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A theoretical model of transverse vibration of highline cable of alongside replenishment system was established, which considers the influence of the concentrated loading. The partial differential equation was asymptotically analysed by Galerkin method and muti-scale method. The bifurcation equation of system with higher order nonlinear terms was obtained by the solvability condition of eliminating the secular terms. Local bifurcation behavior of highline cable was studied with the software Mathematica. Bifurcation models and transition sets of system were obtained. The result shows that there are many kinds of bifurcation behaviors in highline cable of alongside replenishment system.
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Keywords:
- bifurcation /
- highline cable /
- stability /
- multi-scale method
[1] ［1］LU Y J 1996 Shipbuliding of China 37 17 (in Chinese) ［卢永锦 1996 中国造船 37 17］
[2] ［2］He X J, Zhang L X, Ren A D 2009 Journal of Naval University of Engineering 21 52 (in Chinese) ［何学军、张良欣、任爱娣 2009 海军工程大学学报 21 52］
[3] ［3］Rega G 2004 Am. Soc. Mech. Eng. 57 443
[4] ［4］Srinil N, Rega G 2007 Int. J. Nonlinear Mech. 42 180
[5] ［5］Zhao Y Y, Wang L H 2006 J. Sound Vib. 4-5 1073
[6] ［6］Wang L H, Zhao Y Y 2006 Acta Mech. Solida Sin. 27 230 (in Chinese) ［王连华、赵跃宇 2006 固体力学学报 27 230］
[7] ［7］Chen Z L, Tang J S, Den M Y 2006 Noise and Vibration Control 26 41(in Chinese) ［陈自力、唐驾时、邓旻涯 2006 噪声与振动控制 26 41］
[8] ［8］Chen Z L 2006 Ph.D. dissertation (Changsha: Hunan University (in Chinese) ［陈自力 2006 博士学位论文 (长沙：湖南大学)］
[9] ［9］Ilin R F, Karyachenko N V 2007 Int. Appl. Mech. 43 101
[10] ］Sun X J, Xu W, Ma S J 2006 Acta Phys. Sin. 55 610(in Chinese) ［孙晓娟、徐伟、马少娟 2006 55 610］
[11] ］Zhang Q C, Wang W, He X J 2008 Acta Phys. Sin. 57 5384 (in Chinese) ［张琪昌、王炜、何学军 2008 57 5384］
[12] ］Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431(in Chinese) ［季颖、毕勤胜 2009 58 4431］
[13] ］Nayfeh A H, Mook D T 1979 Nonlinear oscillations (New York: John Wiley and Sons)
[14] ］Lu Q S 1995 Bifurcation and singularity ( Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) p67 ［陆启韶 1995 分岔与奇异性 (上海：上海科技教育出版社) 第67页］
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[1] ［1］LU Y J 1996 Shipbuliding of China 37 17 (in Chinese) ［卢永锦 1996 中国造船 37 17］
[2] ［2］He X J, Zhang L X, Ren A D 2009 Journal of Naval University of Engineering 21 52 (in Chinese) ［何学军、张良欣、任爱娣 2009 海军工程大学学报 21 52］
[3] ［3］Rega G 2004 Am. Soc. Mech. Eng. 57 443
[4] ［4］Srinil N, Rega G 2007 Int. J. Nonlinear Mech. 42 180
[5] ［5］Zhao Y Y, Wang L H 2006 J. Sound Vib. 4-5 1073
[6] ［6］Wang L H, Zhao Y Y 2006 Acta Mech. Solida Sin. 27 230 (in Chinese) ［王连华、赵跃宇 2006 固体力学学报 27 230］
[7] ［7］Chen Z L, Tang J S, Den M Y 2006 Noise and Vibration Control 26 41(in Chinese) ［陈自力、唐驾时、邓旻涯 2006 噪声与振动控制 26 41］
[8] ［8］Chen Z L 2006 Ph.D. dissertation (Changsha: Hunan University (in Chinese) ［陈自力 2006 博士学位论文 (长沙：湖南大学)］
[9] ［9］Ilin R F, Karyachenko N V 2007 Int. Appl. Mech. 43 101
[10] ］Sun X J, Xu W, Ma S J 2006 Acta Phys. Sin. 55 610(in Chinese) ［孙晓娟、徐伟、马少娟 2006 55 610］
[11] ］Zhang Q C, Wang W, He X J 2008 Acta Phys. Sin. 57 5384 (in Chinese) ［张琪昌、王炜、何学军 2008 57 5384］
[12] ］Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431(in Chinese) ［季颖、毕勤胜 2009 58 4431］
[13] ］Nayfeh A H, Mook D T 1979 Nonlinear oscillations (New York: John Wiley and Sons)
[14] ］Lu Q S 1995 Bifurcation and singularity ( Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) p67 ［陆启韶 1995 分岔与奇异性 (上海：上海科技教育出版社) 第67页］
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