#### Table of Content

20 August 2020, Volume 42 Issue 4
Review
SUPERSONIC BIPLANE —— A POSSIBLE BOOMLESS CONFIGURATION
LIU Rongjian, BAI Peng
2020, 42(4):  397-404.  DOI: 10.6052/1000-0879-19-482
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The concept of the supersonic biplane was proposed by Adolf Busemann, a German aerodynamist, in 1935. In recent years, the supersonic biplane has re-attracted the aeronautical scientist's interest in order to meet the needs of supersonic transport's low sonic boom and low supersonic cruise drag. In this paper, the working mechanism of the typical supersonic biplane is summarized. The basic problems faced by the application of the supersonic biplane, such as non-design point characteristics and three-dimensional problems, are introduced. Finally, the key problems and the application prospects of the supersonic biplane in the future are prospected.

Applied Research
DROP FORMATION FROM A CAPILLARY TUBE IN THE PRESENCE OF SURFACTANT 1)
CHEN Yazhou, ZHOU Zhiqiang, PENG Jie
2020, 42(4):  405-412.  DOI: 10.6052/1000-0879-19-484
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In this study, the growth of an incompressible Newtonian drop from a vertical circular capillary tube in the presence of surfactant is analyzed. The flow is assumed to be axisymmetric and can be reduced to a spatially one-dimensional system by using the Taylor expansion and the lubrication approximation. The finite difference method combined with a coordinate transform is adopted for the numerical simulation. The results show that the existence of the surfactant will promote the breakup process of the drop, and prolong the limit length. Furthermore, the surfactant concentration has a more critical influence on the interface shapes than the surfactant activity.

EFFECTIVENESS OF THE PROPELLENT CROSS-FEED TECHNOLOGY FOR LAUNCH VEHICLE
XIAO Zhiwen, WU Di
2020, 42(4):  413-417.  DOI: 10.6052/1000-0879-19-483
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This paper presents a simple method to estimate and optimize the maximum launch capability of low Earth orbit (LEO) with different launch modes and trajectories, combined with trajectory optimization. The numerical calculation is carried out for the CZ-7 rocket, to analyze the specific effect and the characteristics of the optimal launch trajectory when launching with the cross-feed technology. The results show that the maximum launch capability of the LEO can be increased by 3 t (about 20%) and the maximum axial acceleration during the launch can be reduced by nearly 50% if for the CZ-7, the propellant cross-feed technology is applied in the launching process. With the help of the propellant cross-feed technology, the launch capability of such lift launch vehicle can be greatly improved.

LIMIT CYCLE FLUTTER CHARACTERISTICS RELATED TO CONTROL SURFACE OF LARGE AIRCRAFT1)
LÜ Jihang, LUO Linyin
2020, 42(4):  418-423.  DOI: 10.6052/1000-0879-20-009
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The freeplay of the control surfaces is a cause of the structural nonlinearity, which will easily lead to the limit cycle flutter. According to the design requirements, considering the center freeplay of the control surface, rational function approximations of the unsteady aerodynamics in the frequency-domain are constructed based on the Minimum-State Approximation Formula, with the nonlinear stiffness caused by the center freeplay being described by the subsection function. Then the nonlinear response characteristics and the behaviors of the limit cycle flutter due to the freeplay on the control surface are studied. Results show that due to the influence of the central freeplay in the nonlinear system, the limit cycle oscillation is produced below the linear flutter speed, and the limit cycle amplitude increases with the increase of the flight speed or the center gap.
