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2022 Vol. 54, No. 10

Research Review
Xu Wanhai, Ma Yexuan
Vortex-induced vibration (VIV) of cylindrical structures is a very common phenomenon in daily life. Cylinder structures, such as pipelines in ocean engineering, high-rise buildings, stay cables in civil engineering and heat exchangers in nuclear engineering, etc. are frequently affected by vortex-induced vibrations, which can induce fatigue damage and make the failure of structures. At present, the VIV mechanism of cylindrical structures in vertical incoming flow has been comprehensively understood. However, when the cylinder structure is inclined in the flow field, the wake flow of the inclined cylinder is significantly different from that of the vertical one, and the fluid-structure interaction mechanism is more complex. Earlier, independence principle (IP) was proposed to simplify the problem of flow around an inclined stationary cylinder. In the assumption of the Independence Principle, the incoming flow velocity can be decomposed into one part that is vertical to the cylinder axis, and the other that is parallel to the cylinder axis. Only the velocity component vertical to the cylinder axis is considered and the influence of the velocity component parallel to the cylinder axis is ignored. In recent years, a large number of experimental and numerical studies have been carried out to investigate the VIV characteristics of an inclined cylinder and the applicability of Independence Principle. To deepen the understanding of the VIV characteristics and mechanisms of inclined cylinder, this paper summarizes and expounds the response characteristic, wake flow characteristic and hydrodynamic characteristic in “vortex-induced vibration of an inclined cylinder.”. The scope of the application of Independence Principle, the VIV mechanisms and VIV suppression of inclined cylindrical structures are discussed in depth, and the future research direction of this problem is prospected.
2022, 54(10): 2641-2658. doi: 10.6052/0459-1879-22-186
Wen Guilin, Liu Jie, Chen Zijie, Wei Peng, Long Kai, Wang Hongxin, Rong Jianhua, Xie Yimin
The continuum topology optimization method can extensively improve the structural performance from the mechanical essence, which can provide designers with a variety of innovative design candidates. Due to these advantages and significant help to engineering, the continuum topology optimization method has been rapidly developed in recent years. This field has been developed relatively mature in dealing with linear topology optimization design problems. And it has been successfully applied to the high-performance design of all sorts of engineering structures. However, a large number of nonlinear issues are inherently involved in practical engineering. If they are assumed as linear problems, significant errors will often generate, and even wrong results may be obtained. This may ultimately lead to substantial engineering safety accidents. Under the demand-driven background of important engineering fields such as aerospace, mechanical engineering, marine engineering, high-speed trains, and architectural engineering, nonlinear continuum topology optimization methods have made remarkable progress in recent years. This paper aims to systematically review three types of nonlinear continuum topology optimization methods involving material nonlinearity, geometric nonlinearity, and boundary nonlinearity, with the typical methods comprehensively discussed and reviewed. Finally, the current difficulties (e.g., the poor numerical analysis accuracy, the low computational efficiency, limited to the field of statics, etc.) and future development directions (e.g., the large deformation and large strain problems, the nonlinear dynamic problems, the large-scale topology optimization design problems, etc.) of nonlinear continuum topology optimization methods are highlighted. This research review can provide a comprehensive knowledge sorting for beginners in the field of nonlinear continuum topology optimization. Moreover, it can also provide due help for scholars engaged in nonlinear continuum topology optimization methods.
2022, 54(10): 2659-2675. doi: 10.6052/0459-1879-22-179
Theme Articles on Design and Application of Elastic Wave and Mechanical Metamaterials
Jiang Heng, Huang Guoliang
2022, 54(10): 2676-2677. doi: 10.6052/0459-1879-22-481
Wang Kai, Zhou Jiaxi, Cai Changqi, Xu Daolin, Wen Guilin
Metamaterial, a type of burgeoning man-made material/structure, possesses a periodic/quasi-periodic structure and is able to change the transmission properties of the electromagnetic wave, the acoustic wave and the elastic wave. Due to its enormous potentiality in the field of the spaceflight, national defence and civilian, the metamaterial attracted great interest, inspired a new wave of research and obtained consecutive important achievement since it was proposed. Elastic wave metamaterial is a kind of metamaterial which is capable of realizing the attenuation and manipulation of the elastic wave on the basis of the interaction of the elastic wave and the periodic/ quasi-periodic structure. Band structure design is an important tool for the elastic wave metamaterial to execute the wave manipulation and attenuation. The location, width and wave suppression performance of the frequency band are related to the nature of materials, the lattice constant of the metamaterial, and the resonant frequency of the local resonator. Because of the limitations such as the carrying capacity, the overall size, and the structure of the local resonator, it is still difficult to obtain an elastic wave band gap in the frequency range around 100 Hz through the conventional metamaterials. This review introduces the fundamental principle of the metamaterial for opening elastic wave band gaps firstly, and then elaborates the low-frequency elastic wave metamaterial from three aspects: the fundamental configuration of the metamaterial, the low-frequency band gap optimization and tuning, and some potential applications. The fundamental configurations of low-frequency elastic wave metamaterials mainly include three aspects: Bragg scattering metamaterials, conventional local resonant metamaterials and quasi-zero-stiffness local resonant metamaterials. The low-frequency band tunability achieved by both the passive and active approaches detailed as well. This review summarizes the current knowledge of the low-frequency elastic wave metamaterial, analyzes the inadequacies and the advantages in current research, and outlines future research prospects.
