输流管道横向振动机理及其控制研究
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摘要
输流管道在航空航天工程、水利工程、石油化工、农业及人们日常生活中都有着广泛应用。由于流固耦合的作用,当管道内流体的流速较高或其发生脉动时,常常会引起管道的强烈振动,严重时会导致管道破裂损毁而造成无法估计的损失。为了使管道能够安全稳定地在各行业中发挥作用,就需要对其振动机理及如何控制振动进行深入研究。
本文首先分析了输流管道流固耦合振动问题的研究现状,然后采用理论结合实验的方法对输流管道的稳定性、参数共振、具有内共振的强迫振动以及振动控制等问题展开研究,结论可为工程中管道的稳定性分析和危害评估提供必要的理论依据,也为管道振动的可行性控制奠定了理论基础。全文主要研究内容包括:
(1)建立了输流管道系统的力学模型,利用牛顿法推导了管道横向非线性振动微分方程,并进行了无量纲化和离散化,得到了最简形式的运动微分方程。
(2)对两端支承及弹性地基上管道系统的静态和动态稳定性进行了分析。利用Galerkin离散法和复模态方法计算了系统的固有频率和临界流速,并应用平均法得到了脉动内流作用时管道的前两阶主参数共振和组合共振区域,讨论了地基的线性刚度、剪切刚度及其它一些参数对系统稳定性的影响。研究发现,系统的固有频率和稳定性将随流速的增大而降低;地基的剪切刚度对系统稳定性的影响相当显著,不能忽略;同时管道预紧力、流体介质与管道质量比、粘弹性系数和管内介质平均流速等参数也会对系统的稳定性产生一定的影响。
(3)利用增量谐波平衡法对管道非线性运动方程进行求解,并用数值方法对结果进行了验证。根据方程解的情况分析了脉动流作用下管道系统的动态响应特性。结果表明,增量谐波平衡法是求解非线性振动问题的精确有效的半解析半数值方法;随着脉动流频率的增大,系统响应振幅的解会出现分岔情况,导致系统可能出现零响应,稳定响应,或零响应、稳定、不稳定响应共存的情况;系统发生第几阶参数共振,第几阶模态就对响应起主要作用,而其它模态的影响很微弱。
(4)利用多元L-P法和增量谐波平衡法对两端铰支和两端固定管道具有内共振的横向强迫振动进行研究,并对两种方法的结果进行比较分析。讨论了前两阶主共振和组合共振响应情况及内共振与外激励幅值的关系,并分析了各模态的振动情况。研究发现,在系统第2阶固有频率约为第1阶固有频率3倍的情况下,当外激励频率接近前两阶固有频率或其和的一半时,系统将发生内部共振,两个模态相互激励。但某些内共振的发生取决于外激励幅值的大小。
(5)采用陶瓷压电片作为控制激励器和模态传感器,根据最优控制方案对弹性地基上脉动流管道的参数共振实施了主动控制,并分析了控制参数对控制效果的影响。数值模拟结果表明,本文设计的最优控制器可使管道的各种参数共振均得到较好的控制,同时还具备一定的抗参数扰动能力。
(6)对脉动流作用下输流管道的动态稳定性进行了实验研究。建立了输流管道实验系统,给出了一些关键参数的有效测量方法,并对两种管道的第一阶1/2次谐波参数共振进行了重点观察与分析,用实验的方法确定了相应的参数共振区域。将其与理论共振区域进行对比,结果在定性上吻合得比较好。同时对误差产生的原因进行了讨论。
Now, pipes conveying fluid have been extensively applied in aeronautic and aerospace engineering, hydraulic engineering, petrochemical industry, agriculture and our daily life. Due to the effect of fluid-structure interaction (FSI), pipes always vibrate violently when the inner flow velocity is high or pulsatile, which may even result in pipe rupture in some serious cases and cause incalculable loss. So, in order to make the pipe work safely and stably in all industries, an intensive study of the vibration mechanism and its control of the pipe conveying fluid should be made.
In this dissertation, the existing achievements in pipe FSI vibration are summarized first, then the stability, parametric resonance, forced vibration with internal resonance and vibration control of pipes are investigated by using theoretical and experimental methods. The conclusions in present work may provide a theoretical basis for the stability analysis and hazard assessment of the pipes in the engineering, and also establish the theoretical foundation for the feasible vibration control of the pipes. The main contents are as follows:
(1) The mechanical systems of pipes conveying fluid are modeled, and the differential equations of transverse nonlinear vibration for the pipes are derived through Newton's method. After nondimensionalization and discretization, a differential equation of motion with simplest type is obtained.
