【作者】 刘敬喜；

【导师】 刘土光； 李天匀；

【作者基本信息】 华中科技大学 ， 船舶与海洋结构物设计制造， 2006， 博士

【摘要】 对(黏)弹性介质中充液圆柱壳的自由振动特性、波的频散特性和动响应特性进行了理论分析和相关的实验研究,讨论了弹性介质参数、圆柱壳的几何参数、壳内流体对其动态特性的影响。研究成果可以为海底管道或地下管道的抗震设计及无损检测提供理论指导。本文的主要工作有如下几个方面:首先,建立了弹性介质中有限长充液圆柱壳的自由振动模型,结合壳体理论和弹性动力学运动方程,得到了弹性介质中充液圆柱壳的耦合特征方程。利用Muller三点迭代的方法对超越方程进行了求解。计算结果表明弹性介质刚度系数对圆柱壳的无量纲频率影响最大,随着弹性介质刚度系数的增大圆柱壳无量纲频率增大。壳内流体对弹性介质中圆柱壳的无量纲频率影响较小。其次,提出了求解复杂耦合系统频散特征方程的复平面围线积分方法。采用复平面围线积分方法可以得到频散特征方程所有的复根。弥补了以往传统方法(只能得到频散方程实数根)和近似处理方法(不能够在整个复平面求解所有的复数根)的不足。并对水下弹性薄壁圆柱壳频散特征方程的复根进行了解决。接着在前面分析的基础上,求解了弹性介质中充液圆柱壳的复杂耦合系统频散特征方程,得到了弹性介质中充液圆柱壳的传播波频散特性曲线和衰减波频散特性曲线。计算结果表明壳内流体对圆柱壳中的传播波数影响很大。弹性介质刚度系数对圆柱壳中传播波的起始频率有重要影响。管内流体在弹性介质刚度系数较小时与圆柱壳的耦合比较强烈,随着弹性介质刚度系数的增加流体与圆柱壳的耦合越来越弱。然后,对(黏)弹性介质中充液和无液圆柱壳在集中简谐力作用下的动响应进行了分析。计算结果揭示圆柱壳周围弹性介质的存在使得圆柱壳的位移响应比真空中圆柱壳或真空充液圆柱壳的位移响应小。随着弹性介质刚度系数的增大,位移响应逐渐减小。随着弹性介质刚度系数的增大,壳内流体对响应的影响逐渐减小。对于黏弹性介质,由于阻尼的影响,圆柱壳在中低频段的位移响应减小,峰值明显降低,响应曲线变得比较光滑。随着频率的增大,黏弹性介质的阻尼作用逐渐减小。最后,对黏弹性介质中充液圆柱壳在集中简谐载荷作用下的响应进行了定性的试验分析。从试验结果可以看出,由于土壤粘性的存在使得管道的响应随距离的增大衰减很快。高频信号的衰减速度比低频信号结构振动减速度较快。本文是国家自然科学基金资助项目“埋地供水管漏损的声信号特征及捡漏定位装置”(No 60002005)的部分内容。更多还原

【Abstract】 In this thesis, the waves’free vibration, dispersion and dynamic characteristics of fluid-filled cylindrical shells in infinite (visco)elastic medium are studied theoretically and experimentally. The effects of elastic medium, cylindrical shell’s geometry parameter and fluid in shells on the dynamic characteristics are discussed as well, and the results offers theory guidance for the anti-seismic design and non-destructive detection of seabed pipelines and underground pipelines. The major work of this paper is presented as follow. First, construct a free vibration analysis model of fluid-filled cylindrical shells; use theory of shell and equations of elastic-dynamics to derive the coupling equation of the model; and solve the transcendental equation by Muller root-finding method. Case studies show that the non-dimension have been more affected by rigidity of elastic medium, and the non-dimension frequencies of cylindrical shells increase with the rigidity ratio of elastic medium increasing, while fluid in shells has little effect to the non-dimension frequency of cylindrical shells.Secondly, the contour integration method in complex plane is put forward to solve the dispersion equation of complicated coupling system. All the complex roots of dispersion equation are derived by using the contour integration method in complex plane, which overcomes the shortcomings of traditional method which can only get the real root and approximate disposal method which can’t derived all the complex roots in the whole complex plane. The complex roots of dispersion equation of submerged cylindrical shells are solved out.Sequentially, based on the above analysis, the complicated coupling system dispersion equation of fluid-filled cylindrical shells in infinite elastic medium is resolved, and thus get the dispersion curves of free propagation waves and attenuating wave of fluid-filled cylindrical shells in infinite elastic medium. Case studies show that the numbers of propagation wave are more affected by the fluid in shells; original frequency of propagation waves are affected by the rigidity of elastic medium; when the rigidity of elastic medium is small, the coupling of fluid and structure is strong, and the coupling decreases with the increase of rigidity of elastic medium.Then, dynamic responses of both fluid-filled and empty cylindrical shells in viscoelastic are analyzed by concentrating harmonic load. Case studies show that displacement response of cylindrical shells in viscoelastic medium is smaller than fluid-filled cylindrical shells by concentrating harmonic force. The displacement response decreases with the increase of rigidity of elastic medium and with the increase of rigidity of elastic medium, the displacement response is less affected by fluid. Because of the damping of the viscoelastic medium, the displacement response of cylindrical shells surrounding by viscoelastic medium decrease in low and middle frequency bands; response peaks fall and the response curves become smooth, and the effects of damping of viscoelastic medium decreases with the increase of frequency,.Finally, dynamic response of fluid-filled cylindrical shells in viscoelastic is analyzed experimentally under concentrating harmonic load. The results show that displacement response attenuates with the increase of distance because of damping of soil. The speed of vibration decaying of high frequency signal is faster than low frequency signal.The work presented in this paper is part of the contents of the project”Acoustic Signal Characteristics of Leak by Buried Water Supply Pipelines and the Leak Detection Equipment”(No 60002005), which is supported by the National Natural Science Foundation of China.更多还原