THE MECHANISM OF THE INTERACTION BETWEEN NANOPARTICLE AND LIPIDS MONOLAYER OF PULMONARY SURFACTANT 1)
JIAO Fengxuan, SANG Jianbing, LIU Zhaoyang, LI Yang
2020, 42(4):  424-429.  DOI: 10.6052/1000-0879-20-034
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The inhaled nanoparticles (NPs) are first met by the biological barrier inside the alveolus known as the lung surfactant (LS). They can reach deep into the lung and interfere with the biophysical properties of the lung components. The interaction mechanisms of the gold nanoparticles (AuNPs) with the LS monolayer and the consequences of the interactions on the lung function are not well understood. Coarse-grained molecular dynamics simulations are carried out to study the interaction between the AuNPs and the LS monolayers at the nanoscale. It is observed that the presence of the AuNPs deforms the monolayer structure, changes the biophysical properties of the LS monolayer, and the results also indicate that the AuNPs with different shapes have different effects on the LS monolayer. These findings could help to identify the possible consequence of the airborne NPs inhalation.

FREE VIBRATION ANALYSIS OF CARBON NANOTUBES BASED ON THE MESHLESS METHOD1)
LI Lin, SHI Feng, XIANG Song, ZHAO Weiping, WANG Yanbing
2020, 42(4):  430-434.  DOI: 10.6052/1000-0879-20-014
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Free vibration of carbon nanotubes is analyzed by the meshless method. Several numerical examples are used to verify the convergence of the present method. The natural frequencies of the carbon nanotubes of different length-to-diameter ratios are calculated and compared with the available results in published literature. The results show that the present method enjoys a high accuracy, and the meshless method based on the thin-plate spline radial basis function can successfully be used to analyze the free vibration of carbon nanotubes.
THE IMPACT MECHANICAL PROPERTIES OF COAL CONTAINING GAS1)
YANG Dan, LIU Yang
2020, 42(4):  435-441.  DOI: 10.6052/1000-0879-20-101
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In order to obtain the impact mechanical properties of coal containing gas, the mechanical properties of coal samples with adsorption gas pressures of 0 MPa, 2 MPa, 4 MPa and 6 MPa are determined by the uniaxial compression test method. The results show that the compressive strength, the elastic modulus and the impact energy index of coal samples decrease linearly and the peak strain increases linearly with the increase of the adsorbed gas pressure. With the increase of the adsorbed gas pressure, the failure type of the coal body changes from brittleness to ductility, and the portion of the separation failure portion is enhanced. The adsorbed gas accelerates the process of instability and failure of the coal body, and makes the coal and rock gas dynamic disaster change from the rock burst dominated type to the coal and gas outburst dominated type.
DYNAMIC ANALYSIS OF A LOADED SHOULDER-POLE DURING WALKING
Liu Rongmei
2020, 42(4):  442-446.  DOI: 10.6052/1000-0879-20-022
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A dynamic model and the related equations for a loaded shoulder-pole during walking are established. Three frequencies are involved, i.e. the vibration frequency of the load simplified as a pendulum, the walking frequency and the vertical vibrant frequency of the loaded shoulder-pole. Numerical calculation results indicate that in order to make the walking comfortable, the above three frequencies should be coordinated. When the walking frequency is 70%,$\sim$80% of the vertical vibrant frequency of the loaded shoulder-pole, the vertical additional dynamic reaction force on the shoulder is about 30% of the weight of the load and is in the same direction with the vertical moment of the shoulder. When the vibration frequency of the load simplified as a pendulum is 25%,$\sim$30% of the walking frequency, the swing of the loads and the horizontal additional dynamic reaction force on the shoulder are relatively small.
WIND TUNNEL TEST AND STABILITY STUDY OF ICED QUAD BUNDLE CONDUCTOR1)
MIN Guangyun, LIU Xiaohui, Yan Bo, SUN Ceshi, CAI Mengqi
2020, 42(4):  447-454.  DOI: 10.6052/1000-0879-20-006
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The aerodynamic coefficients of the iced quad bundle conductor and a single conductor are obtained under four different conditions through wind tunnel test. The equivalent aerodynamic coefficients of the central axis of the quad bundle conductor are obtained by the equivalent method and compared with those of a single conductor under the same conditions. Based on the Den Hartog's galloping mechanism and the Nigol's torsional mechanism, the stable and unstable regions of the equivalent coefficients of the iced quad bundle conductor are determined. The results of this paper can be used in the research of the galloping and the simulation of the galloping of the iced conductor.
