Meccanica最新文献

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Variations in wake structures and fluid forces around a square cylinder with four small control square rods at low Reynolds number 低雷诺数下带有四根小控制方杆的方形圆柱体周围尾流结构和流体力的变化
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-03-22 DOI: 10.1007/s11012-025-01968-6
Salwa Fezai, Fakher Oueslati, Safa Mnefgui
{"title":"Variations in wake structures and fluid forces around a square cylinder with four small control square rods at low Reynolds number","authors":"Salwa Fezai,&nbsp;Fakher Oueslati,&nbsp;Safa Mnefgui","doi":"10.1007/s11012-025-01968-6","DOIUrl":"10.1007/s11012-025-01968-6","url":null,"abstract":"<div><p>Numerical prediction of fluid flow past a square cylinder with 4 control square rods placed in a channel is carried out using an in-house code based on finite volume method (FVM) and a full multi-grid technique (FMG). The flow features are extracted in terms of streamlines, iso-vortices, and drag (CD) and lift (CL) coefficients evolutions for steady and unsteady regimes. Numerical results demonstrated significant effect due to the addition of control rods by delaying the onset of flow instability, increasing the critical Reynolds number (Re<sub>c</sub>) from 50 to 80. For instance, at Re = 10, the flow around the square cylinder with control rods exhibits two large recirculation lobes, while higher Reynolds numbers lead to six elongated lobes. On another hand, at unsteady regime for the square cylinder without control rods, the critical Reynolds number for vortex shedding is predicted to be approximately 48.064. The flow remains steady up to Re ≈ 87 with control rods, transitioning to unsteady flow at Re ≈ 93, indicating a substantial delay compared to the cylinder without rods. It is also seen that oscillatory flow with rods is aperiodic, whereas it is periodic without rods. Moreover, the impact of control square rods on time averaged drag and lift coefficients is analyzed and discussed. It is found that Strouhal number (St) variation shows an enhancement up to Re ≈ 140 without rods, followed by a decline, while control rods lead to a drop in St despite increased frequencies. Additionally, drag coefficient is reduced by up to 58.31% with control rods, and lift coefficient peaks at Re = 1 without rods, declining with higher Re.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"927 - 951"},"PeriodicalIF":1.9,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Composite control design for double-pendulum overhead cranes 双摆桥式起重机复合控制设计
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-03-20 DOI: 10.1007/s11012-025-01961-z
Weiqiang Tang, Rui Ma, Hongmei Jiang, Haiyan Gao
{"title":"Composite control design for double-pendulum overhead cranes","authors":"Weiqiang Tang,&nbsp;Rui Ma,&nbsp;Hongmei Jiang,&nbsp;Haiyan Gao","doi":"10.1007/s11012-025-01961-z","DOIUrl":"10.1007/s11012-025-01961-z","url":null,"abstract":"<div><p>Eliminating or reducing swing and enhancing the robustness of closed-loop systems have always been hot issues in crane control research. To this end, a novel composite control strategy combining adaptive input shaper and double closed-loop PD feedback is proposed for double-pendulum overhead cranes. Firstly, based on the dynamic model of the double-pendulum system, an extremely insensitive input shaper acting on the acceleration signal is designed. The shaped signal can realize the direct adjustment of multiple stages of the trolley movement. Secondly, this input shaper is combined with double closed-loop PD control used for the displacement and the hook swing angle to form a novel composite control structure. This structure makes the closed-loop system robust against uncertainties. In order to further improve the adaptability of the control structure to complex working conditions, an adaptive input shaper optimization algorithm is proposed. The algorithm is based on a novel performance function that reflects the residual swing. The pulse amplitude and action time of the shaper can be adjusted online through iterative calculation of acceleration and hook swing angle. Finally, the results show that the proposed control strategy can reduce the swing angle and ensure the robustness of the system. In addition, compared with other control strategies of the same type, it performs better in swing suppression.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"891 - 909"},"PeriodicalIF":1.9,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A nonlinear iterative approach to predict large deflections of a novel spring-loaded ornithopter wing 一种预测新型弹簧翼大挠度的非线性迭代方法
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-03-16 DOI: 10.1007/s11012-025-01944-0
Joydeep Bhowmik, Sriram Palika, Debopam Das
