研究两端弹性支承输流管道含圆周方向裂纹时的非线性动力学特性。首先,推导出裂纹管道的模态函数与局部柔度系数,然后运用Galerkin离散技术将管道运动方程在模态空间中展开,采用非线性动力学仿真方法得到管道系统响应随各参数变化的分岔图和最大Lyapunov指数图。数值结果表明,这种两端弹性支承的特殊边界裂纹管道在参数激励、自激励和外激励联合作用下,表现出丰富的非线性动力学特性,分别出现周期运动、概周期运动、阵发性混沌和混沌等多种响应形式。
Abstract
The nonlinear dynamical characteristics of a twoend elastically supported pipe with circular crack conveying fluid were studied. Firstly, the expressions of vertical vibration modal functions and the local flexibility coefficients of the cracked pipe were derived. Then, its equations of motion were discretized in the modal space with Galerkin method. Bifurcation diagrams and the maximum Lyapunov exponents of the pipe system responses versus various parameters were acquired by using the nonlinear dynamic simulation technique. The simulation results showed that the cracked piping system has abundant nonlinear dynamical characteristics; it exhibits multiple response forms, such as, periodic motion, quasiperiodic motion, intermittent chaos and chaotic motion and so on.
关键词
弹性支承 /
裂纹管道 /
非线性动力学特性 /
分岔 /
混沌
{{custom_keyword}} /
Key words
elastic supports /
cracked pipe /
non-linear dynamic characteristics /
bifurcation /
chaos
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 金基铎, 杨晓东, 尹峰. 两端铰支输流管道在脉动内流作用下的稳定性和参数共振[J]. 航空学报, 2003, 24(4): 317-322. JIN Ji-duo, YANG Xiao-dong, Yin feng. Stability and parametric resonances of a pinned-pinned pipe conveying pulsating fluid[J]. Chinese Journal of Aeronautics, 2003, 24(4): 317-322. (in Chinese)
[2] 梁峰, 杨晓东, 闻邦椿. 脉动流激励下输流管道参数共振IHB方法研究[J]. 振动与冲击, 2008, 27(9): 44-46. Liang Feng, Yang Xiao-dong, Wen Bung-chun. Analysis of parametric resonanaces for pipes conveying pulsating fluid with IHB method[J]. Journal of Vibration and Shock, 2008, 27(9): 44-46. (in Chinese)
[3] Panda L N, Kar R C. Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances[J]. Journal of Sound and Vibration, 2008, 309: 375-406.
[4] Wang L. A further study on the non-linear dynamics of simply supported pipes conveying pulsating fluid[J]. International Journal of Nonlinear Mechanics, 2009, 44:115-121.
[5] He Y, Ye J, Chen X, et al. Discussion on calculation of the local flexibility due to the crack in a pipe[J]. Mechanical Systems and Signal Processing, 2009, 23: 804-810.
[6] Yoon H I, Son I S. Dynamic behavior of cracked simply supported pipe conveying fluid with moving mass[J]. Journal of Sound and Vibration, 2006, 292: 941-953.
[7] 蔡逢春, 臧峰刚, 梁艳仙. 含裂纹两端铰支输流管道在振荡流作用下的非线性动力特性研究[J]. 振动与冲击, 2012, 31(4):162-167. Cai Feng-chun, Zang Feng-gang, Liang Yan-xian. Nonlinear dynamic behaviors of a cracked hinged-hinged pipe conveying pulsating fluid[J]. Journal of Vibration and Shock, 2012, 31(4): 162-167.
[8] 包日东, 金志浩, 闻邦椿. 端部约束悬臂输流管道的动力学特性[J]. 工程力学, 2009, 26(1): 209-215. Bao Ri-dong, Jin Zhi-hao, Wen Bang-chun. Dynamical behaviors of restrained cantilever pipe conveying fluid[J]. Engineering Mechanics, 2009, 26(1): 209-215. (in Chinese)
[9] 包日东, 金志浩, 闻邦椿. 端部约束悬臂输流管道的分岔与混沌响应[J]. 振动与冲击, 2008, 27(5): 36-39. Bao Ri-dong, Jin Zhi-hao, Wen Bang-chun. Bifurcation and chaotic response of restrained cantilever pipe with conveying fluid[J]. Journal of Vibration and Shock, 2008, 27(5): 36-39. (in Chinese)
[10] 包日东, 金志浩, 闻邦椿. 分析一般支承输流管道的非线性动力学特性[J]. 振动与冲击, 2008, 27(7): 87-90. Bao Ri-dong, Jin Zhi-hao, Wen Bang-chun. Analysis of nonlinear dynamic characteristics of commonly supported fluid conveying pipe[J]. Journal of Vibration and Shock, 2008, 27(7): 87-90. (in Chinese)
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}