stress, and temperature play a critical role in the stability and safety of foundation engineering. To more comprehensively elucidate the dynamic response mechanisms of two-dimensional saturated soils under thermo-hydro-mechanical coupling, this study employs the Youssef’s fractional order generalized thermoelastic theory in conjunction with Darcy’s law. The dynamic responses of two-dimensional saturated soils subjected to mechanical or thermal loading on the surface are systematically investigated. Using the normal mode analysis, analytical expressions for various non-dimensional variables were derived. A systematic investigation was conducted to examine the effects of variations in loading frequency, fractional order coefficient, porosity, and permeability under different boundary conditions on the distributions of non-dimensional excess pore water pressure, temperature, vertical displacement, and vertical stress. The research findings indicate that under different boundary conditions, the loading frequency exerts a significant influence on all non-dimensional parameters. The fractional order coefficient and permeability coefficient have a minimal impact on the non-dimensional vertical stress under mechanical loading and show no significant effect on the vertical displacement under thermal loading. The dynamic responses of various physical variables are significantly influenced by different boundary conditions. The findings of this study provide a theoretical foundation for the design of foundation engineering and nuclear waste disposal, offering valuable guidance in these fields.
  • Research on micro-vibration suppression of LPBF integrated structure-function micro-scale powder damper structures
    ZHANG Tianhao, CHEN Jie, YANG Qin, TANG Jingang, XIANG Zheng, ZHANG Chenyu, HUANG Shuke
    Journal of Vibration and Shock. 2026, 45(7): 50-55.
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    With the increasing miniaturization and integration of electronic instruments and precision equipment, internal micro-vibrations severely impact their performance and lifespan. While particle damping combined with laser powder bed fusion (LPBF) technology offers potential for suppressing micro-vibrations, related research remains scarce and urgently needs exploration. To investigate the vibration-damping performance of LPBF-fabricated damping components under micro-vibration conditions, this study designed and fabricated integrated self-sealing powder damping beams with varying numbers of baffles. Their damping properties were characterized using dynamic mechanical analyzer (DMA). The results show that the loss factor gradually increases with the number of baffles, a trend closely related to the powder–inner wall contact area. Compared to a hollow beam, the beam with 11 baffles exhibited a 48% improvement in loss factor under certain conditions, demonstrating significantly superior micro-vibration damping performance over both hollow and solid beams. This study provides valuable insights for regulating and optimizing the damping performance of LPBF-based self-sealing powder structures under micro-vibration conditions.
  • BP neural network-based sliding mode control method for multi-axial real-time hybrid simulation
    ZHANG Tao1, 2, TAN Ping1, 2, YAO Hongcan1, 2, SHANGGUAN Yuekun1, 2, ZHOU Huimeng2
    Journal of Vibration and Shock. 2026, 45(7): 56-66.
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    To address the challenges of coupling effects and delay accumulation in multi-axial real-time hybrid simulation, a sliding mode control compensation method based on BP neural network is proposed, using a Benchmark control problem of a three-layer three-span steel frame. The BP neural network adjusts the weight threshold through data normalization, hidden layer output calculation and error feedback to achieve nonlinear delay prediction. The sliding mode controller dynamically decouples the actuator and suppresses the jitter by constructing the sliding mode surface function with integral terms and the saturation control law. In MATLAB, the state-space model is combined to integrate the neural network training results and the sliding mode control module to achieve multi-axis cooperative control and delay compensation. This method effectively reduces the coupling effect between actuators, enhances the robustness of multi-degree-of-freedom collaboration under complex working conditions, and offers a new method for evaluating dynamic responses of engineering structures.
  • Research on a highstatic-lowdynamic stiffness isolator based on an electromagnetic shunt damper
    WU Wenpeng, HAN Xu, ZHANG Ming, LI Hongtao, CUI Haodong, SUN Feng
    Journal of Vibration and Shock. 2026, 45(7): 67-74.
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    In nonlinear vibration isolation systems with insufficient damping, behaviors like jumping can occur, reducing isolation performance. An electromagnetic shunt damper-based isolator with high static-low dynamic stiffness is proposed to address this. It controls stiffness and damping via current and negative resistance adjustment. The electromagnetic coupling coefficient was derived using the equivalent loop method, and the effect of size parameters was analyzed. A negative resistance circuit using an operational amplifier was designed to lower impedance and increase damping. A dynamic model was developed to evaluate the damper and negative resistance effects. A segmented control strategy was introduced for coordinated stiffness and damping control. Experiments show that, compared to passive isolation, the segmented-control isolator lowers the initial isolation frequency by 16.5% and reduces the resonance peak by 56.5%, achieving superior broadband isolation.