THE DURABILITY OF GLASS FIBER REINFORCED COMPOSITE REBARS IN SALT LAKE HIGH AND COLD AREA1)
LI Shuangying, ZHAO Jianchang
2020, 42(4):  455-462.  DOI: 10.6052/1000-0879-20-087
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The durability tests of glass fiber (GFRP) and GFRP-reinforced steel rebars are carried out under the action of multiple environmental factors in Salt Lake Area. The environmental types and the action time influence the ultimate tensile strength, the elastic modulus and the ultimate strain. It is shown that the tensile strength of the GFRP rebars and the GFRP steel rebars decreases gradually with the increase of the corrosion cycles, the freeze-thaw cycles and the dry-wet cycles in Salt Lake, and the brine under the coupling of multiple factors, but the tensile strength reduction of the GFRP rebars is small, the ultimate tensile strength reduction of GFRP steel rebars is not significant, especially when the GFRP steel rebars is put in Salt Lake for more than 90 days. With the brine and more than 150 cycles of freeze-thaw, the yield strength of the GFRP bars is almost non-existent and close to the ultimate tensile strength, and the elastic modulus of the GFRP bars decreases and then increases with the increase of age, however, the elastic modulus of the GFRP rebars decreases gradually, which is not very large in comparison with the GFRP rebars under various coupling factors, and the ultimate tensile strength and the elastic modulus of the GFRP rebars under various coupling factors are smaller than those under a single factor, and the relationship with the corrosivity is: Salt Lake Brine + dry-wet cycle + freeze-thaw coupling > Salt Lake Brine + dry-wet cycle > freeze-thaw > Salt Lake Brine.
SHEAR TEST AND FINITE ELEMENT SIMULATION OF POLYURETHANE POLYMER GROUTING MATERIALS1)
WANG Daolu, WANG Chaojie, SHI Mingsheng, ZHAO Peng, FAN Bingsen, LI Yang
2020, 42(4):  463-469.  DOI: 10.6052/1000-0879-19-463
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The shear mechanical properties of polymer are investigated in this paper by torsion experiment. The failure characteristics of the cell at the fracture surface are observed under scanning electron microscope (SEM). Furthermore, based on the finite element analysis, the deformation and mechanical properties and the distribution of shear stress are analyzed. It is shown that the density has a significant effect on the shear strength and the shear modulus of the polymer material, which can be significantly improved with the increase of the density of the polymer. The cell distribution of the polymer follows the minimum energy principle. A higher density of the polymer means smaller surface area and surface energy, which would make the system more stable. The face centered cube building model can simulate the shear deformation behavior of the fitted material well, and the higher the density, the better the fitting effect.
Research on Education
THE INNOVATIVE TRAINING SYSTEM FOR INTERNATIONAL TALENTS IN ENGINEERING HIGHER EDUCATION UNDER THE BELT AND ROAD POLICY1)
LI Gang, SUN Lisha, YAN Jun, ZHENG Yonggang, YANG Chunqiu
2020, 42(4):  470-474.  DOI: 10.6052/1000-0879-19-402
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Under the Belt and Road Policy, we adopt a training system for international talents and construct the global cooperation and interaction theories of the universities in order to face the challenge of higher education. Under the influence of new technology, new industry and new mode of the economic development, new requirements are set for the training of engineering talents and it is necessary to have a new concept, a new structure, and a new system with quality for the innovation training system of internationalization for engineering talents. This paper focuses on the construction of new internationalized training system for engineering talents, with international interaction and courses in order to cultivate more international talents majoring in engineering, aeronautics and space and mechanics for China's economic development.
