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This paper focuses on the response in parametrically excited systems caused by constant excitation. Taking a maneuvering cracked rotor system as an example, we formulate the vibration equations with two degrees of freedom, in which the breathing of the crack constitutes parametric excitation, and the maneuver load of the maneuvering rotor is simplified as a constant excitation, and it is supposed that the rotor system is balanced without the consideration of eccentricity. By solving the equations with harmonic balance method, each order of harmonic components related with the rotating speed and the constant excitation is derived to analyze the corresponding resonance of the system. Results show that the constant excitation plays a decisive role in the parametrically excited primary and super-harmonic resonances of the system that agrees with the gravity dominance in common cracked rotor systems without maneuver load. And the stronger the constant excitation, the greater the resonances. Moreover, the orientation of the constant excitation makes a great impact on the parametrically excited primary resonance, but does not have a significant effect on the parametrically excited super-harmonic resonances. Results implies that constant excitation may increase the parametrically excited super-harmonic resonances of the cracked rotor systems, which is disadvantageous to the operating of the system. From another point of view, however, constant excitation can be used for early detection of crack faults in rotor systems.
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Keywords:
- parametrically excited system with two degrees of freedom /
- constant excitation /
- cracked rotor system /
- maneuver load
[1] Ji J C, Chen Y S 1997 J. Vib. Eng. 10 491 (in Chinese)[季进臣, 陈予恕 1997 振动工程学报 10 491]
[2] Xiao X W, Xiao G H, Yang S Z 2002 J. Vib. Eng. 15 315 (in Chinese) [肖锡武, 肖光华, 杨叔子 2002 振动工程学报 15 315]
[3] Ying Z G, Chen Z H, Ni Y Q, Gao Z M 2007 Chinese J. Comput. Mech. 24 678 (in Chinese) [应祖光, 陈昭晖, 倪一清, 高赞明 2007 计算力学学报 24 678]
[4] Wei K X, Meng G 2008 Chinese J. Theor. Appl. Mech. 40 273 (in Chinese) [魏克湘, 孟光 2008 力学学报 40 273]
[5] Shi P M, Li J Z, Liu B, Han D Y 2011 Acta Phys. Sin. 60 094501 (in Chinese) [时培明, 李纪召, 刘彬, 韩东颖 2011 物理学报 60 094501]
[6] Zhu W Q 1990 Appl. Math. Mech. 11 155 (in Chinese) [朱位秋 1990 应用数学和力学 11 155]
[7] Xie W X, Xu W, Lei Y M, Cai L 2005 Acta Phys. Sin. 54 1105 (in Chinese)[谢文贤, 徐伟, 雷佑铭, 蔡力 2005 物理学报 54 1105]
[8] Niu Y J, Xu W, Rong H W, Wang L, Feng J Q 2009 Acta Phys. Sin. 58 2983 (in Chinese) [牛玉俊, 徐伟, 戎海武, 王亮, 冯进钤 2009 物理学报 58 2983]
[9] Tu Z, Peng H, Wang F, Ma H 2013 Acta Phys. Sin. 62 030502 (in Chinese) [屠浙, 彭皓, 王飞, 马洪 2013 物理学报 62 030502]
[10] Zhang Y Q, Chen J J, Tang L D, Lin L G 2009 J. Mech. Strength 31 871 (in Chinese) [张耀强, 陈建军, 唐六丁, 林立广 2009 机械强度 31 871]
[11] Chen G 2007 China Mech. Eng. 18 2773 (in Chinese)[陈果 2007 中国机械工程 18 2773]
[12] Bai C Q, Xu Q Y, Zhang X L 2006 Appl. Math. Mech. 27 159 (in Chinese)[白长青, 许庆余, 张小龙 2006 应用数学和力学 27 159]
[13] Yang J D, Xu P M, Wen B C 2002 Acta Mech. Solida Sin. 23 115 (in Chinese)[杨积东, 徐培民, 闻邦椿 2002 固体力学学报 23 115]
[14] Yang J D, Xu P M, Wen B C 2002 Chinese J. Appl. Mech. 19 10 (in Chinese)[杨积东, 徐培民, 闻邦椿 2002 应用力学学报 19 10]
[15] Leng X L, Meng G, Zhang T, Fang T 2006 J. Vib. Eng. 19 212 (in Chinese)[冷小磊, 孟光, 张韬, 方同 2006 振动工程学报 19 212]
