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《Mechanics and Engineering》 2005-03
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PLANAR VIBRATIONS OF A THIN ELASTIC ROD WITH CIRCULAR CROSS SECTION

LIU Yanzhu (Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China)  
Based on the Kirchhoff 's theory the planar vibrations of a thin elastic rod with circular cross section are studied. The dynamical equations of the rod are established in the Frenet coordinates of the centerline as the reference frame. In the case of planar motion the torsional vibration is decoupled from the flexural vibration. The torsional vibration of a rod with arbitrary planar shape and the flexural vibration of a straight rod without torsion under axial compression are discussed. It is proved that conditions of Lyapunov's and Euler's stability of equilibrium of a straight rod in static analysis are necessary conditions of its dynamic stability. The influence of the axial force and the inertial effect of the cross section on the natural frequency of flexural vibration is considered.
【Fund】: 国家自然科学基金项目(10472067)资助.
【CateGory Index】: O321
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【Citations】
Chinese Journal Full-text Database 2 Hits
1 LIU Yanzhu(Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China);MECHANICAL PROBLEMS ON ELASTIC ROD MODEL OF DNA[J];Mechanics and Engineering;2003-01
2 LIU Yanzhu (Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China);HOMOGENEOUS TORSIONALVIBRATION OF A HELICAL THINELASTIC ROD[J];Mechanics and Engineering;2004-06
【Co-citations】
Chinese Journal Full-text Database 8 Hits
1 Liu Yanzhu (Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030,China);STABILITY OF A THIN ELASTIC HELICAL ROD WITH NONCIRCULAR CROSS SECTION IN RELAXED STATE[J];Journal of Dynamics and Control;2005-04
2 Xue Yun1 Chen Liqun2 (1.Department of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 200235,China)(2.Department of Mechanics, Shanghai University, Shanghai 200444,China);LYAPUNOV STABILITY OF A STRAIGHT ELASTIC ROD WITH NON CIRCULAR CROSS SECTION UNDER FORCE SCREW[J];Journal of Dynamics and Control;2008-03
3 FANG Yuan~1,WANG Hui~1,TANG Yan~2,WANG Hong~1(1.College of Textile and Materails,Zhejiang Sci-Tech University,Hangzhou, Zhejiang 310018,China;2.Key Laboratory of Materials-Textiles,Ministry of Education,Zhejiang Sci-Tech University,Hangzhou,Zhejiang 310018,China);Dynamics analysis of computer hosiery machine′s knitting system based on ANSYS/LS-DYNA[J];Journal of Textile Research;2009-07
4 Liu Yanzhu(Department of Engineering Mechanics,Shanghai Jiao Tong University, Shanghai,200030);STABILITY OF EQUILIBRIUM OF A HELICAL ROD UNDER AXIAL COMPRESSION[J];Acta Mechanica Solida Sinica;2005-03
5 YANG Bin,ZHAO Wei-jia,HUANG Jian-fei,JIA Mei-juan(Qingdao University,Qingdao 266071,P.R.China);High-precision Numerical Method and Simulation for Dynamic Equations of Elastic Rod[J];Science Technology and Engineering;2009-02
6 Xue Yun Liu Yanzhu Chen Liqun (Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China) (School of Mechanical and Automation Engineering, Shanghai Institute of Technology, Shanghai 200235, China) (Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China);ON ANALYTICAL MECHANICS FOR A SUPER-THIN ELASTIC ROD[J];Acta Mechanica Sinica;2005-04
7 LIU Yanzhu (Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China);ELASTIC ROD IN KOVALEVSKAYA CASE[J];Mechanics and Engineering;2003-05
8 LIU Yanzhu (Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China);HOMOGENEOUS TORSIONALVIBRATION OF A HELICAL THINELASTIC ROD[J];Mechanics and Engineering;2004-06
【Secondary Citations】
Chinese Journal Full-text Database 2 Hits
1 Wu Jike, Huang Yonggang(Department of Mechanics, Peking University);THE STABILITY OF ELASTIC CURVED BARS[J];Acta Mechanica Sinica;1987-05
2 LIU Yanzhu(Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China);MECHANICAL PROBLEMS ON ELASTIC ROD MODEL OF DNA[J];Mechanics and Engineering;2003-01
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