2022, 54(10): 2678-2694. doi: 10.6052/0459-1879-22-108
Wang Fanglong, Shen Yizhou, Xu Yanlong, Zhou Shengxi, Yang Zhichun
When broadband elastic waves with different frequencies propagate in a graded structure with a special dispersion relation, the spatial frequency separation and the wave field energy enhancement will occur, that is, the waves will stop propagating forward and have energy accumulation at different positions of the structure, which is called the rainbow trapping of elastic waves. Researches on the rainbow trapping will promote the development of structural health monitoring, vibration control and energy harvesting. In this paper, the rainbow trapping of flexural waves and its application in piezoelectric energy harvesting are studied by using the designed beam with graded pillars. Firstly, band structures of unit cells of the beam are analytically solved by the transfer matrix method. According to the band structures, the mechanism of the rainbow trapping of flexural waves is analyzed: the group velocities of flexural waves with different frequencies will reduce to zero near different cells, thereby the flexural waves will stop forward propagation and be reflected; the superposition of incident and reflected waves, and the energy accumulation resulted by the reduction of group velocity, will significantly enhance the wave field at the reflection position. Secondly, the spatial frequency separation and the wave field energy enhancement of the rainbow trapping of flexural waves are verified by finite element simulations and experiments. Finally, we quantitatively evaluate the energy harvesting performance of the beam with graded pillars and its variation with the frequency of the incident wave comparing to the corresponding bare uniform beam, where PVDF piezoelectric films are pasted on their surfaces, by using finite element multiphysics coupling simulations and corresponding experiments. The results illustrate that the output voltage of the PVDF piezoelectric film of the beam with graded pillars is about 2 times that of the corresponding bare uniform beam in the bandwidth of the rainbow trapping of flexural waves.
2022, 54(10): 2695-2707. doi: 10.6052/0459-1879-22-107
Xiao Boya, Yang Tao, Feng Yafei, Liu Yu, Xu Wenshuai, Chen Meng, Jiang Heng, Wang Yuren
The bending beam bistable structure in mechanical metamaterials has attracted extensive attention in recent years due to its strong active control and high control accuracy. In this paper, a hexagonal bistable structure is designed by using the instability of the centrally compressed bending beam. Firstly, the equivalent bending beam model is established and the basic principle of the bistability of the structure is proved based on the differential equation of beam deformation and the principle of minimum energy. Then, the influence of structural geometric parameters on its mechanical properties is studied by finite element numerical calculation. The range of structural geometric parameters with self recovery and bistable properties is obtained respectively, and the phase diagram between geometric parameters and mechanical properties is drawn. At the same time, the controllable deformation ability of the reconfigurable structure helps to adjust the dispersion characteristics, numerical simulation is used to study the dispersion relationship of the structure with bistable characteristics under the two configurations of tension and compression, and the effects of different structural geometric parameters and configuration changes on the band gap position and range of the structure are compared and analyzed. After that, the frequency response analysis of the periodic structure composed of different configuration cells is carried out to verify the accuracy of the band gap calculation. In conclusion, the mechanical properties, dispersion properties and frequency response analysis of the hexagonal reconfigurable structure show that the overall performance of the structure can be actively controlled through the design of the geometric parameters of the structure, which provides a reliable path for the research and analysis of the elastic wave metamaterial structure with reversible design.
2022, 54(10): 2708-2716. doi: 10.6052/0459-1879-22-366
Ren Yi, Zhang Hao, Zhang Wang, Liu Haidong, Li Zhao, Zhang Mangong
The lattice structure is a porous periodic structure which has the advantages of light weight, high specific strength, high impact resistance, vibration reduction, noise reduction. Meanwhile, the lattice structure has broad application prospects in aerospace, transportation, and other fields. This paper takes the pyramid lattice cylinder structure as the object, The parametric model is determined by independent structural parameters such as width, height and number of arrays, etc. and commercial finite element software was used to calculate the axial vibration characteristics of lattice structure. The influence of key parameters such as cell width, cell height and rod diameter on the damping effect was studied by the dimensionless parameters of normalized frequency and relative bandwidth. Through parameter analysis, a pyramid lattice cylinder structure with low frequency and broadband vibration damping performance has been designed. Then a sample is made by additive manufacturing. The vibration test results show that the experimental results are consistent with the finite element simulation. In the range of 500 Hz to 1500 Hz, the structure shows obvious vibration reduction effect, and the average attenuation strength reaches about 50 dB.