(2) Static and dynamic stabilities of supported pipes and those on the elastic foundation are analyzed. Applying the Galerkin and complex mode methods, the natural frequencies and critical flow velocity are calculated. For the case of pulsating inner flow, the regions of principal parametric resonances for first two modes and combination resonance are obtained using the averaging method. The contributions of the linear, sheer foundation rigidities and other parameters on the stabilities of the systems are discussed. The results reveal that the natural frequencies and the stability decrease with the flow velocity increasing; the effect of the sheer rigidity on the stabilities is great and can't be neglected; moreover, some parameters such as tension force, mass ratio of fluid to pipe, viscoelastic coefficient and mean flow velocity have effect on the stabilities of the systems.
(3) Nonlinear equation of motion for the pipes is solved by incremental harmonic balance (IHB) method, and the results are verified by using numerical simulations. According to the solutions of the equation, dynamic response characteristics of the pipe systems in the case of pulsating inner flow are analyzed. The results demonstrate that the semi-analytical and semi-numerical IHB method is precise and effective for the nonlinear vibration problems; with the pulsation frequency increasing, the solutions of the response amplitude may bifurcate, which results in nonresponse, stable response or unstable response with them; when the parametric resonance of the nth mode occurs, the motion of this mode is dominant, and others may contribute weakly.
(4) Forced vibrations with internal resonance of pinned-pinned and clamped-clamped pipes are researched through the multiple dimensions Lindstedt-Poincaré(MDLP) method, and the results obtained are compared with those of the IHB method. The resonance responses of the first two modes and combination resonance are investigated and the relationship between the internal resonance and excitation amplitude is discussed. The motions of all the modes are analyzed. The results show that the internal resonance may occur as the excitation frequency is near the first, second natural frequency or half the sum of them under the condition that the second natural frequency is three times the first one, when the first two modes are excited by each other. However some of the internal resonances are decided by the excitation amplitude.
(5) With taking the ceramic piezoelectric gauge as the control actuator and modal transducer, parametric resonances of pipes conveying pulsating fluid on elastic foundation are controlled actively base on the optimal theory. The effect of the control parameters on the performance of the controller is analyzed. Numerical simulations demonstrate that all kinds of parametric resonances of the pipes can be controlled well with present optimal controller, and it has the ability to resist the perturbation of parameters.
(6) An experiment is conducted to study the dynamic stability of pipes conveying pulsating fluid. The experimental apparatus is set up and effective methods to measure some important parameters are put forward. The first sub-harmonic parametric resonances of order 1/2 for the two pipes are observed and analyzed. The unstable regions are obtained experimentally and they are compared with the theoretical results. It can be seen that qualitative agreement is fairly good. Furthermore, the reasons inducing errors are discussed.
本文首先分析了输流管道流固耦合振动问题的研究现状,然后采用理论结合实验的方法对输流管道的稳定性、参数共振、具有内共振的强迫振动以及振动控制等问题展开研究,结论可为工程中管道的稳定性分析和危害评估提供必要的理论依据,也为管道振动的可行性控制奠定了理论基础。全文主要研究内容包括:
(1)建立了输流管道系统的力学模型,利用牛顿法推导了管道横向非线性振动微分方程,并进行了无量纲化和离散化,得到了最简形式的运动微分方程。
(2)对两端支承及弹性地基上管道系统的静态和动态稳定性进行了分析。利用Galerkin离散法和复模态方法计算了系统的固有频率和临界流速,并应用平均法得到了脉动内流作用时管道的前两阶主参数共振和组合共振区域,讨论了地基的线性刚度、剪切刚度及其它一些参数对系统稳定性的影响。研究发现,系统的固有频率和稳定性将随流速的增大而降低;地基的剪切刚度对系统稳定性的影响相当显著,不能忽略;同时管道预紧力、流体介质与管道质量比、粘弹性系数和管内介质平均流速等参数也会对系统的稳定性产生一定的影响。
(3)利用增量谐波平衡法对管道非线性运动方程进行求解,并用数值方法对结果进行了验证。根据方程解的情况分析了脉动流作用下管道系统的动态响应特性。结果表明,增量谐波平衡法是求解非线性振动问题的精确有效的半解析半数值方法;随着脉动流频率的增大,系统响应振幅的解会出现分岔情况,导致系统可能出现零响应,稳定响应,或零响应、稳定、不稳定响应共存的情况;系统发生第几阶参数共振,第几阶模态就对响应起主要作用,而其它模态的影响很微弱。
(4)利用多元L-P法和增量谐波平衡法对两端铰支和两端固定管道具有内共振的横向强迫振动进行研究,并对两种方法的结果进行比较分析。讨论了前两阶主共振和组合共振响应情况及内共振与外激励幅值的关系,并分析了各模态的振动情况。研究发现,在系统第2阶固有频率约为第1阶固有频率3倍的情况下,当外激励频率接近前两阶固有频率或其和的一半时,系统将发生内部共振,两个模态相互激励。但某些内共振的发生取决于外激励幅值的大小。
(5)采用陶瓷压电片作为控制激励器和模态传感器,根据最优控制方案对弹性地基上脉动流管道的参数共振实施了主动控制,并分析了控制参数对控制效果的影响。数值模拟结果表明,本文设计的最优控制器可使管道的各种参数共振均得到较好的控制,同时还具备一定的抗参数扰动能力。
(6)对脉动流作用下输流管道的动态稳定性进行了实验研究。建立了输流管道实验系统,给出了一些关键参数的有效测量方法,并对两种管道的第一阶1/2次谐波参数共振进行了重点观察与分析,用实验的方法确定了相应的参数共振区域。将其与理论共振区域进行对比,结果在定性上吻合得比较好。同时对误差产生的原因进行了讨论。
Now, pipes conveying fluid have been extensively applied in aeronautic and aerospace engineering, hydraulic engineering, petrochemical industry, agriculture and our daily life. Due to the effect of fluid-structure interaction (FSI), pipes always vibrate violently when the inner flow velocity is high or pulsatile, which may even result in pipe rupture in some serious cases and cause incalculable loss. So, in order to make the pipe work safely and stably in all industries, an intensive study of the vibration mechanism and its control of the pipe conveying fluid should be made.