    • CIVIL ENGINEERING
  • Prediction model for response of deep-sea hydrate mining riser flow induced vibration based on DT-TCN-KAN
    GUO Xiaoqiang1, HE Liang1, LI Yingwei2, LIU Xianbin3
    Journal of Vibration and Shock. 2026, 45(7): 75-90.
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    In response to the problem of difficulty in obtaining data on the vibration signals of deep-sea hydrate mining risers in the deep sea, a spatiotemporal vibration prediction model for deep-sea hydrate mining risers is constructed considering the mutual correlation between different positions at the same time. The vibration signals of shallow positions are used to predict the vibration signals of deep-sea hydrate mining risers. A spatiotemporal vibration model for mining risers was established to predict the vibration signals of deep mining risers in the future. Based on the structure of the TCN model, creative design was carried out by preprocessing the input data, embedding the dimension segment wise (DSW) mechanism, and two-stage attention (TSA) mechanism model to capture the dependency relationships between variables. The two mechanisms were combined into a dimension two-stage attention mechanism module, abbreviated as the DT module. Using the DSW mechanism, the model can focus on the segmentation of each dimension sequence at different time steps, thereby better capturing the cross dimensional dependencies between variables. Using the TSA mechanism, the dependency between time and variable dimensions is effectively captured, improving the model's ability to capture deep relationships between sequences. Then, using the backbone TCN model to extract the long-term dependencies of the time series, the extracted features are weighted and finally fed into the Kolmogorov-Arnold Networks (KAN) model for nonlinear fitting, which can effectively improve the nonlinear ability of spatiotemporal prediction models and better capture and process the relationships between sequences. Comparing the in-line and cross flow vibration displacements calculated by the prediction model with experimental data, it was found that the DT-TCN-KAN model had the best prediction effect on the vibration displacement of the mining riser.
    • VIBRATION THEORY AND INTERDISCIPLINARY RESEARCH
  • Design and hydrodynamic characteristics analysis of shared mooring arrangement for semi-submersible wind turbines
    GAO Xifeng1, YANG Huan1, XU Wanhai1, 2
    Journal of Vibration and Shock. 2026, 45(7): 91-98.
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    The mooring system constitutes a critical and cost-intensive component of semi-submersible floating wind turbines. Optimizing its design offers a promising approach to reduce costs and enhance efficiency for offshore wind farms. This paper proposes two novel shared mooring configurations: (1) an Anchor Chain-Counterweight system, and (2) a High Modulus Polyethylene Buoy-Counterweight system. Utilizing the finite element software AQWA, a hydrodynamic analysis model for a 5MW semi-submersible floating wind turbine was established. The motion responses of the platform and the mooring line tensions under various operational conditions were investigated, and the mechanics performance of both mooring systems was analyzed. The results demonstrate significant differences in platform displacement and average mooring line tension between the two shared systems. Specifically, the maximum average mooring tension in the HMPE-BCW system was reduced by approximately 21.53% compared to the ACCW system. Furthermore, the incident angle of environmental loads significantly influences both mooring line tension and platform motion responses. Appropriately reducing mooring line tension can improve the balance and economic viability of the mooring system. This study provides theoretical and technical guidance for the optimal design of floating offshore wind systems.
  • Analysis of coupling characteristics and research on decoupling control strategies for multi-degree-of-freedom magnetic suspension active vibration isolation systems
    HUANG Cuicui, LI Zikang, DAI Chunhui, LONG Zhiqiang
    Journal of Vibration and Shock. 2026, 45(7): 99-109.
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    The strong coupling characteristics between multiple degrees of freedom (DOF) in the magnetic suspension active vibration isolation (MSAVI) system will significantly reduce the vibration suppression performance and stability of the system. To eliminate the coupling between the radial DOF of the MSAVI system and the disturbances caused by the external force of the float, a composite decoupling control strategy based on diagonalization feedback and active disturbance rejection control (ADRC) is proposed. Firstly, a multiple-input multiple-output (MIMO) model of the multi-DOF vibration isolation platform is established, with detailed analysis of coupling characteristics in the control system model. The feedback decoupling control is employed to decouple the known model components, while model deviations-induced coupling errors are treated as unmeasurable external disturbances and incorporated into an extended state observer (ESO) for estimation and compensation. Furthermore, to address decoupling errors arising from model parameter mismatches, a novel decoupling strategy combining feedback control with ADRC is developed. Finally, an improved tracking differentiator is implemented to obtain required differential signals, thereby enhancing both decoupling and compensation performance. Simulation results demonstrate that the proposed composite decoupling controller successfully transforms the originally coupled four-DOF radial system into four independent single-DOF systems, and the ESO effectively compensates for force imbalances and significantly improving vibration isolation performance under complex operating conditions.