GEOMETRIC ANALYSIS OF FOUCAULT PENDULUM1)
WANG Ruiyin, YUAN Wei, FENG Fang, JIN Changjiang
2020, 42(4):  478-484.  DOI: 10.6052/1000-0879-19-464
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The Foucault pendulum is well kmown as one of the most beautiful physics experiments, but the explanation of the Foucault pendulum is always difficult in the college physics course. Unlike the method of Newtonian mechanics, which introduces the Coriolis force to explain the rotation of the Foucault pendulum, this paper uses a geometric method to analyze the Foucault pendulum, and it is shown that the rotation of the Foucault pendulum is the result of translating the velocity vector of the pendulum on the sphere. Finally, the equivalence of the geometric method and the Newtonian mechanics method is proven.
THE DYNAMIC ANALYSIS OF THE INTERESTING EXPERIMENT OF ROLLING BALL
ZHOU Liting, XIONG Jufeng
2020, 42(4):  485-488.  DOI: 10.6052/1000-0879-19-481
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This paper quantitatively analyzes the dynamic process of the "Rolling ball" experiment. In the "Rayleigh Ball" experiment, a "strange slope" is constructed to make the homogeneous ball look like a "climbing slope" by controlling the two guides. In this paper, the physical model is constructed based on the principle of the rigid body motion, and the stress and motion processes of the system are analyzed, and the formula of the maximum height of "climbing slope" of the homogeneous ball is derived. Ignoring the air resistance and the friction, when the initial distance of the two rail rods is far smaller than the radius of the ball, the small ball cannot fall and suddenly close the two rails to make them parallel. When the initial angle of the two rails is twice of the tilt angle of the rail, the homogeneous ball can reach the maximum height and the longest distance.
EXPLORATION AND PRACTICE OF HIGHER ORDER CONSTRUCTION FOR TEACHING OF THEORETICAL MECHANICS1)
YE Hongling, YANG Qingsheng, LIU Zhaomiao, LI Xiaoyang
2020, 42(4):  489-494.  DOI: 10.6052/1000-0879-19-447
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The curriculum is the core element in teaching and the quality of the curriculum directly determines the quality of teaching. In order to further promote the reform of the classroom teaching, the idea of the higher-order construction and its practice for theoretical mechanics are discussed, based on the platform of the exploration and the practice of the reforms of teaching theoretical mechanics, as well as the cultivation of students' higher-order thinking ability and higher order design objective of this course. The classroom teaching system of theoretical mechanics named "1+4+$N$" is constructed. The knowledge points of theoretical mechanics course are reorganized and the teaching and the learning are unified. Taking the composition motion of points as an example, the implementation paths and strategies of higher-order course construction are analyzed.
PROMOTING TEACHING BY USING COMPETITION PROBLEMS IN ENGINEERING MECHANICS TEACHING1)
CHANG Liwu, DU Yazhi
2020, 42(4):  495-498.  DOI: 10.6052/1000-0879-19-457
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This paper puts forward ways and methods of inspiring students' learning interest in engineering mechanics using the mechanical contest problems in cultivating students' creative thinking ability and mechanical modeling ability. By adjusting the content of the teaching examples, increasing the interest of the examples, strengthening the training of mechanical modeling and enhancing the consciousness of qualitative analysis, the problems encountered in the training for the mechanical competition are effectively solved. The results show that the teaching mode of "promoting teaching by competition" can effectively stimulate students' enthusiasm for learning mechanics and help them master the core content of the course.