[16] Lin F S, Meng G 2002 J. Mech. Strength 24 320 (in Chinese)[林富生, 孟光 2002 机械强度 24 320]
[17] Zhu C S, Chen Y J 2006 Acta Aeronaut. Astronaut. Sin. 27 835 (in Chinese) [祝长生, 陈拥军 2006 航空学报 27 835]
[18] Wei H T, Fan X M 2001 Tenth Conference of the structural strength and vibration of aero-engine Anhui, China, October 1, 2000 p315 (in Chinese) [魏海涛, 范晓明 2001中国航空学会第十届航空发动机结构强度与振动会议论文集 2000 p315]
[19] Xu M, Liao M F, Liu Q Z 2002 J. Aerospace Power 17 105 (in Chinese) [徐敏, 廖明夫, 刘启洲 2002 航空动力学报 17 105]
[20] Yang Y F, Ren X M, Qin W Y 2007 J. Aerospace Power 22 1007 (in Chinese) [杨永锋, 任兴民, 秦卫阳 2007 航空动力学报 22 1007]
[21] Yu Y B 2009 Master Thesis (Xi'an: Xi'an Technological University) (in Chinese) [于渊博 2009 硕士学位论文(西安: 西安工业大学)]
[22] Hou L, Chen Y S, Cao Q J 2014 Commun. Nonlinear Sci. Numer. Simul. 19 286
[23] Hou L, Chen Y S 2014 Sci. China Technol. Sc. 57 203
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[1] Ji J C, Chen Y S 1997 J. Vib. Eng. 10 491 (in Chinese)[季进臣, 陈予恕 1997 振动工程学报 10 491]
[2] Xiao X W, Xiao G H, Yang S Z 2002 J. Vib. Eng. 15 315 (in Chinese) [肖锡武, 肖光华, 杨叔子 2002 振动工程学报 15 315]
[3] Ying Z G, Chen Z H, Ni Y Q, Gao Z M 2007 Chinese J. Comput. Mech. 24 678 (in Chinese) [应祖光, 陈昭晖, 倪一清, 高赞明 2007 计算力学学报 24 678]
[4] Wei K X, Meng G 2008 Chinese J. Theor. Appl. Mech. 40 273 (in Chinese) [魏克湘, 孟光 2008 力学学报 40 273]
[5] Shi P M, Li J Z, Liu B, Han D Y 2011 Acta Phys. Sin. 60 094501 (in Chinese) [时培明, 李纪召, 刘彬, 韩东颖 2011 物理学报 60 094501]
[6] Zhu W Q 1990 Appl. Math. Mech. 11 155 (in Chinese) [朱位秋 1990 应用数学和力学 11 155]
[7] Xie W X, Xu W, Lei Y M, Cai L 2005 Acta Phys. Sin. 54 1105 (in Chinese)[谢文贤, 徐伟, 雷佑铭, 蔡力 2005 物理学报 54 1105]
[8] Niu Y J, Xu W, Rong H W, Wang L, Feng J Q 2009 Acta Phys. Sin. 58 2983 (in Chinese) [牛玉俊, 徐伟, 戎海武, 王亮, 冯进钤 2009 物理学报 58 2983]
[9] Tu Z, Peng H, Wang F, Ma H 2013 Acta Phys. Sin. 62 030502 (in Chinese) [屠浙, 彭皓, 王飞, 马洪 2013 物理学报 62 030502]
[10] Zhang Y Q, Chen J J, Tang L D, Lin L G 2009 J. Mech. Strength 31 871 (in Chinese) [张耀强, 陈建军, 唐六丁, 林立广 2009 机械强度 31 871]
[11] Chen G 2007 China Mech. Eng. 18 2773 (in Chinese)[陈果 2007 中国机械工程 18 2773]
[12] Bai C Q, Xu Q Y, Zhang X L 2006 Appl. Math. Mech. 27 159 (in Chinese)[白长青, 许庆余, 张小龙 2006 应用数学和力学 27 159]
[13] Yang J D, Xu P M, Wen B C 2002 Acta Mech. Solida Sin. 23 115 (in Chinese)[杨积东, 徐培民, 闻邦椿 2002 固体力学学报 23 115]
[14] Yang J D, Xu P M, Wen B C 2002 Chinese J. Appl. Mech. 19 10 (in Chinese)[杨积东, 徐培民, 闻邦椿 2002 应用力学学报 19 10]
[15] Leng X L, Meng G, Zhang T, Fang T 2006 J. Vib. Eng. 19 212 (in Chinese)[冷小磊, 孟光, 张韬, 方同 2006 振动工程学报 19 212]
[16] Lin F S, Meng G 2002 J. Mech. Strength 24 320 (in Chinese)[林富生, 孟光 2002 机械强度 24 320]
[17] Zhu C S, Chen Y J 2006 Acta Aeronaut. Astronaut. Sin. 27 835 (in Chinese) [祝长生, 陈拥军 2006 航空学报 27 835]
[18] Wei H T, Fan X M 2001 Tenth Conference of the structural strength and vibration of aero-engine Anhui, China, October 1, 2000 p315 (in Chinese) [魏海涛, 范晓明 2001中国航空学会第十届航空发动机结构强度与振动会议论文集 2000 p315]
[19] Xu M, Liao M F, Liu Q Z 2002 J. Aerospace Power 17 105 (in Chinese) [徐敏, 廖明夫, 刘启洲 2002 航空动力学报 17 105]
[20] Yang Y F, Ren X M, Qin W Y 2007 J. Aerospace Power 22 1007 (in Chinese) [杨永锋, 任兴民, 秦卫阳 2007 航空动力学报 22 1007]
[21] Yu Y B 2009 Master Thesis (Xi'an: Xi'an Technological University) (in Chinese) [于渊博 2009 硕士学位论文(西安: 西安工业大学)]
[22] Hou L, Chen Y S, Cao Q J 2014 Commun. Nonlinear Sci. Numer. Simul. 19 286
[23] Hou L, Chen Y S 2014 Sci. China Technol. Sc. 57 203
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