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2025, Volume 46, Issue 3

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Dynamics and Control
Solid Mechanics
Applied Mathematics

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2025, 46(3)

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Dynamics and Control

Dynamic Responses of a Monolithic Beam Subjected to High-Velocity Impact Loading, With Occupant Safety Considered

ZHANG Dujiang, ZHAO Zhenyu, ZHANG Zhiyang, GAO Huiyao, LU Tianjian

2025, 46(3): 271-282. doi: 10.21656/1000-0887.450325

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Abstract:
To improve the protective structure design of armored vehicles against intensive blast loadings and ensure the safety of occupants, the dynamic responses of a monolithic beam subjected to impact loading, with occupant safety considered, was studied. First, experiments were carried out to characterize the dynamic performances of the monolithic beam attached with a mass-spring-damping system subjected to foam projectile impact. Then, the numerical simulations and theoretical analysis were conducted. At a relatively high foam projectile velocity, there is good agreement between numerical, experimental and theoretical results. The effects of the foam projectile velocity, the block mass, the spring stiffness, and the damping coefficient on the peak displacements and accelerations of the mass block were discussed by means of the numerical model. The results show that, the peak displacements and accelerations of the mass block increase with the foam projectile velocity. The block mass and the spring stiffness have little effect on the peak displacements and accelerations of the mass block. The peak accelerations of the mass block decrease with the block mass, but increase with the spring stiffness and the damping coefficient. The theoretical and numerical methods have verified correctness, providing a support for the rapid design of high-performance protective structures against intensive impact loads.

Rigid-Flexible-Thermal Coupling Dynamic Modeling and Hybrid Control of Membrane Antenna Spacecraft

CHEN Cheng, LIU Xiang

2025, 46(3): 283-297. doi: 10.21656/1000-0887.450094

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Abstract:
Large space membrane antenna has a great prospect in the fields of deep space exploration, space-based early warning and earth observation. Due to the large-size and high-flexibility of the membrane structure, the membrane antenna spacecraft poses challenging dynamic and control issues. Meanwhile, to maintain the working performance of the antenna, the pointing accuracy and surface accuracy must be kept strictly. Therefore, accurate dynamic modeling and effective active control of large membrane antenna are of great significance and practical interest, and attract a lot of attentions in recent years. The rigid-flexible-coupling dynamics and hybrid control of membrane antenna spacecraft were studied. First, based on the nonlinear finite method the nonlinear dynamic model for the membrane antenna structure was established, and the nonlinear dynamic model order reduction was also studied. Then, in view of the thermal flux, the rigid-flexible-thermal coupling dynamic model for the spacecraft was established by means of the hybrid coordinate method. With the component synthesis vibration suppression method and the cable-actuator-based nonlinear vibration control method, a hybrid control system was designed to control the attitude motion meanwhile reduce the nonlinear vibration.

Study on Coupling Vibration Characteristics of Articulated Flexible Drilling Tools in Ultra-Short Radius Horizontal Wells

LUO Min, MO Yahu, LI Qiaozhen, XU Tingting, LIN Zhiqiang

2025, 46(3): 298-309. doi: 10.21656/1000-0887.450054

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Abstract:
The frequent frictional collision between flexible drilling pipe and guide screen as well as drill bit and rock may lead to the failure of flexible drill pipe due to coupling vibration in the side-drilling technology of ultra-short radius horizontal wells, which directly affects drilling safety and efficiency. The coupling vibration mechanics and the finite element model for the articulated flexible drilling tool in the inclined section were established with the contact nonlinearity between flexible drilling pipe and guiding screen and effects of rock force on drill bit. The deformation diagrams of the articulated flexible drilling tool and the acceleration curves of the transverse, longitudinal and torsional vibrations of the flexible drilling tool in different positions, were obtained by analyses of the coupling vibration dynamic responses of the articulated flexible drilling tool. And the effects of bit weights and rotational speeds on the coupled vibration characteristics of articulated flexible drilling tools were discussed. The results show that, the lateral vibration of the flexible drill pipe becomes more severe as the drill is closer to the bit, while the torsional vibration decreases periodically with the well depth. The larger the bit weight is, the bigger the lateral and torsional vibrations of the flexible drilling pipe will be; the larger the rotational speed is, the smaller the lateral vibration of the flexible drilling pipe will be; the longitudinal and torsional vibrations is less affected by the rotational speed.