  • Method and application of  nonlinear structural dynamic modification
    QIAN Jiahui1, WANG Tong1, ZHOU Bin2
    Journal of Vibration and Shock. 2026, 45(7): 110-117.
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    Flexible lightweight structures are essential in aerospace design due to their low weight, foldability, and high specific strength. However, in modal testing, contact sensors introduce added mass, affecting identification accuracy. Moreover, the large deformation characteristics of such flexible structures introduce pronounced geometric nonlinearity, leading to added nonlinear stiffness and increasing analytical complexity, making direct application of linear methods unsuitable. This paper proposes a nonlinear structural dynamic modification method for flexible lightweight structures, which effectively accounts for the effects of added mass and nonlinear stiffness. Experimental validation shows that the corrected contact sensor results deviate by less than 0.4% from non-contact laser measurements. Simulations further confirm the method’s accuracy and reliability under varying mass distributions. A nonlinear case study further demonstrates its high efficiency and accuracy, with significantly improved computational efficiency compared to the traditional arc-length method.
    • CIVIL ENGINEERING
  • Study on hysteretic performance of X-shaped diagonal energy-dissipating joints in concrete filled steel tubular diagrid structures
    WANG Bin1, 2, HAN Mengqi1, SHI Qingxuan1, 2, CAI Wenzhe3
    Journal of Vibration and Shock. 2026, 45(7): 118-129.
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    To address the problems of insufficient ductility and energy-dissipating capacity, and a single seismic defense in diagrid structures, a design strategy was proposed in which the X-shaped diagonal joints were configured as energy-dissipating connections. This approach aims to control seismic damage and improve structural seismic performance. A new shear type friction damper was developed for use as the energy-dissipating connector within the X-shaped diagonal joints. The new damper incorporates a decoupled configuration that effectively eliminates the influence of axial forces under combined compressive shear or tensile shear loading conditions at the joints. The configuration and working mechanism of the diagonal energy-dissipating joints were described in detail, including an analysis of its force relationship and energy-dissipating mechanism. A hysteretic model of the joints was established. In the simplified numerical model, the inclined column was modeled as fiber beam column elements, while the damper was idealized as four rigid plates connected through zero length elements. These zero length elements were used to simulate the damper’s force transfer and energy-dissipating behavior, thus resulting in a simplified analytical model for the diagonal joints. A numerical model of the diagonal energy-dissipating joints was developed based on the OpenSees platform. The hysteretic performance of the energy-dissipating joints was compared with that of the rigidly connected diagonal joints. The effects of damping force, initial axial force, diagonal angle, and loading protocol on the bearing capacity, deformation, and energy-dissipating capacity of the diagonal energy-dissipating joints were investigated. The results indicate that the proposed hysteretic model and simplified numerical model show good agreement. The diagonal energy-dissipating joints achieves high ductility and energy-dissipation at a relatively low strength cost. To prevent strength and ductility degradation due to premature yielding of the diagonal column when the damper activates, it is recommended that the axial force in the inclined column at the onset of damper sliding should not exceed 75% of their axial yield capacity. Furthermore, the diagonal energy-dissipating joints exhibit stable energy-dissipating performance under variations in initial axial load caused by the structure’s self weight. To ensure adequate load capacity and energy dissipation efficiency, the diagonal angle of the energy-dissipating joint should be controlled within a range of 45° to 60°.
  • Momentum-accelerated alternating minimization for identification of multiple moving vehicle loads
    XU Bohao, YU Ling, HOU Yingxin, RAN Kai
    Journal of Vibration and Shock. 2026, 45(7): 130-137.
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    To address the issue of decreased light vehicle load identification accuracy due to the significant difference in magnitudes between light and heavy vehicle loads under multi-load conditions, a method is proposed for identifying multiple moving vehicle loads based on momentum-accelerated alternating minimization. By constructing a weighted matrix based on the noise variance of each channel and using a multi-regularization model, the moving vehicle load identification problem is reformulated. A constrained optimization equation is proposed to solve for the regularization parameters. An alternating minimization framework is proposed, which alternately updates dynamic load variance, dynamic load and static load. A momentum acceleration is introduced for both the dynamic load variance and static load to enhance convergence efficiency and stability. Numerical simulations demonstrate that the proposed method offers significant advantages in identifying light vehicle loads, with performance improvements becoming more pronounced as the number of loads increases. Experimental validation further confirms that the method can effectively identify actual moving vehicle static loads, showing good engineering applicability and potential for practical implementation. 