{"title":"A nonlinear iterative approach to predict large deflections of a novel spring-loaded ornithopter wing","authors":"Joydeep Bhowmik,&nbsp;Sriram Palika,&nbsp;Debopam Das","doi":"10.1007/s11012-025-01944-0","DOIUrl":"10.1007/s11012-025-01944-0","url":null,"abstract":"<div><p>In this study, a new design of an ornithopter wing has been introduced whose stiffness can be controlled and varied according to design requirements using a spring introduced at the trailing edge. The new patented wing design consists of a leading edge spar, supported by an arrangement of ribs. One or more springs can be attached to the trailing edge which keeps the wing taut and maintains the span-wise twist of the wing when a load is applied. A numerical iterative approach has been developed to calculate the large deformations of the wing when a known load distribution is applied to this wing. Notably, this method overcomes the limitations of conventional Finite Element Methods, accounting for multiple ribs and spring configurations. Experimental validation confirms the accuracy of the proposed approach, offering a significant advancement in modelling complex ornithopter wing deformations and paving the way for improved design optimisation.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"875 - 889"},"PeriodicalIF":1.9,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Control-oriented modelling and analysis of transient rolling contact behaviour of tires 面向控制的轮胎瞬态滚动接触特性建模与分析
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-03-12 DOI: 10.1007/s11012-025-01960-0
Yingjie Zhu, Jianwei Lu, Ping Jiang
{"title":"Control-oriented modelling and analysis of transient rolling contact behaviour of tires","authors":"Yingjie Zhu,&nbsp;Jianwei Lu,&nbsp;Ping Jiang","doi":"10.1007/s11012-025-01960-0","DOIUrl":"10.1007/s11012-025-01960-0","url":null,"abstract":"<div><p>With the progress in active chassis control technologies, transient tire dynamics play more important role specially in large wheel slip range. This study aims to reveal the longitudinal transient characteristics of tires due to tread compliance involving large slip and to develop a transient tire model for the application of controller design. In this paper, a novel longitudinal transient tire model is developed based on the transient slip variable defined by the average tread deformation in the adhesion region, and the proposed model is validated by comparing it with the unsteady-state brush tire model and simulation with discrete brush tire model. For controller design analysis, an asymmetric vertical pressure distribution is introduced with the aim to obtain the brush tire model with continuous nature under all slip conditions. Specially, although only the longitudinal transient behavior of tires is addressed in this paper, the idea of this paper can still be used in the transient dynamics modelling of tires under pure lateral slip and combined slip conditions.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"861 - 874"},"PeriodicalIF":1.9,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A novel rapid positioning method for dynamic load location based on Newmark explicit method and modal shape comparison method 一种基于Newmark显式法和模态振型比较法的动载荷定位新方法
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-03-04 DOI: 10.1007/s11012-025-01955-x
Zhengshu Wang, Jinhui Jiang
{"title":"A novel rapid positioning method for dynamic load location based on Newmark explicit method and modal shape comparison method","authors":"Zhengshu Wang,&nbsp;Jinhui Jiang","doi":"10.1007/s11012-025-01955-x","DOIUrl":"10.1007/s11012-025-01955-x","url":null,"abstract":"<div><p>Accurately determining the location and magnitude of loads acting on a structure is crucial for structural design, optimization, and health monitoring. However, identifying the source of vibration through direct measurement is extremely challenging. Therefore, developing a rapid and accurate method for dynamic load location identification is essential. This paper focuses on proportionally damped continuous systems and proposes a novel and efficient method for dynamic load location identification. The traditional \"response-system-load\" framework for dynamic load identification is transformed into a \"response-modal response-system-modal load\" framework based on the Newmark explicit method, determining the modal loads of various orders in the vibration system. The modal shapes corresponding to the load location are then determined using the least squares inverse method, and the load location is identified by calculating the mode shape deviation function. Subsequently, an iterative strategy for dynamic load location identification is proposed to further enhance the computational efficiency of the method on complex structures. Simulated results demonstrate that, compared to the virtual load method, this method does not require load identification for every possible point, but only needs to identify modal loads once, significantly improving the speed of dynamic load location identification. Furthermore, the algorithm demonstrates high precision and excellent noise resistance in the identification of sinusoidal loads, broadband random loads, and impact loads. It also demonstrates robust adaptability under conditions of model uncertainties. To further verify the performance of the algorithm in practical applications, experimental studies on dynamic load identification were conducted on a simply supported beam system, and the results show that the algorithm is effective.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"841 - 859"},"PeriodicalIF":1.9,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimized input shaping for multi-mode hanging chains using a modal model approach 采用模态模型方法优化多模态悬链的输入整形