Analysis of Wind Vibration Response of Large-Span Asymmetric Suspension Structures With Series Inerter Dampers

TIAN Chong, TAN Zhiqiang, LU Xinglong, PANG Yingbo, QIN Yuanyuan, GE Xinguang

2025, 46(3): 310-323. doi: 10.21656/1000-0887.450078

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Abstract:
Aimed at the significant problem of bidirectional random wind vibration responses of large-span asymmetric suspension structures, a strategy was proposed to suppress the vibration of large-span suspension structures with series inerter dampers (SIDs) as the energy damping system (EDS). For the complexity of the random wind vibration response analysis method, a concise closed-form solution was presented. Firstly, the dynamic equations for the horizontal and vertical coupled vibrations of the EDS under downwind excitation were established, and the finite element dynamic analysis technology was applied to obtain the real modal dynamic parameters of the large-span suspension structure to reconstruct the dynamic equations for the EDS based on the real modal theory. Secondly, based on the complex mode method and the pseudo-excitation method, the frequency domain unified solutions for the displacements, interlayer displacements and forces of the EDS were obtained. The quadratic decomposition method for the response power spectrum density function was used to obtain concise closed-form solutions for the 0th-, 2nd-, and 4th-order spectral moments and variances of the above responses of the EDS subjected to the Davenport spectrum. Finally, the correctness of the proposed method was verified through a numerical example, and based on this, the characteristics of SIDs in suppressing bidirectional vibrations of suspension structures were studied. The results show that, the horizontal and vertical vibration accelerations of the suspension parts of large-span suspension structures significantly affect vibration serviceability, so that bidirectional vibrations need to be considered in engineering design, and SIDs to reduce the horizontal vibrations can effectively reduce bidirectional vibrations.

Solid Mechanics

Morphology Control and Suppression of Lithium Dendrite Growth in Solid-State Electrolytes Based on Phase-Field Simulation

YANG Jiayue, ZHAO Ying

2025, 46(3): 324-339. doi: 10.21656/1000-0887.450096

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Abstract:
The safety concerns regarding the flammability and explosivity of traditional liquid electrolyte (LE) lithium batteries have spurred the development of all-solid-state lithium batteries with solid-state electrolytes (SSE). However, the issue of lithium dendrite growth remains a critical challenge to be urgently addressed to commercialize solid-state lithium batteries. Hence, a thorough investigation of the morphology control mechanisms and suppression strategies for lithium dendrite growth within solid-state electrolytes is crucial for improving the cycle life of solid-state lithium batteries and promoting their widespread application. Based on the phase-field method, a multi-physical fields coupling model integrating mechanics and electrochemistry, was constructed to dynamically demonstrate the morphology and mechanical behavior of lithium dendrite growth. Then the model parameters and different conditions were explored to regulate and suppress the morphology of lithium dendrite. The results indicate that, a low-level interfacial reaction rate coefficient can effectively slow down the growth rate of lithium dendrite, while also significantly narrowing the high mechanical stress range at the dendrite root. With the change of the lithium-ion anisotropic diffusion degree within solid-state electrolyte materials, the transition of dendrite morphology from fibrous to flat can be achieved. The polycrystalline nucleation exhibits inhibitory effects on the lateral branches close to each other, with the maximum stress being 3 to 5 times higher than that of single-crystal nucleation. Solid-state electrolytes with a high elastic modulus exert notable mechanical inhibitory effects on lithium dendrite growth. This work can serve as a valuable reference for the optimization design of solid-state electrolytes to suppress dendrite growth in solid-state lithium metal batteries.

Numerical Study on Flow and Heat Transfer Characteristics of the Molten Salt Single Tank Heat Storage Process

LIANG Wuzhou, WU Bin, LIU Zhongyuan, LI Yong, ZHANG Jiajie, MA Suxia

2025, 46(3): 340-352. doi: 10.21656/1000-0887.450186

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Abstract:
Aimed at the application of heat storage technology in the field of new energy consumption, a molten salt single tank integrating the heat storage and the heat exchange was proposed. The single tank heat storage characteristics and molten salt heat transfer laws during the heat storage process were numerically simulated and analyzed. The effects of spiral tube spacings and inlet/outlet layout positions on the heat storage process were discussed. The results show that, the molten salt temperature increases gradually in the heat storage process, while the molten salt density decreases and the natural convection forms in the tank. The spiral structure of the tube makes 3 vortices be formed in the flow field of the molten salt. With the spiral tube positioned at the bottom of the tank, the heat storage completion time can be shortened by 34.1% due to a stronger natural convection, compared with the cases at the center and the top of the tank. The increase of the spiral tube diameter may enlarge the heat transfer area and speed up the heating rate of the molten salt. With the increase of the spiral tube spacing, the heating range of the molten salt will be larger, and the heat storage completion time will be shortened slightly. The natural convection of the molten salt is stronger in the inlet-down and outlet-up case since the inlet position is closer to the tank bottom.