  • Experimental study on disturbance response model of surrounding rock during TBM tunneling under isobaric condition
    LIU Yuancheng1, DENG Ronggui1, FENG Wei1, 2, YANG Bai1, 3, WANG Tuo1, 4
    Journal of Vibration and Shock. 2026, 45(7): 138-148.
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    In order to explore the disturbance characteristics of surrounding rock during TBM excavation, this study is based on the DXL tunnel engineering and uses similar model experiments to investigate the radial displacement release characteristics and cumulative variation characteristics of circumferential strain energy in the surrounding rock space in front and behind the TBM face at 45 °, 90 °, and 180 ° under bidirectional isobaric conditions as the TBM face moves. Research has shown that: (1) During TBM tunnel excavation, the radial displacement release rate and circumferential strain energy accumulation increment of the monitoring surface can be divided into three stages: early, middle, and late. Among them, the radial displacement release rate of the surrounding rock in the middle stage accounts for 65% of the total, and the circumferential strain energy change accounts for 74.1% of the total, which is the most severe stage for the displacement release rate and circumferential strain energy change of the tunnel body. (2) During the excavation process of TBM under bi-directional isobaric conditions, the circumferential strain energy of the tunnel surrounding rock forms different strength accumulation zones, which can be divided into four boundary ranges: high, secondary high, medium, and low. Among them, the surrounding rock layer within 1.5R is the area with the most concentrated strain energy and a high risk of failure; The circumferential strain energy of layers outside 3.0R is relatively low.
    • SHOCK
  • Experimental study on dynamic responses of U-corrugated sandwich plate under water impact
    GUO Kailing1, 2, LIU Ding2, LIAO Yong3, ZHU Ling2
    Journal of Vibration and Shock. 2026, 45(7): 149-157.
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    In this paper, the sandwich structure water-entry slamming experimental platform was built, and the slamming load and structural dynamic responses of aluminum U-corrugated sandwich panels were studied. Meanwhile, the protective effects of different types of sandwich structures under slamming loads were compared and analyzed. Results reveals that the difference between the slamming forces measured using the pressure-based method and those computed from acceleration data is only 6.3%, which validates the reliability of the experimental slamming pressure testing system. The slamming pressure across the U-corrugated sandwich plate shows an uneven distribution, characterized by greater magnitudes at the center and a gradual decrease toward the edges. Asymmetric deformation was observed in the U-corrugated sandwich plate, demonstrating higher strain peaks at the central region compared to the surrounding areas. Moreover, at the same measurement point, the strain in the Y-direction is substantially greater than that in the X-direction. Under equivalent mass conditions, significant differences in slamming pressure and plate deformation were observed among different sandwich plate configurations at identical drop heights. Comparative analysis revealed that the U-corrugated sandwich plate exhibited the lowest peak slamming pressure and minimal back-face deformation when compared to aluminum plates and honeycomb sandwich plates, demonstrating superior impact protection performance of the U-corrugated sandwich plate.
  • Research on impact response and failure modes of metal/foam sandwich panels
    ZHANG Mengdi1, SHEN Yanjie2, 3, CHEN Jianzhao2, 3, CAO Xiaojian1, 2, YAO Lu1, 2
    Journal of Vibration and Shock. 2026, 45(7): 158-166.
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    Metal/foam sandwich panels are widely used due to their high specific strength, specific stiffness, and energy absorption efficiency. To further enhance the impact resistance of the sandwich structure, reinforcing rib structures can be bonded within the metal plate on one side of the metal/foam sandwich panel. In order to investigate the mechanical response and failure characteristics of metal/foam sandwich panels with different structures under varying impact energies systematically, drop-weight impact tests were conducted to obtain the mechanical responses and damage morphologies, and the impact resistance behaviors of different structures were analyzed deeply. The results indicate that impact energy significantly affects the damage morphologies and response characteristics of the sandwich panels. As the impact energy increases, the damage modes continuously intensify, including faceplate indentation, interface delamination, and core crushing. Meanwhile, the peak impact load, maximum displacement, and total energy absorption all increase. Compared to the basic structure of C-S-1, the peak impact load of the sandwich panels with reinforcing ribs (C-S-2 and C-S-3) increased by 62% and 168%, respectively. The minimum displacement was reduced by 39% and 63%, but the specific energy absorption decreased by 34% and 60%, respectively. This suggests that the introduction of reinforcing ribs effectively inhibits crack propagation and core failure, enhances the local stiffness and peak load capacity, and reduces permanent deformation to some extent, but at the cost of a reduction in specific energy absorption efficiency.