GEOMETRIC AND MATHEMATICAL ANALYSIS OF THE ASSUMPTION OF SMALL DEFORMATION1)
LI Wenjuan, FENG Weiming, WANG Shaowei
2020, 42(4):  499-503.  DOI: 10.6052/1000-0879-20-018
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Small deformation, one of the basic assumptions in mechanics, plays a critical role in the derivations and the applications of many theories in mechanic, for example, the beam and plate theories, and the mechanics of materials. The interpretation and the use of the small deformation assumption are important since wrong results may come from the misunderstanding of the concept of "small deformation". This paper studies a simple example of statically indeterminate problems. In the statically indeterminate truss, the equilibrium equations derived from the free-body diagram of the member must be complemented by relations involving deformations and obtained from the geometry of the problem. The importance of the concept of small deformation in geometric relationships is shown. It is indicated that the same definition of small deformation but different geometric relationships can result in different complementary equations in which, of course, only one of them is correct. The wrong use of small deformation assumption in the geometric relationships is pointed out to further highlight the correct concept of the small deformation.
THE PROBLEM OF I-II COMBINED PLANE CRACK SOLVED WITH WESTERGAARD STRESS FUNCTION
JIANG Yuchuan, PU Chunqing
2020, 42(4):  504-507.  DOI: 10.6052/1000-0879-19-476
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It is not easy to obtain directly the stress field at the crack tip of I-II combined mode plane crack problem. In this paper, the Westergaard stress function is used to solve the plane crack problem of I-II combined mode, complete with the expressions of the stress components at the crack tip. The method is simple in the derivation procedure and explicit in the physical concept, and the results are shown to agree well with available results in open literature. At the same time, the superposition principle is applied to transform the force on the crack surface into the force on the outer boundary for the problem of I-II combined plane crack with force on the crack surface.
DETERMINATION OF THE CRITICAL DEFLECTION OF A SLENDER COLUMN1)
LIU Ronggang, BIAN Wenfeng, LI Suchao, LIU Wei, JIN Songbo
2020, 42(4):  508-510.  DOI: 10.6052/1000-0879-19-491
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The connotation of the critical force for the ideally elastic slender column is redefined by using rigorous boundary conditions. Based on the approximate differential equation of the deflection curve and the energy method, the limit expression of the critical force is derived, which can be used for solve the deflection uncertainty problem of slender columns under the critical force.
THE CONVERSION FORMULA OF CONSTRAINED FORCES AND THE TWO-FORCE BAR METHOD FOR FORCE ANALYSIS OF STATICALLY DETERMINATE STRUCTURE1)
WANG Zhen, SHU Kai'ou
2020, 42(4):  511-515.  DOI: 10.6052/1000-0879-19-494
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For a simple statically determinate structure, there is one equilibrium equation for one unknown force. On this basis, the constrained force conversion formula and the transformation idea of two-force bar are proposed to simplify the force analysis of statically determinate structures.
The Field of Mechanics
BLOOD FLOW IN THE CIRCULATORY SYSTEM1)
QIAO Aike
2020, 42(4):  516-522.  DOI: 10.6052/1000-0879-19-334
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The blood flow in the circulatory system of human body is the most changeful. This paper discusses the common arterial vessel diseases such as atherosclerosis, aneurysm and aortic dissection. The biomechanical mechanisms related with these vascular diseases and their treatment therapies are analyzed, and the health care of the circulatory system is suggested.
DISCUSSION ON TWO PROBLEMS OF THEORETICAL MECHANICS IN COLLEGE MECHANICS COMPETITION1)
FU Jingyu, ZHAO Zenghui, SUN Wei
2020, 42(4):  526-532.  DOI: 10.6052/1000-0879-19-377
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For two mechanical contest problems, two simplified coordinate systems are used, that is, the "Serret--Andoyer approximate coordinate system" and the "virtual coordinate system" , respectively, based on the Euler dynamics equation. On this basis, the solutions of the stability conditions of the small ball in the synchronous rotation of the big ball in the 9th problem of the 1st national youth mechanics competition are is discussed. The results show that it has lower stability critical speed requirements. This will be more conducive to improving the stability of the rotation structure. For the problem of rotation balls in the 3rd problem of the 12th National Zhou Peiyuan University Mechanics Competition, the universal motion law at any latitude is derived. When the initial angular momentum of the system is zero, a simple and magical motion mode occurs.