2022, 54(10): 2717-2725. doi: 10.6052/0459-1879-22-168
Wang Hairui, Shen Xuejing, Wang Zhouheng, Jia Lu, Li Chuanlei, Zhu Longji, Zhao Danyang
Origami metamaterials can regulate and control macroscopic deformation by continuous deformation of their internal microstructure. Hence, mechanical properties such as Poisson's ratio, stiffness, and modulus of the metamaterials can be adjusted and designed. This work theoretically studied the mechanical behavior of origami metamaterials under the synergy of complex internal configuration and folding motion, with the methods of torsion spring equivalent and energy principle. Here, we established a mechanical model to describe the folding deformation of the metamaterials, and analyzed the influence of geometric parameters on external loading. Through parameter analysis, it is found that the external loading exhibits monotonicity during the unfolding process and does not have stability. The external loading can show three situations such as monotonicity, mono-stability and bi-stability during the folding process, which are closely related to the parameters. This work provides important guidance to origami metamaterials for improving the design of the configuration and the regulation of their performance.
2022, 54(10): 2726-2732. doi: 10.6052/0459-1879-22-356
Zhu Yilin, Jiang Songhui, Yu Chao
In a previous work, the authors proposed novel enhanced hexa-missing rib chiral auxetic meta-materials (with straight ligaments and wavy ligaments), exhibiting tunable negative Poisson’s ratio and elastic modulus . The previous work, however, was limited in the finite element (FE) analysis. To facilitate the understanding of the underlying microstructure-property relationship and further provide guidelines of meta-material designs to yield target mechanical parameters, a mechanics model under infinitesimal deformation framework was developed by a simple energy-based approach. The considered chiral auxetic honeycombs consist of a set of zigzag ligaments, which can be assumed as simple supported Euler-Bernoulli beams. Therefore, the strain energy of an arbitrary shaped Euler-Bernoulli beam with concentrated forces and moments subjected to the end is derived firstly. Then, theoretical formulations of the effective Poisson’s ratio and elastic modulus for the enhanced hexa-missing rib chiral auxetics are further formulated with considering the equilibrium condition and displacement consistent condition. It is found that the theoretical formulations have a succinct form only if the length ratio between the outer and inner part of the zigzag ligaments is 2:1. To facilitate the application of the theoretical formulations, A graphical user interface (GUI) is developed based on MATLAB so that the effective Poisson’s ratio and elastic modulus of a specific design can be obtained directly by simply inputting the corresponding independent geometric parameters. The obtained analytic solutions, as compared with systematic FE calculations (conducted on one unit-cell with considering periodic boundary condition), elucidated different roles of the microstructure geometry on the effective mechanical parameters of the considered auxetic honeycombs. Results show that a wide range of targeted mechanical parameters can be obtained by adjusting the geometrical structure.
2022, 54(10): 2733-2746. doi: 10.6052/0459-1879-22-188
Fluid Mechanics
Li Hu, Luo Yong, Liu Xuliang, Wu Conghai, Han Shuaibin, Wang Yimin
For the supersonic flow, the shock waves interact with the turbulent structures to generate high intensity shock-associated noise. High fidelity numerical simulation of shock-associated noise requires the shock-capturing scheme to have the properties of high-order accuracy, low dissipation and low dispersion. It is also necessary to reduce the nonlinear effect caused by the nonlinear implementation of scheme as much as possible. The existing upwind/symmetric hybrid weighted non-linear compact scheme with sixth order accuracy (called by CCSSR-HW-6 scheme, Journal of Computational Physics, 2015, 284: 133-154) introduces two-stage weighting strategy to construct the numerical flux at the cell center based on the symmetric stencil. Each stage of weighting in CCSSR-HW-6 scheme must design a nonlinear function for the weighting coefficient, which makes the nonlinear effect enhanced. In this paper, a weighted optimization compact scheme (called by WOCS scheme) is established through optimizing the nonlinear characteristics of original CCSSR-HW-6 scheme. The error integral function of modified wavenumber is chosen as the optimization objective function. The accuracy verification shows that the WOCS scheme has more than fifth order accuracy. The analysis of spectral property shows that compared to original CCSSR-HW-6 scheme, the dissipation error and the nonlinear effect of WOCS scheme are significantly reduced. Numerical experiments on several typical shock-associated noise problems show that the WOCS scheme not only improves the resolving ability of high-frequency waves, but also significantly attenuates the non-physical oscillations in numerical solution caused by the nonlinear effect.
