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20 June 2019, Volume 41 Issue 3
Review
2019, 41(3):  255-264.  doi:10.6052/1000-0879-18-226
Abstract ( 444 )   HTML( 352 )   PDF (2779KB) ( 352 )

This is the question asked in class: is it possible to obtain the covariant derivative of natural base vectors? To answer this question, the idea of axiomazitaion is introduced, the concepts of the generalized component and the generalized covariant derivative are defined. Based on these new concepts, the classical covariance is developed into the generalized covariance, and the classical covariant differentiation is developed into the generalized covariant differentiation. This paper summarizes the main difficulties and the important points of the above explorations, and shows the abstractions of the generalized covariant derivatives and the advances of the generalized covaraibilities.

Applied Research
STUDY ON INFLUENCING FACTORS OF FINE DYNAMIC MODEL OF CED400 HIGH SPEED PANTOGRAPH1)
YE Ziyou, LIU Longfei, WU Rongping, WU Mengzhen, XU Xianghong
2019, 41(3):  265-269.  doi:10.6052/1000-0879-19-087
Abstract ( 255 )   PDF (1160KB) ( 79 )
Fine dynamic modeling and vibration characteristics analysis of pantographs have great significance in structural optimization design and equipment performance improvement. For high speed pantograph with reliable structure and excellent performance, not only the overall dynamic characteristics, but also the local vibration characteristics become the key link. The fine dynamics modeling method of pantograph was studied and it was found that the proper mass distribution of the main components in pantograph and their connection setting characteristics are the important guarantee to obtain the natural vibration characteristics of the actual structure.
2019, 41(3):  270-277.  doi:10.6052/1000-0879-18-468
Abstract ( 232 )   PDF (781KB) ( 93 )
In order to study the influence of the gap collision on the dynamic response of the system, the nonlinear discrete dynamics equations of the unilateral constrained simply supported beam system are derived by using the Rayleigh-Ritz function as the mode function of an ideal simply supported beam. The dynamic response characteristics of the system under the fundamental harmonic excitation and its influence on the applicability of the linear equivalent method of the resonant frequency are studied by numerical methods. It is shown that the local collision caused by the gap of the nonlinear dynamic system will lead to the system vibration energy transfer between the various modes of the system, which makes the linear equivalent method invalid. Even in nonlinear analysis, it is necessary to consider the modes in which the natural frequency of the system is much larger than the upper limit of the excitation band.
2019, 41(3):  278-282.  doi:10.6052/1000-0879-19-013
Abstract ( 270 )   PDF (365KB) ( 69 )
This paper presents a stochastic vibration control strategy based on a piezoelectric stack inertial actuator and investigates the influence of the time delay on the control effectiveness. Firstly, the dynamic characteristics of the piezoelectric stack inertial actuator are analyzed, and the stochastic dynamic model of the main structure with an inertia actuator is established. Then, the LQG (linear quadratic Gaussian) control strategy is proposed and the influences of the system parameters (such as the inertia mass and the stiffness of the actuator) on the control effectiveness are discussed. Finally, the time delay is considered in designing the control strategy and a method of using the time delay is proposed to optimize the control strategy. The results show that the piezoelectric stack inertial actuator is very effective for the random vibration control, and the control effectiveness can be further optimized when the time delay $\tau=0.025$s.
2019, 41(3):  283-287.  doi:10.6052/1000-0879-19-024
Abstract ( 264 )   PDF (1946KB) ( 119 )
2019, 41(3):  288-293.  doi:10.6052/1000-0879-18-480
Abstract ( 246 )   PDF (209KB) ( 45 )
Deepwater shallow sediments are weakly structured and unconsolidated. The deformation and failure is one of the key points in the study of deepwater shallow sediments. The modified Cambridge model was widely used in the studies of deepwater shallow sediments except for the borehole stability analysis, in which deepwater shallow sediments are still regarded as ideal elastic plastic materials. The formation is divided into three parts: the elastic zone, the flow zone and the plastic zone. In the elastic zone, the formation is linear elastic. In the flow zone, the modified Cambridge model is applied. In the plastic zone, the formation obeys the Mohr-Coulomb criterion. In this paper, the stress distribution of each region is solved, and on the basis of the solution, combined with the excess pore pressure, the borehole stability analysis model of deepwater shallow sediments is established. The calculation results agree with actual data, which verifies the proposed model.
