Dynamic analysis and regulation of the flexible pipe conveying fluid with a hard-magnetic soft segment

Applied Mathematics and Mechanics - The recently developed hard-magnetic soft (HMS) materials can play a significant role in the actuation and control of medical devices, soft robots, flexible...     

New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections

正Kun ZHOU1,2, Qiao NI1,2, Wei CHEN1,2, Huliang DAI1,2,3,Zerui PENG1,2,, Lin WANG1,2,     

Utilization of nonlinear vibrations of soft pipe conveying fluid for driving underwater bio-inspired robot

Creatures with longer bodies in nature like snakes and eels moving in water commonly generate a large swaying of their bodies or tails, with the purpose of producing significant frictions and collisions between body and fluid to provide the power of consecutive forward force. This swaying can be idealized by considering oscillations of a soft beam immersed in water when waves of vibration travel down at a constant speed. The present study employs a kind of large deformations induced by nonlinear vibrations of a soft pipe conveying fluid to design an underwater bio-inspired snake robot that consists of a rigid head and a soft tail. When the head is fixed, experiments show that a second mode vibration of the tail in water occurs as the internal flow velocity is beyond a critical value. Then the corresponding theoretical model based on the absolute nodal coordinate formulation (ANCF) is established to describe nonlinear vibrations of the tail. As the head is free, the theoretical modeling is combined with the computational fluid dynamics (CFD) analysis to construct a fluid-structure interaction (FSI) simulation model. The swimming speed and swaying shape of the snake robot are obtained through the FSI simulation model. They are in good agreement with experimental results. Most importantly, it is demonstrated that the propulsion speed can be improved by 21% for the robot with vibrations of the tail compared with that without oscillations in the pure jet mode. This research provides a new thought to design driving devices by using nonlinear flow-induced vibrations.

     

Vortex-induced vibration of pipes conveying fluid using the method of multiple scales

The nonlinear dynamics of supported pipes conveying fluid subjected to vortex-induced vibration is evaluated using the method of multiple scales. Frequency response portraits for different internal fluid velocities under lock-in conditions are obtained and the stability of steady-state responses is discussed. Results show that the internal fluid velocity has a prominent effect on the oscillation amplitude and that the steady-state responses incorporating unstable solutions in the lock-in region are also obtained. In addition, the effects of two kinds of fluctuating lift coefficients on the steady-state responses are compared with each other.     

Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

In this study,the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional(3 D)theoretical model.The complete nonlinear governing equations are discretized via Galerkin’s method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm.Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions.A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio,the flow velocity,and the gravity parameter on the post-buckling behavior of the pipe.Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter.It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached.Just beyond the critical flow velocity,the pipe would lose stability by static divergence via a pitchfork bifurcation,and two possible nonzero equilibrium positions are generated.It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter.Unlike a pipe with two immovable ends,however,the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors.The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity.In addition,the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.     

Extremely large-amplitude oscillation of soft pipes conveying fluid under gravity

In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity. Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe. The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value. As the inclination angle is equal to π, the pipe experiences, in turn,buckling instability, regaining stability, and flutter instability with the increase in the flow velocity. Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations. Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.     

基于时序参数法的BFRP蠕变行为预测

本文研究了基于时序参数法的玄武岩纤维增强复合材料(BFRP)板弯曲蠕变行为．为了提高模型理论预测的精度,文中将整个实验时长的数据进行了合理的细化分组,且每组时长尽可能相同,然后对细化分组的数据组分别进行直接外推法拟合,得到各数据组对应的拟合方程参数,最后获得了BFRP板弯曲蠕变行为的理论预测模型．对比模型预测值和实验值可以发现：模型预测值随着时间的增长,越来越接近于实验值,最后二者的相对误差几乎为零．该结果表明：文中建立的蠕变预测模型具有足够高的精度,可以应用于BFRP的蠕变行为的预测．     

STABILITY AND MODE EVOLUTION CHARACTERISTICS OF A CANTILEVERED FLUID-CONVEYING PIPE ATTACHED WITH THE LUMPED MASS 1)

本文主要研究通过调控集中质量对悬臂输流管稳定性和振动模态特性的影响规律,为输流管动力学性能的可控性提供理论指导和实验依据. 首先基于扩展的哈密顿原理,建立了含集中质量悬臂输流管的非线性动力学理论模型. 基于线性动力学特性分析,研究发现集中质量沿管道轴向位置变化对输流管发生颤振失稳的临界流速有重要影响.并通过伽辽金前四阶模态截断处理线性矩阵方程式,定性地分析了集中质量位置与质量比的变化对于输流管稳定性影响的变化.实验结果表明, 输流管的颤振失稳模态随集中质量位置的变化发生了转迁. 此外,基于动力学理论分析, 发现集中质量比值对失稳临界流速也有重要的影响,且主要取决于集中质量的安装位置. 基于非线性特性,进一步分析了集中质量对输流管振动幅值的影响. 实验和理论研究发现,集中质量位置从固定端向自由端变化时, 输流管振幅表现出先增大后减小趋势,且振动模态也从二阶转迁到三阶.本研究有望为输流管振动驱动应用提供理论支撑与指导意义.     

Non-planar responses of cantilevered pipes conveying fluid with intermediate motion constraints

In this paper, the nonlinear responses of a loosely constrained cantilevered pipe conveying fluid in the context of three-dimensional (3-D) dynamics are investigated. The pipe is allowed to oscillate in two perpendicular principal planes, and hence its 3-D motions are possible. Two types of motion constraints are considered. One type of constraints is the tube support plate (TSP) which comprises a plate with drilled holes for the pipe to pass through. A second type of constraints consists of two parallel bars (TPBs). The restraining force between the pipe and motion constraints is modeled by a smoothened-trilinear spring. In the theoretical analysis, the 3-D version of nonlinear equations is discretized via Galerkin’s method, and the resulting set of equations is solved using a fourth-order Runge–Kutta integration algorithm. The dynamical behaviors of the pipe system for varying flow velocities are presented in the form of bifurcation diagrams, time traces, power spectra diagrams and phase plots. Results show that both types of motion constraints have a significant influence on the dynamic responses of the cantilevered pipe. Compared to previous work dealing with the loosely constrained pipe with motions restricted to a plane, both planar and non-planar oscillations are explored in this 3-D version of pipe system. With increasing flow velocity, it is shown that both periodic and quasi-periodic motions can occur in the system of a cantilever with TPBs constraints. For a cantilevered pipe with TSP constraints, periodic, chaotic, quasi-periodic and sticking behaviors are detected. Of particular interest of this work is that quasi-periodic motions may be induced in the pipe system with either TPBs or TSP constraints, which have not been observed in the 2-D version of the same system. The results obtained in this work highlight the importance of consideration of the non-planar oscillations in cantilevered pipes subjected to loose constraints.