Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations

In the practical environment,it is very common for the simultaneous occurrence of base excitation and crosswind.Scavenging the combined energy of vibration and wind with a single energy harvesting structure is fascinating.For this purpose,the effects of the wind speed and random excitation level are investigated with the stochastic averaging method(SAM)based on the energy envelope.The results of the analytical prediction are verified with the Monte-Carlo method(MCM).The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well jump and make a bi-stable energy harvester(BEH)realize the performance enhancement for a weak base excitation.However,as the strength of the wind increases to a particular level,the influence of the random base excitation on the dynamic responses is weakened,and the system exhibits a periodic galloping response.A comparison between a BEH and a linear energy harvester(LEH)indicates that the BEH demonstrates inferior performance for high-speed wind.Relevant experiments are conducted to investigate the validity of the theoretical prediction and numerical simulation.The experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind speeds.However,as the speed of the incoming wind is up to a particular level,the disadvantage of the BEH becomes clear and evident.

Theoretical Analysis of the Galloping Energy Harvesters under Bounded Random Parameter Excitation

In this paper,the response properties of galloping energy harvesters under bounded random parameter excitation are studied theoretically.The first-order approximate solution of the galloping energy harvester is derived by applying the multi-scales method.The expression for the largest Lyapunov exponent that determines the trivial solution is derived,and the corresponding simulation diagrams,including the largest Lyapunov exponent diagrams and time domain diagrams,verify our results.Then the steady-state response moments of the nontrivial solution are studied using the moment method,and the analytical expressions for the first-order and second-order moments of the voltage amplitude are obtained,respectively.The corresponding results show that wind speed enhances the steady-state response moments of the voltage amplitude.Meanwhile,the voltage output can be controlled by adjusting the cubic coefficient.To further verify the response characteristics of the galloping energy harvester,the stationary probability density functions of the displacement and velocity are obtained by the Monte-Carlo simulation method.The results show that the wind speed enhances the displacement of the bluff and the damping ratios should be reduced asmuch as possible to improve the performance.What’smore,the piezoelectric materials also impact the performance of the energy harvester.

Study on Galloping Stability Mechanism of Conductor and Its Application to Anti-Galloping of Transmission Lines

Galloping of conductor is a major hazard to safe operation of transmission lines. This paper introduces the basic galloping stability mechanism of conductor, design method of anti-galloping and the application of anti-galloping double pendulum and integral eccentric pendulum in China. Galloping stability mechanism of conductor was established based on vertical galloping mechanism developed by Den Hartog and torsional galloping mechanism developed by O. Nigel. A design method of anti-galloping was derived and anti-galloping double pendulum and integral eccentric pendulum were developed. Applications to several transmission lines including a 500 kV transmission line of large span indicated that they have played important roles in anti-galloping.

Incident flow effects on the performance of piezoelectric energy harvesters from galloping vibrations

In this paper, we investigate experimentally the concept of energy har- vesting from galloping oscillations with a focus on wake and turbulence effects. The .harvester is composed of a unimorph piezoelectric cantilever beam with a square cross-section tip mass. In one case, the harvester is placed in the wake of another galloping harvester with the objective of determining the wake effects on the response of the harvester. In the second case, meshes were placed upstream of the harvester with the objective of investigating the effects of upstream turbulence on the response of the harvester. The results show that both wake effects and up- stream turbulence significantly affect the response of the harvester. Depending on the spacing between the two squares and the opening size of the mesh, wake and upstream turbulence can positively enhance the level of the harvested power.

