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The line spectrum characteristics of the radiated waterborne noises of an underwater vehicle can be reconstructed using the technique of chaotification, which can improve the acoustic stealth of the underwater vehicle. According to the particular application background, in this paper we study the chaotification issue with nonlinear time-delay feedback control for a double-layer vibration isolation floating raft system under multi-source excitation. From a simplified two-dimensional floating raft system model, a chaotification method with nonlinear time-delay feedback control is presented completely. It provides a standard procedure for line spectrum chaotification design. Numerical simulation results show the feasibility of this method. Under multi-source excitation, the effects of the control gain, time-delay and feedback frequency parameters on chaotification are investigated, and discussion is also extended to the case of the single-source excitation.
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Keywords:
- multi-source excitation /
- vibration isolation floating raft /
- nonlinear time-delay feedback control /
- chaotification
[1] Hasler M 1995 Phil. Trans. R. Soc. A 353 115
[2] Chen G R, Mao Y B, Chui C K 2004 Chaos, Soliton. Fract. 21 749
[3] Qi G Y, Sandra B M 2014 Chin. Phys. B 23 50507
[4] Freeman W J 1995 Int. J. Intell. Syst. 10 71
[5] Sharma A, Gupte N 1997 Pramana-J. Phys. 48 231
[6] Yang R, Zhang B 2007 Acta Phys. Sin. 56 3789(in Chinese)[杨汝, 张波 2007 56 3789]
[7] Zhang L S, Cai L, Feng C W 2011 Acta Phys. Sin. 60 060306(in Chinese)[张立森, 蔡理, 冯朝文 2011 60 060306]
[8] Liu S, Chen L Q 2013 Chin. Phys. B 22 100506
[9] Lou J J, Zhu S J, He L, Yu X 2005 J. Sound Vib. 286 645
[10] Yu X, Zhu S J, Liu S Y 2007 J. Sound Vib. 306 835
[11] Liu S Y, Yu X, Zhu S J 2008 J. Sound Vib. 310 855
[12] Lou J J, Zhu S J, He L, He Q W 2009 Chaos, Soliton. Fract. 40 1367
[13] Wen G L, Lu Y Z, Zhang Z Y, Ma C S, Yin H F, Cui Z 2009 J. Sound Vib. 324 954
[14] Ikeda K, Matsumoto K 1987 Physica D 29 223
[15] Celka P 1997 Physica D 104 127
[16] Li Y L, Xu D L, Fu Y M, Zhou J X 2011 Chaos 21 033115
[17] Li Y L, Xu D L, Fu Y M, Zhou J X 2012 Chaos, Soliton. Fract. 45 1092
[18] Wang X F, Chen G R, Yu X H 2000 Chaos 10 771
[19] Wang X F 2003 Chaos Control: Theory and Applications (Berlin:Springer) pp 179-204
[20] Zhang J, Xu D L, Zhou J X, Li Y L 2012 Chaos, Soliton. Fract. 45 1255
[21] Lou J J, He Q W, Zhu S J 2004 Appl. Math. Mech. 25 1299(in Chinese)[楼京俊, 何其伟, 朱石坚 2004 应用数学和力学 25 1299]
[22] Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431(in Chinese)[季颖, 毕勤胜 2009 58 4431]
[23] Yang D S, Dong L, Shi J, Lan C F 2011 J. Vib. Shock 30 19(in Chinese)[杨德森, 董雷, 时洁, 兰朝凤 2011 振动与冲击 30 19]
[24] Yan S, Sheng M P, Chen X L 2006 Noise Vib. Control 26(4) 26(in Chinese)[颜松, 盛美萍, 陈晓利 2006 噪声与振动控制 26(4) 26]
