| 方孟孟,郭长青.分布随从力作用下双参数非线性弹性地基上简支输流管道的参激振动[J].南华大学学报(自然科学版),2019,33(3):69~77.[FANG Mengmeng,GUO Changqing.Parametric Vibration of Simply Supported Pipes Conveying Fluid on Two-parameter Nonlinear Elastic Foundation with Distributed Follower Force[J].Journal of University of South China(Science and Technology),2019,33(3):69~77.] |
| 分布随从力作用下双参数非线性弹性地基上简支输流管道的参激振动 |
| Parametric Vibration of Simply Supported Pipes Conveying Fluid on Two-parameter Nonlinear Elastic Foundation with Distributed Follower Force |
| 投稿时间：2018-11-01 |
| DOI： |
| 中文关键词: 简支输流管道 非线性弹性地基 分布随从力 周期运动 混沌运动 分岔 |
| 英文关键词:simply supported pipes conveying fluid nonlinear elastic foundation distributed follower force period motion chaotic motion bifurcation |
| 基金项目:国家自然科学基金项目(51678286) |
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| 摘要点击次数: 756 |
| 全文下载次数: 431 |
| 中文摘要: |
| 建立了非线性Pasternak地基上分布随从力作用下输流管道在振荡流作用下的运动方程,采用Galerkin法将系统的偏微分方程离散为常微分方程组。计算了简支输流管道的非线性动力响应,并利用分岔图、相平面图、Poincare映射图,分析了分布随从力、平均流速、地基剪切刚度对系统周期运动和混沌运动的影响。结果表明:以分布随从力为分岔参数,系统交替出现混沌运动和周期运动;以平均流速为分岔参数,系统具有非常复杂的动态响应,出现大范围的混沌运动和倍周期运动;增大地基剪切刚度不仅可以增加系统的稳定性,同时还对混沌运动有抑制作用;随着随从力增大,系统的稳定性下降。 |
| 英文摘要: |
| The equation of motion of pipes conveying pulsating fluid on a nonlinear Pasternak foundation with distributed follower force is established.The partial differential equation of the system is discretized into ordinary differential equations by using Galerkin method.For simply supported pipes,the nonlinear dynamic responses are obtained numerically.The effects of distributed follower force,mean velocity of the fluid and shear stiffness of the foundation on periodic motion and chaotic motion of the system are analyzed with bifurcation diagrams,phase plane and Poincare map.The results show that:with the distributed follower force as bifurcation parameter,chaotic motion and periodic motion appear alternately;with the mean velocity of fluid as bifurcation parameter,the dynamic responses are very complex,including large-range chaotic motion and multi-periodic motion;increasing the shear stiffness of the foundation can not only increase the stability of the system,but also suppress the chaotic motion;the stability of the system decreases with increasing follower force. |
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