2022, 54(10): 2747-2759. doi: 10.6052/0459-1879-22-254
Chang Siyuan, Xiao Yao, Li Guangli, Tian Zhongwei, Cui Kai
High-pressure capturing wing (HCW) novel aerodynamic layout has good aerodynamic performance in the hypersonic design state, and the import of the new lift wing provides more lift for it under subsonic conditions, but its aerodynamic stability characteristics at subsonic speed have yet to be studied further. In this paper, a parametric HCW concept configuration was presented based on the basic design principle of HCW aerodynamic layout, by adding an HCW with single support to a delta wing-body combination. The influence of wing dihedral/anhedral angle variations on subsonic aerodynamic characteristics of HCW configuration at the angle of attack (AOA) range of 0° to 10° was studied by utilizing uniform experimental design, computational fluid dynamics numerical simulation, and Kriging surrogate model, which regarded the dihedral/anhedral angles of both HCW and delta wing as the design variables. Specifically, the variation law of lift-drag characteristics, longitudinal and lateral-directional stability characteristics, and flow field vortex structures were analyzed. The results show that the influence of wing dihedral/anhedral angles on the lift-drag ratio (L/D) at low AOA is more significant than that at high AOA. The increase in HCW dihedral angle improves L/D of configuration, while the increase in HCW anhedral angle or delta wing dihedral angle reduces L/D. As the delta wing anhedral is increased from 0°, L/D has a slight improvement initially and then slowly reduces. The longitudinal stability, which is generally less affected by wing dihedral/anhedral angles, slightly improves as the HCW dihedral angle increases but reduces as the delta wing dihedral angle increases. Moreover, the lateral stability improves as the HCW or delta wing dihedral angle increases but reduces as the anhedral angle increases. However, at the high angle of attack, the improvement of lateral stability may be limited while the delta wing has a large anhedral angle. As for the directional stability, the increase in HCW dihedral angle improves it, while HCW anhedral angle reduces it. In particular, the increase in both the dihedral and anhedral angles of the delta wing can improve the directional stability, but the effect of the anhedral angle is stronger.
2022, 54(10): 2760-2772. doi: 10.6052/0459-1879-22-217
Chen Jinfeng, Zhang Jinlong, Yang Wenwu, Dong Yuhong
The exchange and transport characteristics of pollutants in the hyporheic zone are one of the important issues affecting the water resources environment. In this paper, the high Schmidt number mass transfer phenomenon of a channel oscillatory flow with a highly permeable sediment layer at the bottom is numerically investigated by using large eddy simulations. A modified Darcy-Brinkman-Forcheimer model describes the bottom highly permeable sediment layer using the volume-averaged Navier-Stokes equation and convective diffusion equation for the flow and transport of metal ion contaminants within the sediment layer. We explore the statistical characteristics and the instantaneous structure of flow field and concentration field, and the dynamic influence of oscillating flow inside and outside the sediment-water interface on the transport of pollutants. In addition, the variation of the effective diffusivity at the sediment-water interface with oscillation period and oscillation angle is also studied. The results show that the turbulence component of concentration flux plays a dominant role in vertical mass transport, and the streamwise and spanwise velocity, the fluctuations of turbulence intensity and pollutant concentration follow the quasi-periodic variation of periodic oscillation driving force. At the same time, it is found that there is a clear correlation between the variation of turbulent concentration flux at the sediment-water interface and the intensity of normal turbulence, and the effective diffusivity at the sediment-water interface increases at larger oscillation angles and low-frequency oscillations, which mainly comes from the burst behavior of the fluid at the sediment-water interface that significantly promotes turbulent mixing and material exchange, and then the concentration scalar is acted on by a convection-diffusion mechanism, which in turn enhances the vertical mass transport of pollutants.
2022, 54(10): 2773-2783. doi: 10.6052/0459-1879-22-227
Zhang Yu, Li Tianfu, Luo Kang, Wu Jian, Yi Hongliang
Abundant dynamic effects on an ion-selective surface provide a new solution for the development of microfluidic technology. If an increasing bias voltage is applied to the electrolyte solution with the ion-selective surface, the passing ion current will experience a complex nonlinear evolution. A convection phenomenon will be triggered when the imposed voltage exceeds a critical threshold. This convection is called the electroconvection near the ion-selective surface or the second kind of electroosmosis. The numerical investigation of the electroconvection attracted a number of studies. In the present work, a numerical model of the lattice Boltzmann method (LBM) based on multi-block grid refinement is proposed to simulate this model problem. The grid information exchange equations of the multi-block grid refinement method for solving the flow, potential, and ion concentration are given, which overcomes the requirement of a high concentration gradient boundary for the computational resolution. The current-voltage characteristic curve obtained by the numerical model firstly increases rapidly with the increase of voltage and then reaches a saturation state. This result is in good agreement with the theoretical solution. What is more, the results also show that after the convection occurs, the flow tends to form large rolls under a relatively low voltage which is slightly higher than the stability threshold, and the flow intensity increases exponentially. While under a relatively high voltage, multiple small rolls are formed firstly, and these rolls merge into larger rolls subsequently. The ion transport efficiency is higher when the large rolls are formed. It is worth noting that our multi-block LBM method is suitable not only for the electric convection on the ion-exchange surface but also for some other numerical studies of electrohydrodynamics.