[25] Lu Q, Mei S W, Sun Y Z 2008 Nonlinear Control of Power Systems (Beijing: Tsinghua University Press) pp24-85 (in Chinese)[卢强, 梅生伟, 孙元章 2008 电力系统非线性控制 (北京: 清华大学出版社) 第24-85页]
[26] Chen G R, Wang X F 2006 Chaotification of Dynamical Systems-Theory, Methods and Applications (Shanghai: Shanghai Jiao Tong University Press) pp111-136 (in Chinese)[陈关荣, 汪小帆 2006 动力系 统的混沌化-理论、方法及应用(上海: 上海交通大学出版社)第111-136页]
[27] Yang Q C, Zhu S J, Lou J J, Wu H P 2013 J. Theor. Appl. Inf. Technol. 48 429
[28] Yang Q C, Lou J J, Liu S Y, Diao A M 2013 Telkomnika 11 63
[29] Zhou J X, Xu D L, Zhang J, Liu C R 2012 Chaos, Soliton. Fract. 45 815
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[1] Hasler M 1995 Phil. Trans. R. Soc. A 353 115
[2] Chen G R, Mao Y B, Chui C K 2004 Chaos, Soliton. Fract. 21 749
[3] Qi G Y, Sandra B M 2014 Chin. Phys. B 23 50507
[4] Freeman W J 1995 Int. J. Intell. Syst. 10 71
[5] Sharma A, Gupte N 1997 Pramana-J. Phys. 48 231
[6] Yang R, Zhang B 2007 Acta Phys. Sin. 56 3789(in Chinese)[杨汝, 张波 2007 56 3789]
[7] Zhang L S, Cai L, Feng C W 2011 Acta Phys. Sin. 60 060306(in Chinese)[张立森, 蔡理, 冯朝文 2011 60 060306]
[8] Liu S, Chen L Q 2013 Chin. Phys. B 22 100506
[9] Lou J J, Zhu S J, He L, Yu X 2005 J. Sound Vib. 286 645
[10] Yu X, Zhu S J, Liu S Y 2007 J. Sound Vib. 306 835
[11] Liu S Y, Yu X, Zhu S J 2008 J. Sound Vib. 310 855
[12] Lou J J, Zhu S J, He L, He Q W 2009 Chaos, Soliton. Fract. 40 1367
[13] Wen G L, Lu Y Z, Zhang Z Y, Ma C S, Yin H F, Cui Z 2009 J. Sound Vib. 324 954
[14] Ikeda K, Matsumoto K 1987 Physica D 29 223
[15] Celka P 1997 Physica D 104 127
[16] Li Y L, Xu D L, Fu Y M, Zhou J X 2011 Chaos 21 033115
[17] Li Y L, Xu D L, Fu Y M, Zhou J X 2012 Chaos, Soliton. Fract. 45 1092
[18] Wang X F, Chen G R, Yu X H 2000 Chaos 10 771
[19] Wang X F 2003 Chaos Control: Theory and Applications (Berlin:Springer) pp 179-204
[20] Zhang J, Xu D L, Zhou J X, Li Y L 2012 Chaos, Soliton. Fract. 45 1255
[21] Lou J J, He Q W, Zhu S J 2004 Appl. Math. Mech. 25 1299(in Chinese)[楼京俊, 何其伟, 朱石坚 2004 应用数学和力学 25 1299]
[22] Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431(in Chinese)[季颖, 毕勤胜 2009 58 4431]
[23] Yang D S, Dong L, Shi J, Lan C F 2011 J. Vib. Shock 30 19(in Chinese)[杨德森, 董雷, 时洁, 兰朝凤 2011 振动与冲击 30 19]
[24] Yan S, Sheng M P, Chen X L 2006 Noise Vib. Control 26(4) 26(in Chinese)[颜松, 盛美萍, 陈晓利 2006 噪声与振动控制 26(4) 26]
[25] Lu Q, Mei S W, Sun Y Z 2008 Nonlinear Control of Power Systems (Beijing: Tsinghua University Press) pp24-85 (in Chinese)[卢强, 梅生伟, 孙元章 2008 电力系统非线性控制 (北京: 清华大学出版社) 第24-85页]
[26] Chen G R, Wang X F 2006 Chaotification of Dynamical Systems-Theory, Methods and Applications (Shanghai: Shanghai Jiao Tong University Press) pp111-136 (in Chinese)[陈关荣, 汪小帆 2006 动力系 统的混沌化-理论、方法及应用(上海: 上海交通大学出版社)第111-136页]
[27] Yang Q C, Zhu S J, Lou J J, Wu H P 2013 J. Theor. Appl. Inf. Technol. 48 429
[28] Yang Q C, Lou J J, Liu S Y, Diao A M 2013 Telkomnika 11 63
[29] Zhou J X, Xu D L, Zhang J, Liu C R 2012 Chaos, Soliton. Fract. 45 815
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