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对固结于旋转刚环上内接柔性梁的刚柔耦合动力学特性进行了研究. 在精确描述柔性梁非线性变形基础上, 利用Hamilton变分原理和假设模态法, 在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下, 推导出一次近似耦合模型. 忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量, 对简化模型做无量纲化处理. 首先分析在非惯性系下内接悬臂梁的动力学响应, 并与外接悬臂梁进行比较; 其次研究内接悬臂梁的稳定性;最后分析内接悬臂梁失稳临界转速的收敛性. 研究发现, 与外接悬臂梁存在动力刚化效应不同,内接悬臂梁存在着动力柔化效应; 给出了内接悬臂梁无条件稳定的临界径长比以及失稳的临界转速的计算方法; 若第一阶固有频率随转速增大而减小,则该内接悬臂梁处于有条件稳定; 随着模态截断数的增加,内接悬臂梁失稳的临界转速减小且有收敛值.The rigid-flexible coupling dynamic properties of an internal cantilever beam attached to a rotating hub are studied in this paper. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model is derived from Hamilton theory and assumed mode method, taking into account the second-order coupling quantity of axial displacement caused by transverse displacement of the beam. The simplified first-order approximation coupling model which neglects the effect of axial deformation of a beam is presented. The simplified model is transformed into dimensionless form in which dimensionless parameters are identified. Firstly, the dynamic response of an internal cantilever beam is compared with that of an external cantilever beam, which are both in non-inertia system. Then, the stability of an internal cantilever beam is analyzed. Finally, the convergence of critical rotating speed of an internal cantilever beam is analyzed. Generally, it is pointed that an internal cantilever beam has a dynamic softening phenomenon, which is different from the dynamic stiffening phenomenon of an external cantilever beam. The critical ratio of the internal radius to the length of the beam for unconditional stability and the critical rotating speed of conditional stability of an internal cantilever beam are derived. When the first natural frequency decreases as the rotating speed increases, the dynamic system of the internal cantilever beam is conditionally stable. As the number of modes increases, the critical rotating speed of an internal cantilever beam decreases, and it has a convergent value.
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Keywords:
- internal cantilever beam /
- first-order approximation simplified model /
- dynamic softening /
- critical rotating speed
[1] Kane T R, Ryan R R, Banerjee A K 1987 J. Guid. Contr. Dyn. 10 2
[2] Zhang D J, Huston R L 1996 Mech. Struct. Mach. 24 3
[3] Liu J Y, Hong J Z 2004 J. Sound Vib. 278 1147
[4] Wu S B, Zhang D G 2011 J. Vib. Eng. 24 1 (in Chinese) [吴胜宝, 章定国 2011 振动工程学报 24 1]
[5] He X S, Yan Y H, Deng F Y 2012 Acta Phys. Sin. 61 024501 (in Chinese) [和兴锁, 闫业毫, 邓峰岩 2012 物理学报 61 024501]
[6] Southwell R, Gough F 1921 British A. R. C. Rep. Memo. 766
[7] Putter S, Manor H 1978 J. Sound Vib. 56 175
[8] Yoo H H, Shin S H 1998 J. Sound Vib. 212 5
[9] He X S, Song M, Deng F Y 2011 Acta Phys. Sin. 60 044501 (in Chinese) [和兴锁, 宋明, 邓峰岩 2011 物理学报 60 044501]
[10] Chen S J, Zhang D G 2011 Chin. J. Theo. Appl. Mech. 43 4 (in Chinese) [陈思佳, 章定国 2011 力学学报 43 4]
[11] Xiao S F, Chen B 1997 Sci. China A 29 10 (in Chinese) [肖世富, 陈滨 1997 中国科学 (A辑) 29 10]
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[1] Kane T R, Ryan R R, Banerjee A K 1987 J. Guid. Contr. Dyn. 10 2
[2] Zhang D J, Huston R L 1996 Mech. Struct. Mach. 24 3
[3] Liu J Y, Hong J Z 2004 J. Sound Vib. 278 1147
[4] Wu S B, Zhang D G 2011 J. Vib. Eng. 24 1 (in Chinese) [吴胜宝, 章定国 2011 振动工程学报 24 1]
[5] He X S, Yan Y H, Deng F Y 2012 Acta Phys. Sin. 61 024501 (in Chinese) [和兴锁, 闫业毫, 邓峰岩 2012 物理学报 61 024501]
[6] Southwell R, Gough F 1921 British A. R. C. Rep. Memo. 766
[7] Putter S, Manor H 1978 J. Sound Vib. 56 175
[8] Yoo H H, Shin S H 1998 J. Sound Vib. 212 5
[9] He X S, Song M, Deng F Y 2011 Acta Phys. Sin. 60 044501 (in Chinese) [和兴锁, 宋明, 邓峰岩 2011 物理学报 60 044501]
[10] Chen S J, Zhang D G 2011 Chin. J. Theo. Appl. Mech. 43 4 (in Chinese) [陈思佳, 章定国 2011 力学学报 43 4]
[11] Xiao S F, Chen B 1997 Sci. China A 29 10 (in Chinese) [肖世富, 陈滨 1997 中国科学 (A辑) 29 10]
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