2022, 54(10): 2784-2795. doi: 10.6052/0459-1879-22-161
Solid Mechanics
Wu Hua, Zou Shaohua, Xu Chenghui, Yu Yajun, Deng Zichen
The rapid development of micro/nano technology and the wide application of ultrashort pulsed laser technology have put forward an urgent need for generalized heat conduction and thermoelastic coupling theory to describe ultrafast thermal shock at micro/nano scale. Based on extended thermodynamic principle, a generalized thermoelastic coupling theory considering the dual-phase-lagging effect of heat conduction and the rate of higher order heat flux is established. Inspired by Green-Naghdi (GN) generalized heat conduction model, thermal "elastic" and "viscous" element models are proposed, which are similar to the series and parallel models of viscoelastic constitutive relations in the field of mechanics. The Cattanoe-Vernotte (CV), GN, dual-phase-lag (DPL) and Moore-Gibson-Thompson (MGT) heat conduction models were obtained by series and parallel methods. Theoretical derivation further shows that the newly formulated model corresponds to the Burgers model of heat conduction. In these models, the proportional relationship between the relaxation time of each phase lag is also obtained. Laplace transform method is used to study the transient response of one-dimensional structure under thermal shock and moving heat source. The results show that the present model overcomes the paradox of infinite thermal wave velocity. When the boundary thermal shock load is applied, the results obtained by the new model have higher peak and the smallest affected region. And under the effect of moving heat source, the new model can generate a larger peak response. The new model could coupled with the classical elastic theory and built a generalized thermoelasticity. With this theory, the jump of stress at wavefront of thermal wave and elastic wave can be clearly observed. Theoretically, this paper promotes the combination of extended thermodynamics and continuum mechanics, which is of enlightening significance to the study of fundamental theoretical problems far from equilibrium of extreme mechanics. For applications, this work can provide theoretical basis and numerical method for the transient response analysis under the moving heat sources.
2022, 54(10): 2796-2807. doi: 10.6052/0459-1879-22-225
He Jiaqi, Jia Xiaoxuan, Wu Weida, Zhong Jiehua, Luo Yangjun
Uncertainties in environmental loads and structural parameters are challenging phenomena which influence the structural design, the assessment and prediction of structural performance, and the damage identification of structures in service. These uncertainties may variously be objective or subjective from different sources, requiring appropriate mathematical modeling and quantification to obtain realistic analysis results of the behavior and reliability of engineering structures. In general, these uncertainties in different types and from multiple sources need to be described by different quantification models, involving probabilistic model, imprecise probabilistic model and non-probabilistic model. In addition, uncertainties may be time-varying during service time, and the direct measurements of uncertain variables are sometimes difficult to be carried out during the service of the structure. However, the performance test data, such as displacements, and stresses of structures, may be much more easily obtained when compared with the direct measurements. Facing the above issues, a novel uncertainty quantification model named P-CS (probability-convex set) model is proposed in this paper to enable uncertainties from multiple sources quantified in a uniform model. The P-CS model characterizes uncertainties as a combination of probabilistic random variables and a non-probabilistic convex set based on the principle of probability equivalence, which can make probabilistic model, imprecise probabilistic model and non-probabilistic model expressed under a uniform framework. On the basis of the P-CS model, a Bayesian updating method is proposed in this paper driven by performance test data. In this updating method, the allowable ranges of the parameters of P-CS model are divided into several subintervals respectively and then the credibility distribution of each parameter can be updated according to the performance test data, finally, parameters of P-CS model can be updated based on the posterior credibility distributions. Three numerical examples show the construction methods and the probabilistic and non-probabilistic properties of the P-CS model, and two mechanical examples are presented to validate the proposed Bayesian updating method.
2022, 54(10): 2808-2824. doi: 10.6052/0459-1879-22-173
Sun Liguo, Jiang Shouyan, Du Chengbin
To improve numerical accuracy, the numerical simulation of fracture mechanics problems needs to use dense meshes in the local area of crack propagation, while sparse meshes can be used in the area far away from the local area where the crack is located. Additionally, for the numerical simulation of crack propagation problems, most numerical methods have the problem of local remeshing in the process of crack growth. In this paper, an improved scaled boundary finite element method based on image quadtree are proposed to simulate crack propagation problems. This method can automatically perform the quadtree mesh generation according to the image of the geometric outer boundary of the structural domain without any artificial intervention, and the mesh generation efficiency is also very high. Due to the inherent advantages of the scaled boundary finite element method, the hanging nodes of the quadtree mesh can be directly regarded as new nodes without any special treatment. By introducing the idea of virtual node, the intersection of crack and the boundary of quadtree element is regarded as virtual nodes, and the degrees of freedom of virtual nodes are treated as additional degrees of freedom. The level set functions are used to characterize the crack surface inside the material. The subdomain with the discontinuous crack surface can be identified by the node level set functions, so that there is no need for remeshing during crack propagation, and the geometric characteristics of the interface can be characterized by the additional degrees of freedom of the scaled boundary finite element method. Finally, the performance of the proposed method is verified by several numerical examples. The results show that the proposed improved scaled boundary finite element method has high accuracy in solving the mode I and II stress intensity factors as well as simulating the internal crack growth path of materials.