    • TRANSPORTATION SCIENCE
  • ICEEMDAN-PE-improved WTD based analysis of time-frequency characteristics of wheel-rail forces for a 350 km/h EMU on an No.18 turnout
    SUN Pengtian1, NIU Liubin2, ZHANG Geming3, YANG Fei2, TIAN Xinyu2
    Journal of Vibration and Shock. 2026, 45(7): 167-176.
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    To address the significant issues of non-stationarity, nonlinearity, and noise interference in wheel-rail force signals in high-speed railway turnout areas, this paper proposes a combined method integrating Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), Permutation Entropy (PE), and Improved Wavelet Threshold Denoising (WTD). This approach is applied alongside continuous wavelet transform to analyze the time-frequency characteristics of wheel-rail forces when a 350 km/h EMU passes through an 18# turnout. The method first adaptively decomposes the signal using ICEEMDAN, then utilizes PE to set an adaptive threshold for identifying noise-dominant IMF components, and finally employs the improved WTD to denoise these IMF components, suppressing noise while effectively preserving impact features. Results show that the denoised time-domain signal exhibits a substantial reduction in noise "burrs," with key features such as wheel-rail impacts and load transitions remaining intact. The improved threshold method achieves an average accuracy improvement of approximately 10% compared to traditional methods. Time-frequency analysis reveals that the wheel-rail force response in the turnout area is closely related to structural excitation. The main frequency bands of wheel-rail forces are 35~125Hz and 500~700Hz in the switch zone, and 30~65Hz in the crossing zone. The most severe impact occurs at joint 2, with the dominant  frequency reaching 580~750Hz. This study provides a new method for processing wheel-rail force vibration signals in turnouts, while also offering a theoretical basis and data support for turnout condition assessment.
  • Study on equivalent load for accelerated test of electric drive system considering non-Gaussian service characteristics
    ZHENG Guofeng1, 2, DUAN Yilong1, LIAO Yunlai1, SU Hang2, HONG Hao2, WANG Huan2
    Journal of Vibration and Shock. 2026, 45(7): 177-188.
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    To address the issue that the traditional Gaussian assumption tends to cause deviations in damage assessment during the vibration fatigue acceleration test of electric drive system assemblies, this paper proposes a vibration fatigue accelerated test method that accounts for non-Gaussian characteristics. First, the study adopts the Dirlik frequency-domain fatigue damage spectrum calculation method, and combines it with the skewness and kurtosis indices of structural response signals to complete the non-Gaussian identification and correction of in-service load spectra. Taking the equivalent load for the bench accelerated test of the electric drive system in pure electric vehicles as an example, load spectra of the electric drive system under different typical working conditions were collected; with the measured acceleration signals at the mounts as the target for equivalent load construction, the equivalent load construction method for frequency-based accelerated tests was used to obtain the Power Spectral Density (PSD) spectrum for the bench accelerated test. The equivalent PSD spectrum for the bench accelerated test was compared with the electric drive bench PSD spectrum specified in GB/T 18488-2024 Standard, and both were used as inputs to conduct vibration fatigue simulation verification for the electric drive system. The results show that: the proposed non-Gaussian identification and correction method can accurately characterize the high-order statistical characteristics of non-Gaussian random loads and effectively quantify the impact of non-Gaussian characteristics on fatigue damage; the equivalent PSD spectrum for the bench accelerated test exhibits good consistency with the PSD spectrum loading results specified in the national standard. This verifies the reliability of the proposed method from the perspective of damage equivalence and provides a basis for the accurate design of bench test loads.
  • Research on the dynamics performance of intercity EMUs considering variable stiffness rotary arm nodes
    LUO Jun1, CHI Changxin2, CHEN Junhui1, LI Jing1, ZUO Binhuai1, HOU Maorui2, 3
    Journal of Vibration and Shock. 2026, 45(7): 189-198.
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    The variable stiffness liquid composite swing arm bush can provide smaller stiffness in the low frequency band to improve curve passing performance, and provide larger dynamic stiffness in the high frequency band to ensure vehicle  stability, which provides support for solving the contradictory relationship between high-speed stability and curve passing performance of multiple units. In this paper, a variable stiffness liquid composite swing arm bush is designed. The type test results of the node show that the static radial stiffness is 5 (1±15%) kN/mm, and the dynamic radial stiffness is ≥20 kN/mm. The stiffness of composite rubber joints exhibits strong frequency nonlinearity, and the dynamic stiffness varies significantly across low-frequency and high-frequency ranges. Then, based on the mechanism and data hybrid-driven model, the dynamic model of the variable stiffness liquid composite swing arm bush is constructed, the effectiveness of the variable-stiffness rotating arm node model has been verified, and the co-simulation model of the variable stiffness liquid composite swing arm bush and vehicle dynamics is constructed. The influence of the variable stiffness liquid composite swing arm bush on the motion stability and curve passing performance of intercity multiple units is calculated and analyzed. The results show that compared with the traditional fixed stiffness rotary arm node, the critical speed of linear operation of intercity multiple units with variable stiffness liquid composite swing arm bush is increased. The ride index has been improved, and the safety index under curved road conditions has been further reduced. Through the numerical prediction analysis of wheel wear, when the curve radius is 600 m, the wheel wear of the variable stiffness liquid composite swing arm bush is reduced by 30.5% compared with the fixed stiffness arm node. This paper establishes a foundational framework for the design of rotary arm nodes in inter-city EMUs.