In this dissertation, the existing achievements in pipe FSI vibration are summarized first, then the stability, parametric resonance, forced vibration with internal resonance and vibration control of pipes are investigated by using theoretical and experimental methods. The conclusions in present work may provide a theoretical basis for the stability analysis and hazard assessment of the pipes in the engineering, and also establish the theoretical foundation for the feasible vibration control of the pipes. The main contents are as follows:
(1) The mechanical systems of pipes conveying fluid are modeled, and the differential equations of transverse nonlinear vibration for the pipes are derived through Newton's method. After nondimensionalization and discretization, a differential equation of motion with simplest type is obtained.
(2) Static and dynamic stabilities of supported pipes and those on the elastic foundation are analyzed. Applying the Galerkin and complex mode methods, the natural frequencies and critical flow velocity are calculated. For the case of pulsating inner flow, the regions of principal parametric resonances for first two modes and combination resonance are obtained using the averaging method. The contributions of the linear, sheer foundation rigidities and other parameters on the stabilities of the systems are discussed. The results reveal that the natural frequencies and the stability decrease with the flow velocity increasing; the effect of the sheer rigidity on the stabilities is great and can't be neglected; moreover, some parameters such as tension force, mass ratio of fluid to pipe, viscoelastic coefficient and mean flow velocity have effect on the stabilities of the systems.
(3) Nonlinear equation of motion for the pipes is solved by incremental harmonic balance (IHB) method, and the results are verified by using numerical simulations. According to the solutions of the equation, dynamic response characteristics of the pipe systems in the case of pulsating inner flow are analyzed. The results demonstrate that the semi-analytical and semi-numerical IHB method is precise and effective for the nonlinear vibration problems; with the pulsation frequency increasing, the solutions of the response amplitude may bifurcate, which results in nonresponse, stable response or unstable response with them; when the parametric resonance of the nth mode occurs, the motion of this mode is dominant, and others may contribute weakly.
(4) Forced vibrations with internal resonance of pinned-pinned and clamped-clamped pipes are researched through the multiple dimensions Lindstedt-Poincaré(MDLP) method, and the results obtained are compared with those of the IHB method. The resonance responses of the first two modes and combination resonance are investigated and the relationship between the internal resonance and excitation amplitude is discussed. The motions of all the modes are analyzed. The results show that the internal resonance may occur as the excitation frequency is near the first, second natural frequency or half the sum of them under the condition that the second natural frequency is three times the first one, when the first two modes are excited by each other. However some of the internal resonances are decided by the excitation amplitude.
(5) With taking the ceramic piezoelectric gauge as the control actuator and modal transducer, parametric resonances of pipes conveying pulsating fluid on elastic foundation are controlled actively base on the optimal theory. The effect of the control parameters on the performance of the controller is analyzed. Numerical simulations demonstrate that all kinds of parametric resonances of the pipes can be controlled well with present optimal controller, and it has the ability to resist the perturbation of parameters.
(6) An experiment is conducted to study the dynamic stability of pipes conveying pulsating fluid. The experimental apparatus is set up and effective methods to measure some important parameters are put forward. The first sub-harmonic parametric resonances of order 1/2 for the two pipes are observed and analyzed. The unstable regions are obtained experimentally and they are compared with the theoretical results. It can be seen that qualitative agreement is fairly good. Furthermore, the reasons inducing errors are discussed.
引文
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