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-03-03 DOI: 10.1007/s11012-024-01898-9
Faisal Alobaid, Khalid Alghanim
{"title":"Optimized input shaping for multi-mode hanging chains using a modal model approach","authors":"Faisal Alobaid,&nbsp;Khalid Alghanim","doi":"10.1007/s11012-024-01898-9","DOIUrl":"10.1007/s11012-024-01898-9","url":null,"abstract":"<div><p>This work presents a study on the dynamics and control of a hanging chain suspended from an overhead crane, using modal analysis and input shaping techniques. Two standard input shaping functions, step, and polynomial, are evaluated alongside a piecewise cosine function. The effectiveness of proposed input shaping techniques is evaluated based on their impact on the hanging chain’s various mode shapes contribution. The study introduces a key innovation in solving input coefficients for flexible structures by utilizing the modal model matrix created from the Finite Difference Method in conjunction with Laplace transformations. This approach aims to achieve various solutions for the input functions depending on the number of modes considered in the system. The solution varies depending on the number of modes contributing in the response. This allows for highly precise control and provides insights into their potential applications in dynamic control systems involving flexible structures.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"825 - 840"},"PeriodicalIF":1.9,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical investigation on the effects of stacking pattern and thickness ratio on the ballistic performance of tortoiseshell-like glass composite 堆垛方式和厚度比对类玳瑁玻璃复合材料弹道性能影响的数值研究
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-03-01 DOI: 10.1007/s11012-025-01953-z
Jun Sun, Xin Zhang, Chunxu Zhao, Jun Li, Hai Mei, Xiang Liu, Shilin Yan
{"title":"Numerical investigation on the effects of stacking pattern and thickness ratio on the ballistic performance of tortoiseshell-like glass composite","authors":"Jun Sun,&nbsp;Xin Zhang,&nbsp;Chunxu Zhao,&nbsp;Jun Li,&nbsp;Hai Mei,&nbsp;Xiang Liu,&nbsp;Shilin Yan","doi":"10.1007/s11012-025-01953-z","DOIUrl":"10.1007/s11012-025-01953-z","url":null,"abstract":"<div><p>Transparent protective composites inspired by natural tortoiseshell structures offer a promising solution for high-performance ballistic applications. However, the design optimization of these composites under dynamic impact conditions remains underexplored. This study systematically examines the effects of various stacking patterns, layer thickness ratios, and unit block side lengths on the ballistic performance of tortoiseshell-like glass composites. The results indicate that eccentric staggered configurations significantly outperform aligned and centered configurations due to enhanced stress wave attenuation at complex interfaces. Equal thickness ratios (1:1) optimize energy dissipation by balancing interfacial crack propagation and unit block damage, while unequal ratios degrade performance by concentrating stress in thinner layers. Notably, variations in unit block size have minimal impact on overall impact resistance, as increased interface length compensates for reduced interface density. These findings advance the development of bioinspired protective materials for military, aerospace, and civil safety applications, offering a pathway to mitigate trade-offs between structural weight and ballistic resilience.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"809 - 824"},"PeriodicalIF":1.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Development and kinematic analysis of origami-inspired retractable roof structures 折纸式可伸缩屋顶结构的发展与运动学分析
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-02-26 DOI: 10.1007/s11012-025-01951-1
Jinyu Lu, Jiang-Jun Hou, Ding Lu, Haichen Zhang
{"title":"Development and kinematic analysis of origami-inspired retractable roof structures","authors":"Jinyu Lu,&nbsp;Jiang-Jun Hou,&nbsp;Ding Lu,&nbsp;Haichen Zhang","doi":"10.1007/s11012-025-01951-1","DOIUrl":"10.1007/s11012-025-01951-1","url":null,"abstract":"<div><p>The application of retractable roof structures has enhanced the urban landscape, particularly in large-scale public buildings. Miura-ori is an immensely popular and highly inspiring method of paper folding. In this paper, three novel design families of retractable roof structures, integrating Miura-ori (and its variations) with scissor hinge units, are proposed. A concise overview of the concepts of Miura-ori (including its arched and fan-shaped variations), scissor joint unit, and rigid panel is first provided. Subsequently, coordinated motion conditions for the three proposed retractable roof structures are elaborately derived using geometric formulas, and the corresponding solutions are provided when the coordinated motion is not feasible. Lastly, after parameterizing the rigid-panel model, the motion mechanism of the retractable roof structures is analyzed exhaustively. The results indicate that all three new structures can achieve smooth opening and closing operations without motion interference. The proposed novel retractable roof structures enrich the variety of architectural structures and provide practical guidance for engineering applications.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"785 - 808"},"PeriodicalIF":1.9,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shock physics in compressible thermoelastic and thermoviscoelastic solids 可压缩热弹性和热粘弹性固体中的冲击物理