  • Analysis of environmental vibration response induced by metro trains in overlapping tunnels based on transfer function formulation
    LU Zhiting, LIU Weifeng, LI Donghai
    Journal of Vibration and Shock. 2026, 45(7): 199-207.
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    To study the influence of the upper tunnel on the vibration propagation of the train in the lower tunnel in the case of overlapping tunnels, the analytical model of train-rail coupling is used to obtain the under-rail fulcrum reaction force acting on the base of the tunnel, and the finite element model is used to obtain the transfer function from the base of the tunnel to the prediction point on the ground surface, so as to obtain the surface vibration response caused by the underground train operation in various conditions through the method of transfer function, and to analyse the influence rules on the transfer function and surface vibration response caused by the arrangement of various interlocking tunnels. The transfer function and surface vibration response are analysed by the transfer function method. The results show that: the positional relationship of the overlapping tunnels has a great influence on the transfer function of the tunnel-soil layer as well as the ground surface vibration response; in the frequency domain, the upper tunnel has basically no attenuating effect on the train vibration of the low-frequency band under 10 Hz and sometimes even has an amplifying effect, while for the vibration of the low-frequency band under 10 Hz, the upper tunnel has no attenuating effect. In the frequency domain, the upper tunnel basically has no attenuation effect on the train vibration in the low frequency band below 10Hz, and sometimes even has an amplifying effect, while for the frequency band of 10~100Hz, the upper tunnel has a better damping effect on the train vibration in the lower tunnel; in the surface immediately adjacent to the upper tunnel, local vibration attenuation zones can be formed, and with the increase in the horizontal distance between the upper and lower tunnels, the scope of the vibration attenuation zones becomes larger and the damping amount of the maximum Z vibration level increases. In the analysis of environmental vibration prediction for metro lines, the potential suppressive influence of any parallel tunnel structures on vibration propagation must be considered in light of practical engineering conditions.
  • Fractional order sliding mode control of active suspension based on nonlinear disturbance observer
    LONG Jiangqi, CHU Jinkang, ZHOU Min
    Journal of Vibration and Shock. 2026, 45(7): 208-217.
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    Aiming at the problems that active suspension is susceptible to external interference, nonlinear characteristics and parameter changes, in order to reduce the influence of these problems and improve vehicle riding comfort. A nonlinear disturbance observer (NDOB) based fractional order sliding mode control (FOSMC) strategy for active suspension is proposed. Firstly, a nonlinear active suspension dynamic model is established, and a canopy model which does not require real-time road input measurement is used as a reference model to provide a reference trajectory. Secondly, the above problems are integrated into a system disturbance term, and the lumped disturbance is estimated by nonlinear disturbance observer, and the known force is controlled by fractional order sliding mode control. Finally, particle swarm optimization (PSO) is used to optimize the proposed controller parameters. The simulation results show that compared with traditional sliding mode control, fraction-order sliding mode control and unoptimized nonlinear disturbance observer fraction-order sliding mode control. The proposed controller has a great improvement in reducing the sprung mass acceleration of the body and improving the ride comfort of the vehicle, and has strong robustness.
  • Frame virtual proving ground load process and modal transient fatigue analysis
    HAN Qiang, WANG Lirong, ZHOU Xinnan
    Journal of Vibration and Shock. 2026, 45(7): 218-226.
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    A commercial vehicle multibody dynamics model was developed. Techniques included multibody dynamics, rigid-flexible coupling, load damage editing, and modal transient fatigue analysis. Bushing and shock absorber parameters were measured. Frame damping characteristics were identified across frequencies. Experimental modal analysis was used. Measured structural damping was incorporated. Virtual proving ground simulations employed an identified tire model. Scanned durability roads were utilized. High-fidelity load spectra were acquired. Damage consistency principles guided load spectra editing. Load decomposition efficiency and accuracy improved. A finite element model was built. Modal transient fatigue analysis was performed on the frame assembly. Results were compared with quasi-static methods. Actual vehicle cracking patterns were accurately reproduced. The results show: High-precision dynamic load decomposition with modal transient fatigue predicts >90% of frame cracking risks; Design flaws are prevented; Damage-editing techniques improve efficiency by >31%.
