| THE STABILITY OF AN AXIALLY ACCELERATING BEAM ON SIMPLE SUPPORTS WITH TORSION SPRINGS |
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| 作者姓名： | Yang Xiaodong Chen Liqun |
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| 作者单位： | [1]Department of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang 110034, China [2]Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China [3]Department of Mechanics, Shanghai University, Shanghai 200436, China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （No. 10472060） and Natural Science Foundation of Shanghai Municipality （No. 04ZR14058）. |
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| 摘 要： | The axially moving beams on simple supports with torsion springs are studied. The general modal functions of the axially moving beam with constant speed have been obtained from the supporting conditions. The contribution of the spring stiffness to the natural frequencies has been numerically investigated. Transverse stability is also studied for axially moving beams on simple supports with torsion springs. The method of multiple scales is applied to the partialdifferential equation governing the transverse parametric vibration. The stability boundary is derived from the solvability condition. Instability occurs if the axial speed fluctuation frequency is close to the sum of any two natural frequencies or is two fold natural frequency of the unperturbed system. It can be concluded that the spring stiffness makes both the natural frequencies and the instability regions smaller in the axial speed fluctuation frequency-amplitude plane for given mean axial speed and bending stiffness of the beam.
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| 关 键 词： | 轴向移动梁 自然频率 多重刻度法 稳定性 扭转弹簧 |
| 收稿时间： | 2004-11-04 |
| 修稿时间： | 2005-03-29 |
THE STABILITY OF AN AXIALLY ACCELERATING BEAM ON SIMPLE SUPPORTS WITH TORSION SPRINGS |
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| Yang Xiaodong Chen Liqun.THE STABILITY OF AN AXIALLY ACCELERATING BEAM ON SIMPLE SUPPORTS WITH TORSION SPRINGS[J].Acta Mechanica Solida Sinica,2005,18(4):340-347. |
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| Authors: | Yang;Xiaodong;Chen;Liqun |
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| Abstract: | The axially rnoving beams on simple supports with torsion springs are studied. The general modal functions of the axially moving beam with constant speed have been obtained from the supporting conditions. The contribution of the spring stiffness to the natural frequencies has been numerically investigated. Transverse stability is also studied for axially moving beams on simple supports with torsion springs. The method of multiple scales is applied to the partialdifferential equation governing the transverse parametric vibration. The stability boundary is derived from the solvability condition. Instability occurs if the axial speed fluctuation frequency is close to the sum of any two natural frequencies or is two fold natural frequency of the unperturbed system. It can be concluded that the spring stiffness makes both the natural frequencies and the instability regions smaller in the axial speed fluctuation frequency-amplitude plane for given mean axial speed and bending stiffness of the beam. |
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| Keywords: | axially moving beam natural frequency method of multiple scales |
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