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Table of Content
20 December 2019, Volume 41 Issue 6
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THE MEAN MOTION RESONANCE OF THE KUIPER BELT OBJECTS
LAN Lei, LI Junfeng
2019, 41(6): 643-648. doi:
10.6052/1000-0879-19-167
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The movements of the asteroids in the Kuiper belt are important for us to understand the origin and the evolution of the solar system. Since the Kuiper belt objects (KBO) are a short distance to the Neptune of a great mass, the KBOs are significantly perturbed by Neptune's gravity. In this paper, we focus on two main families: the resonant and the scattered KBOs. The mean motion resonance can prevent the resonant KBOs from a close encounter with the Neptune. Thus most resonant KBOs are stable on their orbits. Here we mainly investigate the resonance width and strength of different resonant ratios with a high eccentricity. As for the scattered KBOs, their evolution is affected jointly by the resonance sticking and the resonance scattering. Here we are mainly concerned with the problem why there are a high number of KBOs in the scattered disc.
Applied Research
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DYNAMICAL EXPLANATION ON TOROFLUX'S PHENOMENA
LIU Yanzhu, ZHANG Weiwei
2019, 41(6): 649-652. doi:
10.6052/1000-0879-19-276
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143
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The dynamic analysis of the toroflux, a toy with torus-spring winded by a steel ribbon, is given in this paper. As two special phenomena, the toroflux can suddenly change its geometrical form, and can rotate rapidly in falling process around a cylindrical body. The topological character of a closed bent rod is applied to determine the curvature and twist of the toroflux, and the elastic potential energies of two different equilibrium states of toroflux are calculated and compared. Then the phenomena of its shape mutation can be examined by the principal of minimal elastic potential energy. Taking a circle ring as an element of the toroflux, and the stretching effect of adjacent rings is considered. The pure rolling of the ring on the cylinder in falling process is analyzed to examine the occurrence of rapidly rotation, and the angular acceleration of the toroflux in falling process is derived. The theoretical results coincide with the data by experiment.
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RESEARCH ON MICRO-STRUCTURE AND ENERGY ABSORPTION MECHANISM OF THE HUMAN SKULL BONE
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XIONG Jian, WU Qianqian
2019, 41(6): 653-657. doi:
10.6052/1000-0879-19-314
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144
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Skull bone plays a significantly important role in sustaining life safety. As a cellular sandwich structure, skull bone is composed of compact bone (panel) and cancellous bone (core). Through the interaction between the skull section and impactor, the variation tendency of energy absorption of human skull bone with impact velocity has been analyzed based on energy conservation law in this paper. The failure topography of the skull bone under different impact velocities has been provided, and the structural energy absorption characteristics also have been reflected according to the failure area of the skull section.
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THE MYSTERIES OF RETROGRADE ASTEROIDS
HUANG Yukun
2019, 41(6): 658-660. doi:
10.6052/1000-0879-19-160
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The discovery of 2015 BZ509, the first asteroid trapped in the retrograde $1:1$ resonance with Jupiter, has raised a public passion for retrograde asteroids. This paper reviews the little-known retrograde asteroids in the Solar System and their origins, and provides an easy-to-understand explanation of the retrograde resonance problem associated with 2015 BZ509.
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TRANSMISSIBILITY OF TRANSVERSE BENDING VIBRATION OF ELASTIC STRUCTURES
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DING Hu, SHAO Zhihua
2019, 41(6): 661-664. doi:
10.6052/1000-0879-19-368
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136
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Vibration transmission is an important part of vibration theory and an important criterion for evaluating vibration control effects. For positive and negative isolation of discrete structures, the transfer rate is clearly defined. Since the vibration of the elastic structure is not only transmitted through one point, it is necessary to discuss how to define the transverse vibration transmission of the elastic structure. Through the elastic beams supported by springs at both ends, three kinds of transmissibility definitions for the positive isolation of the transverse bending vibration of the elastic structure are given, which are the transmissibility of the component forces of the two support ends and the transmissibility of the combined force of the two support points. The results show that the transmissions defined by the three methods may be equal or there may be large differences. More complex than the discrete structure vibration isolation theory. In order to promote the development of basic theories and applications of vibration mechanics, it is recommended that this basic vibration problem be included in the textbook as part of the course on vibration mechanics.
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STATIC AEROELASTICITY METHOD BASED ON EXTERNAL AERODYNAMIC FORCE AND STRIP METHOD
LIU Xiaochen
2019, 41(6): 665-670. doi:
10.6052/1000-0879-19-227
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129
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The static aeroelastic analysis method is applied in the load design in this paper, and an elastic load correction method based on the external rigid aerodynamic force and the modified strip method is developed. The deformation of the structure is calculated by the engineering beam method, the stiffness matrix of different components is obtained, and the aerodynamic force is obtained from the external test or the CFD aerodynamic database interpolation by meshing the model. The data transfer for the displacement and the force between the structure and the aerodynamics field is performed by using the surface spline function method and the shape function area coordinate weighting method, respectively, the elastic load is computed from the deflection of the aerodynamic mesh, that is, the improved strip. On this basis, the computation is iteratively looped until the displacement of the structural model converges. At the same time, the feasibility and the efficiency of the method are verified by analyzing some engineering examples and comparing with the well matured methods.