2019, 41(3):  294-299.  doi:10.6052/1000-0879-18-505
Abstract ( 182 )   PDF (459KB) ( 50 )
Based on the capillary effect and using the freeze thawing method for the sand grain, a sample preparation is suggested to make the sand sample with an arbitrarily sedimentary direction in the range of 0°~90° for any grain composition. A series of triaxial compression shearing tests are performed under a medium confining pressure, the results show that the preparation method combined with the moist sampling and the freeze thawing has a significant influence on the shearing behavior of the sand. With the method, the developing speed of the relation between stress and strain will be decreased, and the ultimate shearing strength will be lowered, but with little influence on the residual shearing strength. Under other stress path conditions of the triaxial test, such as the triaxial tension, the reduced triaxial compression and the triaxial isostress compression, the sample preparation has little influence on the results. The suggested sample preparation method is applicable for the experimental study of the sand inherent anisotropy behavior.
2019, 41(3):  300-307.  doi:10.6052/1000-0879-18-462
Abstract ( 205 )
Accurate identification of mesoscopic parameters are the precondition to conduct the discrete element simulation reasonably. Based on the optimization theory, an automatic method for identifying mesoscopic parameters of sand material is proposed in this paper. The PFC software is used to simulate the biaxial compression test of a kind of standard sandy soil. By minimizing the error between the stress-strain curves obtained by conducting the PFC biaxial compression test and the laboratory test, mesoscopic parameters are identified automatically by using the mode search method. Numerical results show that the stress-strain curves obtained by the numerical simulation and the laboratory test agree very well with those based on the mesoscopic parameters obtained by using the proposed method in this paper, with high efficiency and accuracy.
2019, 41(3):  308-313.  doi:10.6052/1000-0879-19-008
Abstract ( 192 )   PDF (2281KB) ( 49 )
The force chain plays a decisive role in the macroscopic and microscopic mechanical properties of granular matter. Based on the discrete element method (DEM), a two-dimensional regular particle system is established to study the influence of the friction coefficient between the particles on the contact force distribution at the bottom of the system under different loads and different defect sizes. The results show that in a defect-free particle system, the contact force distribution at the bottom of the system is affected by the friction coefficient and the point load. As the coefficient of friction increases, the bottom contact force turns from the bimodal form through the platform, gradually to a single peak form. In a system with point defects, the coefficient of friction and the size of the defect have an effect on the force distribution. With a fixed load, as the size of the defect increases, the peak value of the bottom contact force increases significantly; the average value of the force on the bottom is significantly weakened, and the force transmission to the boundary is enhanced. The presence of defects on the central axis of the system weakens the bottom intermediate region. When the defect size exceeds 2 layers, the variation curve of the bottom intermediate force against the friction coefficient changes from an increasing curve to a linearly decreasing curve.
Research on Education
2019, 41(3):  314-319.  doi:10.6052/1000-0879-19-047
Abstract ( 351 )   PDF (287KB) ( 237 )
This paper analyzes the textbooks of mechanics, especially the textbooks and their teaching systems of theoretical mechanics and material mechanics. From the national mechanics courses and texybooks constructed history situation, the achievements and problems of the construction of the mechanics course, national elementary mechanics teaching material usage, the introduction of overseas elementary mechanics textbooks, overseas theoretical mechanics teaching material system analysis, overseas mechanics teaching material system analysis, mechanics courses abroad network resources investigation and analysis, and the teaching technology application and quality evaluation and other aspects are expounded. Finally, through the study of overseas textbooks, due to its comprehensive characteristics and features, for the national elementary mechanics courses and textbooks reform to provide ideas and direction. This paper is one of them, mainly expounds the basic situation of the elementary mechanics textbooks pubilished within China
2019, 41(3):  320-322.  doi:10.6052/1000-0879-18-482
Abstract ( 230 )   PDF (141KB) ( 125 )
Classical Mechanics includes Newtonian Mechanics, Lagrangian Mechanics as well as Hamiltonian Mechanics. Fundamental theories of Classical Mechanics are mainly reflected in the course of Theoretical Mechanics in the current framework of higher education. Students majored in science and engineering are mostly intimidated by the complete knowledge hierarchy of Classical Mechanics. By incorporating the history of mechanics in the course, positive feedbacks from students are obtained.
2019, 41(3):  323-329.  doi:10.6052/1000-0879-19-098
Abstract ( 205 )   PDF (238KB) ( 88 )
The rapid development of emerging fields such as information technology, micro/nano technology and biotechnology in the 21st century has brought opportunities and challenges to the cultivation of talents in the field of mechanics. This paper briefly introduces the basic concepts and the development of idea of university, as well as its evolution in China. By analyzing the needs of social development and the frontier of mechanics research, it is shown that the cultivation objective for the mechanics undergraduate program should be innovative talents with broad humanistic qualities and profound professional knowledge. Based on the experiences of growing undergraduate students majored in theoretical and applied mechanics in Shanghai University in the past 20 years, this paper presents some suggestions to achieve this goal.