    • FAULT DIAGNOSIS ANALYSIS
  • Research on composite fault diagnosis method of rolling bearings based on APFMD
    REN Bin1, LIU Zhexiang1, CHENG Yubo2, HAO Rujiang1, ZHANG Jianchao1
    Journal of Vibration and Shock. 2026, 45(7): 227-239.
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    Aiming at the difficulty of extracting composite fault features when faults are coupled in rolling bearings, a composite fault diagnosis method based on adaptive parameter feature mode decomposition (APFMD) is proposed. Firstly, a comprehensive cyclic sparsity index (CCSI) is established as a fault diagnosis indicator to evaluate signal sparsity and periodic impulsiveness. Secondly, using CCSI as the fitness function of the sparrow search algorithm , the parameters of feature mode decomposition (FMD) are optimized to adaptively select the optimal parameters for FMD. The vibration signal is then decomposed into several mode components using FMD. Subsequently, the kurtosis criterion is utilized to select effective mode components to reconstruct the vibration signal, introducing a virtual multi-channel approach. Finally, the canonical correlation analysis (CCA) algorithm is employed to separate the reconstructed signal into different fault characteristic frequencies, thereby identifying the fault types. Experimental analysis demonstrates that the APFMD method can decompose the composite signal into modes with clear frequency bands and well-defined spectral boundaries, effectively suppressing mode mixing. Furthermore, during the envelope spectrum and CCA analysis, this method accurately extracted characteristic peaks at 108 Hz for the outer race and 171.5 Hz for the inner race, while presenting corresponding harmonics and sidebands spaced at the shaft rotational frequency. Compared to methods such as variational mode decomposition and FMD, the kurtosis values of the reconstructed channels for the outer and inner races were 4.14 and 5.23, respectively, showing improvements over the baseline methods. Additionally, under a signal-to-noise ratio of -5 dB, the method accurately identified the characteristics of the inner and outer races, verifying its effectiveness in the composite fault diagnosis of rolling bearings.
  • Hydraulic turbine cavitation state identification method based on TCN-DCGAN data augmentation
    LIU Zhong1, WU Yitian1, HU Ze’nan2, ZOU Shuyun1, XIE Wenting1
    Journal of Vibration and Shock. 2026, 45(7): 240-247.
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    Aimed at addressing the low accuracy in fault diagnosis caused by the nonlinear, non-stationary nature of hydroturbine cavitation signals and the scarcity of sample data, this paper proposes a data augmentation method based on a temporal convolutional network (TCN)-improved deep convolutional generative adversarial network (DCGAN) for hydroturbine cavitation state recognition. Acoustic emission signals are converted into Gramian angular field (GAF) images to represent cavitation features. The TCN-DCGAN model expands the dataset while maintaining temporal properties and diversity. A convolutional neural network (CNN) model is then used to identify cavitation states from the augmented image dataset. Interpretability analysis is incorporated to support the decisions. Results show the method boosts accuracy by 10% to 13%, surpassing other data augmentation techniques. This approach significantly improves the accuracy and trustworthiness of cavitation diagnosis under small-sample conditions.
  • Structural response reconstruction based on OOA-BiGRU with frequency attention
    HI Jiale1, ZHOU Kang2, ZHI Lunhai1
    Journal of Vibration and Shock. 2026, 45(7): 248-253.
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    To address the problem of missing structural response data due to sensor failures in structural health monitoring, a bi-directional gated cyclic unit network (BiGRU) model that combines frequency-domain attention and Osprey Optimization Algorithm (OOA) is proposed for high-precision reconstruction of acceleration response. The model enhances the modeling ability of key frequency components through frequency-domain attention, and uses OOA to adaptively optimize network hyperparameters, thereby improving the model's reconstruction accuracy and generalization ability. The method was applied to the measured data of One Rincon Hill Tower and verified in the scenario of multiple floor sensors failing, and effective reconstruction of the structural response was successfully achieved. The results show that the reconstruction accuracy of the proposed model in both time domain and frequency domain is better than that of traditional methods. At the same time, it shows good robustness in dealing with data missing caused by sensor failure, and has the potential to be promoted and applied in practical projects.
  • Framework for fault diagnosis of rotor machinery under imbalanced data conditions based on multi-feature fusion FIR filtering
    WANG Yue1, LI Shengxiang2, LI Jin1, LU Guocan1, WU Yafeng1
    Journal of Vibration and Shock. 2026, 45(7): 254-265.
