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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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