2019, 41(3):  330-332.  doi:10.6052/1000-0879-18-397
Abstract ( 227 )   PDF (913KB) ( 60 )
The optimal control is the required course for postgraduates majored in Control Science and Engineering. It is also the degree course for those majored in Mechanics, particularly in the area of dynamics and control. As an elementary course, it has extensive engineering applications with theoretical implications. The focus of this paper is how to improve the teaching and cultivate students' learning interest and innovative ability. The essential problem of the teaching reform, teaching objectives, teaching content and materials are discussed as well as teaching methods. Some measures of the teaching reform, such as the seminar-style teaching and the BOPPPS teaching structure, are successfully applied in the course with good results.
2019, 41(3):  333-336.  doi:10.6052/1000-0879-18-484
Abstract ( 237 )   PDF (163KB) ( 113 )
Theoretical mechanics is a basic course for students majored in engineering. To improve the academic challenge level, increase the difficulty of the course, and expand the depth of the course, the course has to be carefully arranged. After the depth and the breadth of basic courses are expanded, the follow-up professional courses are expanded, with regard to the teaching links, the teaching content, the teaching methods, as well as the practice links, to make a "golden class" for the theoretical mechanics.
2019, 41(3):  337-340.  doi:10.6052/1000-0879-19-026
Abstract ( 187 )   PDF (991KB) ( 91 )
Chinese characters composed of strokes are the great creation of the Chinese nation. The scientific and rational stroke structure determines the beauty of the font of the character. This paper introduces the concepts of the centroid and the moment of inertia. Through the image processing analysis, the normalized font image centroid and the font structure moment of inertia are obtained. These two parameters are used to quantitatively describe the barycenter and the word weight of the font structure. The proposed method can be used to evaluate the font structure of Chinese characters and provide a reference for Chinese character font design.
2019, 41(3):  341-344.  doi:10.6052/1000-0879-19-093
Abstract ( 257 )   PDF (349KB) ( 124 )
Based on the experiences in teaching reform of theoretical mechanics in Sichuan University, this paper mainly focuses on the great potentials of computer application examples in the teaching of theoretical mechanics. This strategy helps students to concentrate on the theories of mechanics by reducing mathematical operations. The batch solutions help students to have an intuitive impression on engineering projects, and the general solutions help students to gain further understanding of solving problems of multiple unknown parameters. Besides, this paper discusses the direction and the purpose of teaching reform, namely, to emphasize the general solutions for solving problems of multiple rigid bodies or parameters with the help of computer. This can help to compile theoretical mechanics textbooks to be better adapted to the development of scientific and technological progress.
2019, 41(3):  345-348.  doi:10.6052/1000-0879-18-424
Abstract ( 294 )   PDF (338KB) ( 122 )
In order to analyze the influence of the friction torque change on the measurement of rigid body inertia, the falling body method is used in the experimental analysis. It is indicated that the friction torque increases significantly with the increase of the system rotation speed, if the average rotation speed of the system in the deceleration process is much higher than that in the acceleration process, and if no correction is made, the calculation results are usually relatively small. At the same time, it is pointed out that the average rotation speed in the acceleration process and the deceleration process are relatively close to each other, the measuring value is mainly affected by the random error. The above results are helpful to further study the friction torque variations against the rotational speed.
2019, 41(3):  349-351.  doi:10.6052/1000-0879-18-366
Abstract ( 224 )   PDF (177KB) ( 106 )
In this paper, the toppling process of a non-uniform slender rod in the initial vertical stationary position on a horizontal support surface is studied. Based on the motion theorem of the center of mass, the law of conservation of mechanical energy and the theorem of fixed axis rotation, the expression of the bearing force of a straight rod without slip is derived. It is pointed out that the necessary conditions for a straight bar to be separated from the horizontal plane include two requirements: the mass distribution of the straight bar and the minimum static friction coefficient between the straight bar and the supporting surface.
The Field of Mechanics--National Zhou Peiyuan Competition on Mechanics
2019, 41(3):  357-365.  doi:10.6052/1000-0879-19-203
Abstract ( 331 )   PDF (2564KB) ( 137 )
National Zhou Peiyuan Competition on Mechanics for college students has been initiated and sponsored by the Editorial Committee of Mechanics in Engineering. After the development for more than 30 years, it has been successfully held for 12 sessions and has provided a platform to show the teaching level of the universities. On the 40th Anniversary of Mechanics in Engineering, this paper reviews the development and organizational mode of National Zhou Peiyuan Competition on Mechanics. The number of attendees and innovations of each session are summarized, and the role of the competition in mechanics teaching and personnel training are illustrated through cases study.
2019, 41(3):  366-369.  doi:10.6052/1000-0879-18-127
Abstract ( 399 )   PDF (1218KB) ( 272 )
This paper presents the problem-solving strategies, the design scheme and the implementation of the competition team from Tsinghua University, as the champion team in the "Theoretical Design and Operation" competition of the 11th Zhou Peiyuan Mechanics Competition for College Students of China. The experiences and the lessons learned from the competition are also presented.