2022, 54(10): 2825-2834. doi: 10.6052/0459-1879-22-189
Wang Jiachen, Zhang Dingli, Sun Zhenyu, Fang Huangcheng, Liu Chang
Due to the remarkable bedding structure of horizontal interbedded surrounding rock, the failure form of horizontal interbedded surrounding rock is quite different from that of homogeneous surrounding rock. The current research on horizontal interbedded surrounding rock focuses on a single failure mode, without considering the diversity of failure modes. In order to explore the failure area of horizontal interbedded surrounding rock, firstly, it is divided into single-layer surrounding rock to analysis according to its bedding plane. The horizontal interbedded surrounding rock failure is divided into three typical failure modes: tensile failure, shear failure at wedge boundary and shear failure at arch boundary. The rock beam-tension analysis model and the arch key block-shear analysis model are established respectively to analysis the failure of single-layer surrounding rock, and the corresponding failure criteria are proposed. And use the slump coefficient and critical height to study the division conditions of different failure modes. This method is applied to mine channel and tunnel engineering examples, and compared with the existing methods to verify the reliability of the failure mechanism model of single-layer surrounding rock. At the same time, it is substituted into the example of abscission damage calculation to verify the practicability of the failure mechanism model of single-layer surrounding rock. Based on this, a horizontal interbedded surrounding rock failure model is established by combining the interlayer continuous conditions and the failure rest conditions of the failure range. The above horizontal interbedded surrounding rock failure model is applied to the example of Bulianta mine roadway, and the results show that the horizontal interbedded surrounding rock failure range predicted by this method is in good agreement with the numerical simulation results and the actual collapse situation. The research achievements can provide a theoretical basis for the design of support scheme of tunnel in horizontal interbedded surrounding rock.
2022, 54(10): 2835-2849. doi: 10.6052/0459-1879-22-133
Dynamics, Vibration and Control
Li Xueyan, Guan Yuhang, Luo Mingtao, Wu Boyu
It is of great significance to identify the modal parameters of engineering structures under environmental excitations. However, the stochastic subspace identification method (SSI), as a time-domain method suitable for the identification of modal parameters under environmental excitations, will produce false modes, loss of real modes, computational efficiency, problem in automatic determination of the system order and other problems due to noise and complex excitations. These problems limit the wide application of this method in practical engineering. In this paper, a stochastic subspace identification method based on the Welch method is proposed. The Welch method is used to reduce the effect of noise, environmental excitations and other uncertainties on vibration response in the frequency domain. It aims to highlight the inherent structural modes from the noise and excitation frequencies. Then, a Toeplitz matrix which contains more structural modes is constructed, and the singular value decomposition of the matrix is performed. Finally, the discrete state matrix is calculated and the eigenvalues are analyzed. In order to determine the modal orders automatically and eliminate the false modes, fuzzy C-means clustering analysis (FCM) and modal mean phase deviation (MPD) analysis are performed on the characteristic parameters obtained from the discrete state matrix constructed by different singular value components. The method proposed in this paper is applied to the measured acceleration response analysis of a long-span suspension bridge and the acceleration response analysis of a 70-story high-rise building. The results are compared with those of frequency-domain decomposition method, traditional stochastic subspace identification method and stochastic subspace identification method based on correlation analysis to verify the effectiveness of the proposed method. It is found that compared with the traditional SSI and the SSI based on correlation analysis, SSI based on Welch method has significant improvement in avoiding modal loss and computing efficiency, and has obvious advantages in automatically identifying and eliminating false modes compared with the frequency domain decomposition method.