Performances of Variable-Node Elements With the Base Force Element Method Under the Complementary Energy Principle

WANG Yao, XU Minyao, ZONG Gang, HOU Changchao

2025, 46(3): 353-370. doi: 10.21656/1000-0887.450059

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Abstract:
To address the problems of uncoordinated nodal displacements at the intersection of the sparse and dense elements, complicated construction of solving equations, and poor spatial scalability, an element model with variable node numbers and positions was proposed with the base force element method (BFEM) under the complementary energy principle, and an explicit solution method in a unified form was established for arbitrary element types. First, a 2D variable mid-edge node element model was established, and the explicit expressions of the contribution of nodes compliance matrix and nodal displacements were introduced. Subsequently, the element model was extended to the 3D form, a variable mid-face node element model was proposed, and the above expressions were also extended to the 3D forms. Hereafter, a sparse and dense mesh hanging element model was established, and the numerical accuracy and applicability of the planar and spatial variable-node element model were demonstrated with the cantilever beam subjected to a bending moment load, a concentrated load, and a tensile load at the end. The numerical results show that, the variable-node element model and the hanging element model in the 2D and 3D forms based on the BFEM have high numerical accuracy. In addition, the nodal displacement coordination at the intersection interface between sparse and dense elements can be ensured only by the shared mid-edge node (2D) and the mid-face node (3D) at the interface without any processing treatment or construction of interpolation functions and constraint functions. Meanwhile, the element models and methods are independent of the element type, element dimensions, nodes' number, and nodes' distribution, etc., and have excellent spatial scalability and programmability.

Numerical Modeling for the Analysis of Crack-Inclusion Problems by the Eigen Iterative Computational Model

GUO Zhao, REN Xiaodan, HE Donghong

2025, 46(3): 371-381. doi: 10.21656/1000-0887.450134

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Abstract:
For the numerical modeling of solid materials containing crack-inclusions, the theory of Eshelby's eigenstrain and equivalent inclusion was incorporated into the boundary integral equations (BIEs). A computation model and an iterative algorithm for the eigen crack opening displacement (COD) and eigenstrain BIEs to address the interaction of crack-inclusions were proposed. Under certain conditions, anisotropic inclusions may be considered as general inclusions. When the elastic modulus of the inclusion is set to zero, the inclusion will degenerate into a hole, and geometrically, with its minimum dimension reduced to zero further it will degenerate into a crack. Thereby, a crack was classified as a special type of inclusion with zero elastic modulus. The discrete form of the boundary integral equation was utilized for the numerical validation of cracks and inclusions, with their boundaries discretized with Gaussian integration points and the boundary point methods, respectively, to conduct stress analysis and investigate the interaction between crack-inclusions. Numerical examples confirm the correctness and feasibility of the eigen iterative model in modeling crack-inclusion problems, demonstrating its high computation accuracy, and providing the theoretical foundation for future large-scale numerical analysis with this computation model.

Applied Mathematics

Finite Time Stabilization of Dynamical Networks Under Pinning Event-Triggered Control

ZHAO Wei, REN Fengli

2025, 46(3): 382-393. doi: 10.21656/1000-0887.450072

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Abstract:
The finite time stabilization problem of dynamical directed networks under pinning adaptive event-triggered control was addressed. Unlike the existing results as for finite time stabilization with event-triggered protocol, in view of the difficulties of the control cost and the large node number, a novel pinning event-triggered protocol was designed. Given its high dimension, the analysis of the finite time stabilization under the pinning event-triggered control for dynamical networks is challenging. Based on the Lyapunov stability theory and the appropriately designed protocol, sufficient conditions were derived to guarantee the finite time stabilization. Finally, an example was given to demonstrate the effectiveness of the theoretical results.

A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping

WANG Yahui, GUO Cheng, DU Yulong

2025, 46(3): 394-411. doi: 10.21656/1000-0887.450150

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Abstract:
The key to whether the WENO scheme can achieve optimal convergence accuracy and maintain essential no-oscillation characteristics near discontinuities lies in the construction of smoothness indicators. The smoothness indicator of the 3rd-order WENO scheme was modified through the construction of a mapping function to correct the smoothness indicators on each candidate stencil with the smoothest indicator. Under the influence of this mapping function, the smoothness indicator of the under-smooth stencil was reduced, thereby the nonlinear weight of the under-smooth stencil was increased. Then the numerical dissipation of the scheme was significantly lowered and its resolution was improved. A series of numerical examples demonstrate that, the new 3rd-order WENO scheme for smoothness indicators based on mapping has higher resolution than the classical WENO-JS3 and WENO-Z3 schemes.

An Efficient Compact Difference Scheme for the Symmetric Regularized Long Wave Equation

GAO Jingying, HE Siriguleng, QING Mei, Eerdunbuhe

2025, 46(3): 412-424. doi: 10.21656/1000-0887.440374

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Abstract:
A new efficient and compact finite difference scheme was constructed to obtain numerical solutions of the symmetric regularized long wave equation. The classic Crank-Nicolson (C-N) scheme and the extrapolation technique were used for discretization of the 1st-order derivatives in the temporal direction, the 4th-order Padé method and the inverse compact operator were applied for discretization of the 1st-order and 2nd-order derivatives in the spatial direction, respectively. The constructed scheme has the linear, uncoupled, and compact features, greatly enhancing the computational efficiency. Additionally, analyses on conservation laws, a priori estimates, stability and convergence were conducted for the new scheme, to prove the 2nd-order temporal and the 4th-order spatial convergence accuracies. Finally, the theoretical correctness and efficiency of the scheme were verified through a numerical example.