Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Unlocking multidirectional and broadband wind energy harvesting with triboelectric nanogenerator and vortex-induced vibration of sphere

A unique oscillating wind-driven triboelectric nanogenerator(OWTENG)based on the sphere's vortex-induced vibration(VIV)behavior is proposed in this study,which can harvest wind energy across a multitude of horizontal directions.With the Euler-Lagrange method,the coupled governing equations of the OWTENG are established and subsequently validated by experimental tests.The vibrational properties and output performance of the OWTENG for varying wind speeds are analyzed,demonstrating its effectiveness in capturing wind energy across a broad range of wind speeds(from 2.20 m/s to 8.84 m/s),and the OWTENG achieves its peak output power of 106.3μW at a wind speed of 5.72 m/s.Furthermore,the OWTENG maintains a steady output power across various wind directions within the speed range of 2.20 m/s to 7.63 m/s.Nevertheless,when the wind speed exceeds 7.63 m/s,the vibrational characteristics of the sphere shift based on the wind direction,leading to fluctuations in the OWTENG's output power.This research presents an innovative approach for designing vibrational triboelectric nanogenerators,offering valuable insights into harvesting wind energy from diverse directions and speeds.

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.

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

In several previous studies,it was reported that a supported pipe with small geometric imperfections would lose stability when the internal flow velocity became sufficiently high.Recently,however,it has become clear that this conclusion may be at best incomplete.A reevaluation of the problem is undertaken here by essentially considering the flow-induced static deformation of a pipe.With the aid of the absolute nodal coordinate formulation(ANCF)and the extended Lagrange equations for dynamical systems containing non-material volumes,the nonlinear governing equations of a pipe with three different geometric imperfections are introduced and formulated.Based on extensive numerical calculations,the static equilibrium configuration,the stability,and the nonlinear dynamics of the considered pipe system are determined and analyzed.The results show that for a supported pipe with the geometric imperfection of a half sinusoidal wave,the dynamical system could not lose stability even if the flow velocity reaches an extremely high value of 40.However,for a supported pipe with the geometric imperfection of one or one and a half sinusoidal waves,the first-mode buckling instability would take place at high flow velocity.Moreover,based on a further parametric analysis,the effects of the amplitude of the geometric imperfection and the aspect ratio of the pipe on the static deformation,the critical flow velocity for buckling instability,and the nonlinear responses of the supported pipes with geometric imperfections are analyzed.

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.

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.

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

The recently developed hard-magnetic soft(HMS)materials can play a significant role in the actuation and control of medical devices,soft robots,flexible electronics,etc.To regulate the mechanical behaviors of the cantilevered pipe conveying fluid,the present work introduces a segment made of the HMS material located somewhere along the pipe length.Based on the absolute node coordinate formulation(ANCF),the governing equations of the pipe conveying fluid with an HMS segment are derived by the generalized Lagrange equation.By solving the derived equations with numerical methods,the static deformation,linear vibration characteristic,and nonlinear dynamic response of the pipe are analyzed.The result of the static deformation of the pipe shows that when the HMS segment is located in the middle of the pipe,the downstream portion of the pipe centerline will keep a straight shape,providing that the pipe is stable with a relatively low flow velocity.Therefore,it is possible to precisely regulate the ejection direction of the fluid flow by changing the magnetic and fluid parameters.It is also found that the intensity and direction of the external magnetic field greatly affect the stability and dynamic response of the pipe with an HMS segment.In most cases,the magnetic actuation increases the critical flow velocity for the flutter instability of the pipe system and suppresses the vibration amplitude of the pipe.

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.

基于人体运动的压电-电磁混合式振动能量采集研究

将人体运动产生的动能转化为可利用的电能为传感器供电一直是能量采研究中的一个热点.如何有效利用人体运动,增强环境适应能力以及提高能量采集性能仍是俘能研究中需要解决的关键问题.论文基于人体运动特性,设计了一种新型的混合式能量采集器,同时具有压电和电磁转化机制.压电俘能是基于压电梁变形产生电能,电磁发电机采用堆叠磁组构型来切割线圈产生电动势.首先建立了混合式能量采集器的动力学理论模型,用来描述输出电压特性,并与实验进行了对比验证.理论与实验研究均表明,混合式俘能器的输出电压在一定激励频率范围内出现两个波峰.通过调节压电梁长度,可以改变峰值大小以及两个峰值间的频段范围.人体运动实验表明,混合式俘能器中可以在短时间内提供较高的电压输出,比如当跑步速度为5 km/h时,3 s内就可以输出1.1 V直流电压驱动传感器工作;跑步时长为30 s时,传感器正常工作时常可以达到77 s.论文设计的混合式俘能器不仅可以快速供电,还具有较强的续航能力,这为电池充电或传感器供电提供了潜在的应用价值.

含非线性能量汇的简支输液管非线性振动控制研究

论文建立了一个含有非线性能量汇(NES)装置并输运脉动内流的简支输液管道理论模型,研究了NES装置对管道的非线性动力学特性与振动控制的影响.利用Galerkin和龙格库塔法,得到了在含NES和不含NES装置时管道动力学响应的数值结果.研究表明, NES装置能有效地抑制管道振动.通过对比可知, NES对管道系统的稳定性和非线性振动控制有着明显的影响.此外,论文还详细讨论了NES装置相关参数对系统的动力学影响.结果表明,增大NES的弹簧刚度k、阻尼σ和质量比ε有利于管道减振,且最佳安装位置在管道中点.此外,增大阻尼σ能缩小失稳激励频率区域,而其他参数的变化对失稳激励频率区域影响较小.

Natural Frequency and Stability Tuning of Cantilevered CNTs Conveying Fluid in Magnetic Field

This paper investigates the dynamics of cantilevered CNTs conveying fluid in lon- gitudinal magnetic field and presents the possibility of controlling/tuning the stability of the CNT system with the aid of magnetic field. The slender CNT is treated as an Euler-Bernoulli beam. Based on nonlocal elasticity theory, the equation of motion with consideration of magnetic field effect is developed. This partial differential equation is then discretized using the differen- tial quadrature method （DQM）. Numerical results show that the nonlocal small-scale parameter makes the fluid-conveying CNT more flexible and can shift the unstable mode in which flutter instability occurs first at sufficiently high flow velocity from one to another. More importantly, the addition of a longitudinal magnetic field leads to much richer dynamical behaviors of the CNT system. Indeed, the presence of longitudinal magnetic field can significantly affect the evolution of natural frequency of the dynamical system when the flow velocity is successively increased. With increasing magnetic field parameter, it is shown that the CNT system behaves stiffer and hence the critical flow velocity becomes higher. It is of particular interest that when the mag- netic field parameter is equal to or larger than the flow velocity, the cantilevered CNT conveying fluid becomes unconditionally stable, indicating that the dynamic stability of the system can be controlled due to the presence of a longitudinal magnetic field.