2022, 54(10): 2850-2860. doi: 10.6052/0459-1879-22-256
Zhu An, Chen Li
The force and position impedance control of dual-arm space robot capture satellite active docking operation is studied. In order to prevent the joints of the space robot from being damaged by impact force generated when contact and impact between the end-effector of the manipulator and the satellite during the process of capture operation, a spring damping buffer device (SDBD) is added between each joint motor and manipulator. In order to solve the problems of nonholonomic dynamic constraints in the process of capture operation and the coordinated control of the closed-chain hybrid system after capture, combined with Newton's third law, velocity constraints of captured points and closed-chain geometric constraints, the closed-chain dynamic model of hybrid system after capture operation is obtained, and the impact effect and impact force are calculated by the law of conservation of momentum. The Jacobian matrix between the docking device relative to the base of space robot is established by analyzing the kinematic relationship of the docking device in the base coordinate system. On this basis, a second-order linear impedance model based on force is established to achieve high precision output force control of the docking device. Considering that the active docking operation requires the controller to have the characteristics of fast convergence and high precision control of position and attitude, a nonsingular fast terminal sliding mode impedance control strategy which combining the advantages of terminal sliding mode and super-twisting sliding mode is proposed. This control strategy can not only realize the rapid response of position, attitude and output force in the process of active docking operation, but also effectively solve the chattering problem of sliding mode to ensure the position, attitude and output force high precision control. The stability of the closed-chain hybrid system is proved by Lyapunov theorem. The impact resistance of the buffer device and the effectiveness of the proposed impedance control strategy are verified by numerical simulation.
2022, 54(10): 2861-2873. doi: 10.6052/0459-1879-22-224
Chen Guotai, Zheng Yanhong, Yi Dan, Zeng Qiaoyun
The study of the origin of abnormal beta oscillations generated in the basal ganglia of the brain can help analyze the pathogenesis of Parkinson's disease. In this paper, the oscillatory dynamics of a modified cortico-basal ganglia (E-I-STN-GPe-GPi) resonance model is systematically investigated. First, the conditions for the stability of the model at the local equilibrium point and the occurrence of Hopf bifurcation are obtained by the Routh-Hurwitz criterion and stability theory, and the range of time delay parameters for the existence of Hopf bifurcation in this resonant model is derived. It was found that increasing the time delay of synaptic transmission could generate Hopf bifurcation in the model and induce beta oscillations, allowing the system to switch between the healthy and Parkinson's disease states.Second, it was revealed that the generation of beta oscillations is related to the strength of synaptic connections associated with the subthalamic nucleus. From the results of numerical simulations, it can be seen that when the subthalamic nucleus is subjected to both excitatory neuronal clusters and stronger facilitation of the globus pallidus external, oscillations are generated. Finally, the effect of GPi-related parameters on its generation of oscillations was analyzed by numerical simulations, and our results revealed that when smaller GPe synaptic connection strengths and larger synaptic transmission time delay are combined, they are more likely to make GPi oscillate with increasing amplitude. It is hoped that the results of this paper can provide some reference for the study of the mechanism of Parkinson's disease.It is hoped that the study of the dynamics characteristics of the E-I-STN-GPe-GPi resonance model in this paper will help us understand the pathogenesis of Parkinson's disease and reveal the origin of abnormal beta oscillations in Parkinson's disease.
2022, 54(10): 2874-2882. doi: 10.6052/0459-1879-22-307
Zhang Yi, Chen Xinyu
Variational principle has great generality, which can be divided into differential and integral, Gauss principle is the variational principle with differential form. Among the existing differential variational principles, only the Gauss principle has the extreme value characteristics, which can be expressed as the Gauss variation of the compulsion function equals to zero. Gauss principle can be used to obtain the motion law of a particle system directly by finding the extreme value of function. Therefore, Gauss principle plays a unique role in the dynamics modeling and approximate calculation of complex systems, such as the design and analysis of robots, approximate solutions of nonlinear vibration equations and dynamics of multi-body systems. This paper deals with the generalized Gauss principle for mechanical systems with variable mass and its extension to higher order nonholonomic mechanics. Firstly, Gauss’s principle of least compulsion for mechanical system with variable mass is established, and extended to second order linear nonholonomic constrained systems by constructing modified compulsion function. Secondly, the generalized Gauss principle of mechanical system with variable mass for arbitrary order cases is proposed, and generalized Gauss’s principle of least compulsion is established, and the generalized compulsion function is constructed to extend the principle to high order nonholonomic constrained systems with variable mass. It is shown that for variable-mass mechanical system with bilateral ideal high-order nonholonomic constraints, the acceleration of real motion minimizes the generalized compulsion function under the $k{\text{-th}}$ Gauss variation in every instant among all the possible accelerations compatible with the constraints in the $k{\text{-th}}$ acceleration space. At the end of this paper, the differential equations of motion of a burning uniform sphere moving along a rough horizontal plane and the variable-mass Hamel problem are derived by applying the generalized Gauss’s principle of least compulsion.