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-02-26 DOI: 10.1007/s11012-024-01893-0
K. S. Surana, E. Abboud
{"title":"Shock physics in compressible thermoelastic and thermoviscoelastic solids","authors":"K. S. Surana,&nbsp;E. Abboud","doi":"10.1007/s11012-024-01893-0","DOIUrl":"10.1007/s11012-024-01893-0","url":null,"abstract":"<div><p>In this paper, we present mathematical models, methods of obtaining their solutions, and the model problem studies for wave propagation in compressible thermoelastic (TE) and thermoviscoelastic (TVE) solid media, i.e., this research addresses shock physics in compressible TVES without memory. The mathematical model consists of conservation and balance laws (CBL) of classical continuum mechanics (CCM) derived using the contravariant second Piola–Kirchhoff stress tensor and the convected time derivative of the covariant Green’s strain tensor up to order <i>n</i>. Constitutive theories are derived using conjugate pairs in the entropy inequality augmented with strain rates up to order <i>n</i> and the representation theorem. The dissipation mechanism in this theory is due to ordered rates of Green’s strain tensor up to order <i>n</i>. This mathematical model permits finite deformation, finite strain, as well as finite strain rate deformation physics and is thermodynamically and mathematically consistent. The solutions of the initial value problem (<i>IVP</i>) described by this mathematical model are obtained using a space-time coupled variationally consistent space-time finite element method based on the space-time residual functional for a space-time strip with time marching. The p-version hierarchical space-time local approximations of higher degree as well as higher-order global differentiability are considered in higher-order scalar product spaces. This permits accurate computations of a posteriori errors in the solution measured in the <span>(L_2)</span> norm of the space-time residual functional and provides means of improving the accuracy of computed solutions. In the research presented in this paper, no assumptions or approximations are made regarding shock wave, shock structure, or its analytic (or non-analytic) nature. This work relies on the mathematical models and the computational infrastructure presented in this paper to reveal and simulate shock physics details: deviatoric stress wave, density wave, their propagations, reflections, and interactions in compressible TVES medium without rheology. Detailed model problem studies are presented to illustrate all aspects of the shock physics. To our knowledge, this work is not available in the published literature. This paper is the first presentation of this research.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"755 - 783"},"PeriodicalIF":1.9,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11012-024-01893-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improving the evaluation of static bifurcations in locally damaged parabolic arches 改进局部损伤抛物线拱静力分岔的评估方法
IF 1.9 3区 工程技术
Meccanica Pub Date : 2025-02-24 DOI: 10.1007/s11012-024-01932-w
U. Eroğlu, G. Ruta, E. Tüfekci, A. Paolone
{"title":"Improving the evaluation of static bifurcations in locally damaged parabolic arches","authors":"U. Eroğlu,&nbsp;G. Ruta,&nbsp;E. Tüfekci,&nbsp;A. Paolone","doi":"10.1007/s11012-024-01932-w","DOIUrl":"10.1007/s11012-024-01932-w","url":null,"abstract":"<div><p>Even local small cracks may induce instability and failure or operativity loss before the crisis for the intact material is actually attained. Thus, damage models and the possibility of their identification have become trendy subjects in structural mechanics. We previously studied buckling and post-buckling of parabolic arches with a local transverse small crack by two perturbations of the finite field equations and boundary conditions. One perturbation describes non-trivial fundamental paths adjacent to the undamaged initial shape, the second describes the germ of a bifurcated path in the vicinity of a critical point. We think the arch consisiting of two undamaged parts, connected by lumped elasticities quantified by notions of linear fracture mechanics, at the cracked cross-section. In this paper we highlight that in a previous investigation of ours on the same subject some physically meaningful terms were wrong in the perturbed equations. This implies that the values of the incremental external load considered in the applications of that investigation need to be amended. Thus, here we present perturbed equations that are complete and, by the same procedure, we find more reliable numerical results for the critical loads and a more refined description of the germ of the post-buckling path, besides providing clear physical interpretation for seemingly paradoxical results.</p></div>","PeriodicalId":695,"journal":{"name":"Meccanica","volume":"60 4","pages":"739 - 754"},"PeriodicalIF":1.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11012-024-01932-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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