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Rotating machinery serves as core equipment in industrial fields such as energy conversion and fluid transport, operating for extended periods under extreme conditions including high temperature and high pressure. This makes it prone to typical faults such as rotor imbalance and bearing wear, resulting in economic losses amounting to tens of billions of dollars globally each year. Therefore, achieving efficient and accurate fault diagnosis and health management has long been a key focus for both academia and industry. In recent years, although deep learning-based diagnostic methods have significantly improved the health management of rotating machinery, challenges such as scarcity of high-value fault samples in industrial settings, difficulties in multi-domain feature collaborative modeling, and a lack of physical guidance in feature extraction continue to severely limit diagnostic performance in small-sample and imbalanced scenarios.To address these issues, this paper proposes a fault diagnosis method based on trainable FIR filtering and a mixed-weight mechanism (FIR_Mix). The method employs a trainable Finite Impulse Response (FIR) filter layer to achieve noise suppression and enhancement of key frequency components, utilizes a multi-task binary classifier to extract category-discriminative features, and incorporates contrastive loss to optimize the clustering structure in the feature space. Ultimately, robust classification is achieved through the fusion of multi-domain features. Experimental results on the HIT aviation bearing dataset and the HUST rotor fault dataset demonstrate that the proposed method maintains high diagnostic accuracy and robustness under sample-scarce and imbalanced conditions, with an average recognition accuracy of 93.5%-an improvement of 3.4 percentage points over the best baseline method. This provides an effective solution for intelligent operation and maintenance of rotating machinery in complex industrial scenarios.
    • ACOUSTIC RESEARCH AND APPLICATION
  • Design of lightweight multi-frequency local resonance damper for broadband sound insulation of high speed train passenger compartment floor
    ZHU Xuezhi1, ZHAO Huashuai2, YU Peijun3, WANG Shiming2, LIU Pengfei1
    Journal of Vibration and Shock. 2026, 45(7): 266-272.
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    The floor of the high-speed train passenger compartment is an important sound insulation component, and its sound insulation performance is poor within the range of 100Hz~500Hz, which is not conducive to noise control inside the train. This article proposes a thin multi frequency resonant layer structure to address this issue. By designing the structure of a thin cantilever plate, tuning the modal frequency, resonant mass, and modal damping ratio, and utilizing its multiple modes, a single cantilever plate can provide effective multi frequency resonant function. This multi frequency resonant layer structure is formed by stacking multiple layers to form a cantilever oscillator type local resonant damper. The cantilever plate in each damper unit is designed with multi frequency parameters to form a continuous bandwidth sound insulation control effect, achieving enhanced sound insulation of the passenger compartment floor. The large component sound insulation test shows that using the cantilever oscillator local resonance damper proposed in this paper can increase the sound insulation of the original floor by 3dB and 5dB in the low frequency range of 100Hz~500Hz within a 15% increase in the additional mass of the floor, achieving lightweight and high sound insulation performance.
  • Research on sound field reproduction and objective evaluation at the occupant’s ear zone in vehicles
    LU Lu, ZHENG Xu, LIU Chi, YU Yong
    Journal of Vibration and Shock. 2026, 45(7): 273-280.
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    The design sound quality for in-cabin vehicle noise required extensive sound field testing. To facilitate such testing, the sound field reproduction method was employed to reproduce the required acoustic environment in a laboratory. The vehicle cabin sound field reproduction method based on multi-channel least-squares equalization was employed, along with the experimental procedure for the reproduction system. The results indicate that the sound pressure level reproduction error at 15 measurement points around the occupant's ears is controlled within ±1.5dB. Psychoacoustic metrics such as loudness, sharpness, and roughness of both the target sound field and the reproduced sound field are calculated, and spatial perception indicators related to auditory perception are also evaluated. These further verify the accuracy of the auditory performance of the reproduced sound field compared to the real vehicle, providing an important basis for automotive acoustic design and sound quality optimization in a laboratory environment.
  • Research on nuclear waste echo localization technology based on parametric sound source
    LI Guangya1, 2, 3, ZHENG Chenzhuo3
    Journal of Vibration and Shock. 2026, 45(7): 281-288.
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    Aiming at the positioning problem of solid residues inside nuclear power plant reactors, existing visual positioning technologies have significant limitations in environments with high steam and strong radiation. The study proposes an echo positioning system based on parametric sound sources. Through ultrasonic nonlinear coupling technology, a 50kHz parametric sound source is generated for sound field measurement experiments. Owing to its longer sound field propagation distance and smaller emission angle, it can realize the positioning and measurement of solid residues in harsh environments such as the interior of reactors. This research provides a reliable solution for the positioning of nuclear waste in strong radiation and high steam environments. 
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