2022, 54(10): 2883-2891. doi: 10.6052/0459-1879-22-202
Biomechanics, Engineering and Interdiscipliary Mechanics
Cheng Linsong, Du Xulin, Rao Xiang, Cao Renyi, Jia Pin
For the original embedded discrete fracture model (EDFM), the linear-distribution assumption is adopted in calculating the pressure distribution in matrix grids containing fracture elements, which leads to the lack of accuracy in solving unsteady interflux in the early stage of oil reservoir development. Therefore, this paper proposes a numerical simulation approach for EDFM coupled Green element method based on two sets of nodes. The main idea of the Green element method with two sets of nodes is to distinguish pressure nodes from flux nodes, in which one set of pressure nodes is set at the vertex of grids and another set of flux nodes is set at the edge-midpoint of grids. It not only meets the local material conservation and has second-order accuracy, but also can be applied to any grid type. In this paper, the Green element method based on two sets of nodes is coupled with EDFM, and a new scheme of mass transfer between matrix cell and fracture elements is derived by adopting the boundary integral form of the unsteady flow control equation, which replaces the linear distribution assumption to improve the simulation accuracy. In addition, the modified EDFM adapts to any form of matrix mesh generation, which extends the limitations of the original EDFM which is only suitable for rectangular matrix mesh and difficult to consider complex reservoir boundaries. The research shows that the proposed model has high accuracy in the early stage and it is verified by the LGR module of commercial software tNavigator® and the original EDFM. Taking the SRV-zoning model considering fracture networks and complex reservoir boundaries as an example, the flexibility of the proposed model for solving complicated problems is demonstrated by comparing the business simulation software named SFEM-COMSOL. This study can be used for the accurate simulation of dynamic production performance in fractured oil reservoirs.
2022, 54(10): 2892-2903. doi: 10.6052/0459-1879-22-250
Yang Liang, Liu Miaoer, Fan Jiakun, Li Fangqiu, Ying Xipeng, Bu Yufeng, Cao Huixin, Zhang Kailun, Yang Jianye, Yang Zhixun
LNG (liquefied natural gas) cryogenic flexible hose is one piece of the key equipment in the process of exploitation, transportation and storage of LNG, which is called as the "blood vessel" of LNG transportation system. With the development of exploitation and transportation of LNG gradually from the offshore to the deep sea in recent years, there is a broader development prospect for LNG cryogenic flexible hose as the core equipment in the LNG transportation system, however, which will face more stringent challenges of structural failures caused by more stringent marine environment at the same time. In this paper, the engineering application background, structural design and internal fluid analysis of LNG cryogenic flexible hose are focused on and the related key technologies are investigated. The research progresses of the above mentioned technologies of LNG cryogenic flexible hose are summarized. Based on the investigations, the flexible structural characteristics of the corrugated structure, the spiral wound structure and the high polymer material in LNG cryogenic flexible hose are classified, the related mechanical mechanism is analyzed and the methods to achieve flexible structural characteristics are summarized. In internal fluid analysis, the responses of calculation and analysis in LNG cryogenic flexible hose are reviewed and combed. In addition, the future research hotspots of LNG cryogenic flexible hose technologies are prospected. The related research work of LNG cryogenic flexible hose technology started relatively late in China, the key technologies of mechanical design and analysis and industrial application of LNG cryogenic flexible hose need to be broken through to improve the ability of domestic design and manufacture of LNG cryogenic flexible hose. It is of great significance to realize independent and controllable key technologies in the development of natural gas resources and to promote the realization of the national strategic goal of "peak carbon dioxide emissions" in China.
2022, 54(10): 2904-2921. doi: 10.6052/0459-1879-22-115
Zhao Jian, Liu Yanchen, Zhu Bing, Li Yang, Li Yaxin, Kong Decheng, Jiang Hongyi
The road identification of off-road vehicles can be carried out according to the dynamic response on different road surfaces, which lays a foundation for adjusting the parameters of the chassis control subsystem to obtain better driving performance. However, it is difficult to analyze the response mechanism of vehicles on different road surfaces due to the complexity of the off-road environment, which brings challenges to accurate road recognition based on vehicle dynamic response. In this paper, an SHAP-RF road recognition algorithm design framework is proposed, which realizes dimensionality reduction of the high-dimensional RF (random forest) road recognition model through the SHAP (Shapley additive explanations) model interpretation method. Firstly, we collected the driving data of the test vehicle on soil road, sand road, good asphalt road, and snow-icing road, and then three secondary driving features were calculated. Furthermore, a total of 105 features of driving data were calculated, including time domain features and frequency domain features. A high-dimensional RF road recognition model was established with all the features as input. The SHAP interpretation method was used to analyze the influence of input features on the recognition results in the high-dimensional model, and the correlation between each feature and road type was extracted to complete feature screening. Finally, a dimensional-reduction RF road recognition model is designed using the selected features. The validation test of the algorithm based on real vehicle data shows that the identification accuracy rate of the dimensional-reduction road recognition model is above 94% for all four kinds of road, and the recall rate is above 93%. Compared with the high-dimensional RF road recognition model, the accuracy rate and recall rate on all kinds of roads drop by no more than 3.2%. This proves that the proposed SHAP-RF road recognition algorithm design framework can reduce the number of input features while ensuring the recognition accuracy of road categories.
2022, 54(10): 2922-2935. doi: 10.6052/0459-1879-22-229