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CALCULATION OF AIRCRAFT DYNAMIC LOADS ON SHIP-DECK AND TEST VERIFICATION
HE Kangle, YANG Mei, SUN Renjun, ZHANG Jiangang
2019, 41(6): 671-675. doi:
10.6052/1000-0879-19-147
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108
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The carrier-based aircraft dynamic loads on the ship-deck are a critical design parameter of the structure. Often the conventional load calculation method can not deal with the carrier-based aircraft abnormal loads (such as in cases of catapult and arresting, free flight hook, off-center landing of carrier-based aircraft), a complete set of design methods and calculations of full-aircraft dynamic loads is proposed, and the dynamic load calculations are made for the full-aircraft dropping test of a certain type of aircraft, and the comparison with the test data verifies the rationality and the feasibility of the design methods and calculations.
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A SERIES METHOD FOR CALCULATION OF THE TORSION DEFORMATION OF THE SHAFT WITH TWO FIXED ENDS
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SHI Wenpu, LIU Shengxiang, LI Hejun
2019, 41(6): 676-680. doi:
10.6052/1000-0879-19-225
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124
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The torsion deformation of the shaft is commonly considered, due to the diversity of its loaded forms and the complexity of the boundary constraints. Its computation and the internal force analysis are often not easy, involve the section-cut method and the unbinding of constraints. In this paper, a series method is put forward to compute the torsion deformation of the shaft with two fixed ends with the help of the generalized function and the periodic extension method, without using the section-cut and the unbinding of constraints and with simple steps. It can be extended to wider applications. In order to show the effectiveness of the method, the general treatment of the material mechanics and the method of this paper are compared through an example.
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VARIATIONAL PRINCIPLES WITH DUAL MIXED VARIABLE AND APPLICATIONS FOR STRAIGHT BEAMS WITH LARGE DEFLECTION
CHEN Yingjie, WANG Chao, LÜ Tingting, CUI Peng
2019, 41(6): 681-687. doi:
10.6052/1000-0879-19-173
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Based on the work reciprocal theorem, the minimum potential energy principle and the principle of the minimum potential action of the dual mixed variable of the displacement and the stress are used to solve the problem of the deformation and the stability of a straight beam with large deflection. The results are compared with the finite element simulation results to verify the feasibility of the proposed method and the accuracy of the calculation results. The method is simple and flexible, and the result is accurate. It provides a new solution to solve the problem of a straight beam with large deflection. It can be directly applied to practical engineering problems.
Research on Education
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TEACHING SYSTEM AND TEXTBOOKS OF ELEMENTARY MECHANICS (III)——FOREIGN TEACHING RESOURSES OF MECHANICS OF MATERIALS AND THE TEACHING SYSTEM ANALYSIS
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YE Zhiming, LI Junfeng, WANG Shibin, WU Zhiqiang, CHEN Liqun, YANG Xiao, WU Jianhua, HUANG Yi
2019, 41(6): 688-698. doi:
10.6052/1000-0879-19-049
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176
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This paper analyzes the textbooks of mechanics, especially, the textbooks and their teaching systems of theoretical mechanics and mechanics of materials, including the national state of the mechanics courses and the textbooks, the achievements and problems, of the teaching system for the elementary mechanics, the introduction of overseas elementary mechanics textbooks, focusing on the teaching of mechanics of materials and the teaching system analysis.
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THE REFORM OF AERODYNAMICS CURRICULUM IN VIEW OF INNOVATION AND ENGINEERING PRACTICE
ZHU Zhibin, HE Guoyi, WANG Qi, WANG Wei
2019, 41(6): 699-702. doi:
10.6052/1000-0879-19-210
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114
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At present, the innovation and entrepreneurship education reform in domestic colleges and universities is steadily advancing, and the related teaching reform of aerodynamics curriculum system is also actively implemented. However, in the early stage of the reform, our school mechanically copied the successful experience of famous schools and only paid attention to the teaching reform of the curriculum system itself, and paid little attention to the external factors outside the curriculum system, which led to the ineffective reform. This paper reviews various external factors affecting the reform of the aerodynamics curriculum in our university from both the levels of the students and the teachers, and puts forward some solutions for problems under the local conditions.
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MEASUREMENT IN TENSILE TEST OF TRUE STRESS-STRAIN CURVES FOR LOW-CARBON STEEL
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LI Kai, XUE Yongjiang
2019, 41(6): 703-708. doi:
10.6052/1000-0879-19-206
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177
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In order to measure the true stress-strain curve of low carbon steel, an experimental teaching system based on a single camera three-dimensional digital image correlation system is developed. The system can be used to measure the three-dimensional surface morphology and the surface strain in the tensile test of a low carbon steel bar, and obtain its true stress-strain curve. This experiment helps the students to understand the mechanical properties of plastic metal materials and cultivate their interest in the scientific research.
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CLASSROOM DEMONSTRATION OF EXPERIMENT IN STRUCTURAL MECHANICS TEACHING
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WANG Lei, LIN Xinyan, ZHANG Wenming, WANG Qinting, MENG Haiping
2019, 41(6): 709-714. doi:
10.6052/1000-0879-19-036
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113
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The experiment is an important part in teaching many science and engineering courses, but it is very difficult for some courses to have a very good effect. As an example, the difficulties of experiment in the course of structural mechanics are discussed in terms of several typical experimental models in this paper. A classroom demonstration is put forward with a number of implementing cases. It is found that the classroom demonstration could increase student's ability to solve problems by combining theory with practice. Finally, an experimental model is suggested for classroom teaching and experiment of structural mechanics.
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DISPLACEMENT CALCULATION FOR STRAIGHT BAR WITH VARIABLE STIFFNESS BASED ON GRAPH MULTIPLICATION METHOD
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HUANG Liang, SUN Xiaohan, HU Xinxin, WANG Bo
2019, 41(6): 715-717. doi:
10.6052/1000-0879-19-075
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134
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When using the graph multiplication method to calculate the displacement of beams of variable cross-section, the graph segmentation is complicated, which often leads to errors. This paper puts forward a stiffness reduction method, a bar of variable cross-section with a certain length can be transformed into two bars of constant section with different lengths, through the relationship between the stiffness and the displacement, and with the superposition, the equivalent displacement can be obtained. This method can be widely applied to the displacement calculation of rods with variable section, to significantly reduce the number of graph multiplications, and the amount of calculation, improve the calculation efficiency and accuracy.
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GEOMETRIC DRAWING METHOD FOR FORM-FINDING AND FORCE-FINDING FOR TRIANGULAR PRISM OF TENSEGRITY
SHANG Renjie
2019, 41(6): 718-723. doi:
10.6052/1000-0879-19-146
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126
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The mechanics and the geometry are inextricably linked. A geometric drawing method can be used to find the form of a triangular prism of tensegrity structure with two parallel end faces, as well as to find the self-equilibrium forces in the triangular prism of tensegrity. The formulae for calculating the force density of self-equilibrium internal forces in triangular prism of tensegrity are derived. The geometric drawing method for form-finding and force-finding is simple in operating, intuitive and adjustable. The method can be implemented in the CAD software, and even can produce drawings on the paper. The formulae of the force density of self-equilibrium internal forces are simple and can be expressed visually. The form finding method is the geometric implementation of the force density method.
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A KIND OF STRUCTURAL MECHANICS TEACHING MODEL
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CHEN Tao, ZHENG Yuanpeng, SUN Feifei
2019, 41(6): 724-727. doi:
10.6052/1000-0879-19-178
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135
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Based on the current teaching status of structural mechanics for undergraduates of civil engineering. It was specially noted that geometric constructional analyses is too abstract. A solution was proposed based on real objects after thorough review of overseas practice. That can be seen as a kind of teaching models to simulate simplified geometric constructional system. The significance of real objects was discussed. Besides this, components, typical usage and demonstration were also described. The results indicated that they have superior benefits for lecturing structure mechanics. This can well reflect the fundamental significance of the subject in civil engineering courses. The traditional teaching together with innovation exploration, simplified illustrations and real objects are critical to the course.
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SOME PROBLEMS IN THE TEACHING OF STRUCTURAL MECHANICS
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TIAN Zhenguo
2019, 41(6): 728-732. doi:
10.6052/1000-0879-19-055
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156
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Based on the teaching practice of structural mechanics, the concepts of geometric structural analysis are used for determining the internal forces of statically determinate structures, with the kinematical method to construct the influence lines of beam structures, and with the principle of virtual work to calculate the reaction forces of supports of statically determinate structures; The differences and the relations among the degrees of freedom, the computational degrees of freedom, the structural dynamic computational degrees of freedom and the degrees of freedom for stability problems are analyzed; The characteristics and the applications of the force method, the displacement method are reviewed. The method of applying the multimedia, the experiment and the numerical simulation in teaching the structural mechanics is discussed. The intrinsic relationship in the structural mechanics, some confusing concepts and the characteristics of various methods, are clarified.
Historiettes in mechanics
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DERIVATION OF LIFT, DRAG AND THE KUTTA--JOUKOWSKI THEOREM FOR AIRCRAFTS
LIU Peiqing, GUO Zhifei
2019, 41(6): 739-744. doi:
10.6052/1000-0879-19-162
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425
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Several fundamental concepts and laws in aerodynamics are introduced and summarized in the article. Lift and drag are the two components of the air's force on the object respectively. They are caused by the relative motion of the object and the air, and proportional to the square of the speed of the motion. The Kutta-Joukowski theorem gives the relationship between the airfoil lift and the airfoil flow, and sparked the study of airfoil performance in the early 20th century. Furthermore, the contradiction between the calculation conclution of the inviscid flow around a cylinder and the experimental observations inspired the study of the viscous flow motion, therefore the Navier--Stokes equation was born. Then Prandt proposed the concept of boundary layer and skillfully solved the relationship between local flow and overall flow. For the wings with large aspect ratio, Prandt proposed a lift surface model based on the lift line assumption, which can obtain the aerodynamic performance of the wing based on the performance of the airfoil.