On the formation and wind enhancement mechanisms of a Mongolian cyclone that caused a transmission line galloping trip in Gansu province

Influenced by strong winds associated with a southeastward-moving Mongolian cyclone,a severe transmission line galloping occurred in Baiyin City,Gansu Province,on 14 April 2020.This caused a tripping incident of the transmission line in this region.Based on the hourly,0.5°×0.5°,ECMWF ERA5 reanalysis data,this study investigated the formation mechanisms of the Mongolian cyclone and its associated strong winds.Results from the vorticity budget indicate that the convergence-related vertical stretching and the upward transport of cyclonic vorticity governed formation of the Mongolian cyclone in this event;whereas,tilting and export of cyclonic vorticity from the central region of the cyclone mainly decelerated the cyclone’s formation.The kinetic energy(KE)budget shows that the wind associated with the Mongolian cyclone was mainly enhanced by the positive work of the pressure gradient force.Unlike some typical strong wind events in Northwest China,during this event,no significant downward momentum transportation from the upper troposphere was found.The vertical transport of KE exerted a slightly favorable effect on the KE increase around the location where the transmission line galloping trip appeared.In contrast,the horizontal transport mainly caused an export of KE from this region,which applied an overall negative effect on the wind enhancement associated with the Mongolian cyclone.

Tracking Galloping Profile of Transmission Lines Using Wireless Inertial Measurement Units

Galloping of power transmission lines might bring about huge damage such as massive power outage and collapse of the transmission towers. To realize forecast of the galloping and provide data for study on the galloping mechanism, this paper proposes an online monitoring system for tracking galloping profile of power transmission lines based on wireless inertial measurement units (WIMUs). The system is composed of three modules: wireless inertial measurement nodes, monitoring base station, and remote monitoring station. After detailing the hardware system, the corresponding software which positions and displays galloping profile of the transmission line in real-time is outlined. The feasibility of the proposed on-line monitoring system is demonstrated through a series of experiments at the State Grid Key Laboratory of Power Overhead Transmission Line Galloping (Zhengzhou, China) by taking into account different vibration patterns.

Enhanced galloping energy harvester with cooperative mode of vibration and collision

The low power and narrow speed range remain bottlenecks that constrain the application of small-scale wind energy harvesting.This paper proposes a simple,lowcost,and reliable method to address these critical issues.A galloping energy harvester with the cooperative mode of vibration and collision(GEH-VC)is presented.A pair of curved boundaries attached with functional materials are introduced,which not only improve the performance of the vibration energy harvesting system,but also convert more mechanical energy into electrical energy during collision.The beam deforms and the piezoelectric energy harvester(PEH)generates electricity during the flow-induced vibration.In addition,the beam contacts and separates from the boundaries,and the triboelectric nanogenerator(TENG)generates electricity during the collision.In order to reduce the influence of the boundaries on the aerodynamic performance and the feasibility of increasing the working area of the TENG,a vertical structure is designed.When the wind speed is high,the curved boundaries maintain a stable amplitude of the vibration system and increase the frequency of the vibration system,thereby avoiding damage to the piezoelectric sheet and improving the electromechanical conversion efficiency,and the TENG works with the PEH to generate electricity.Since the boundaries can protect the PEH at high wind speeds,its stiffness can be designed to be low to start working at low wind speeds.The electromechanical coupling dynamic model is established according to the GEH-VC operating principle and is verified experimentally.The results show that the GEH-VC has a wide range of operating wind speeds,and the average power can be increased by 180%compared with the traditional galloping PEH.The GEH-VC prototype is demonstrated to power a commercial temperature sensor.This study provides a novel perspective on the design of hybrid electromechanical conversion mechanisms,that is,to combine and collaborate based on their respective characteristics.

MODES COMPUTATION AND ANALYSIS FOR LONG MULTI-SPAN BUNDLE CONDUCTORS OF POWER TRANSMISSION LINES WITH GALLOPING CONTROL DEVICES

A new type of element which is suitable for solving the modes of thegalloping long multi-span bundle conductor structures is presented. The element is composed of allsub-conductor segments between two spacers. Based on the linearized governing differential equationsof the conductors, the mass matrix and stiffness matrix of the element in consideration of theconstrained relations imposed on the conductors by spacers are derived. The dynamic characteristicsof the galloping control devices can be directly added to the element. The modes for an actual powerline structure are computed by using the element formula and FEM procedures, where seven cases ofdifferent galloping control device allocations are considered. Compared with the measured data, themethod is shown to be reliable and effective. Analysis and discussions of the computational resultsare given. Some hints that are helpful to further investigation of galloping are also obtained .

A Numerical Study on Piezoelectric Energy Harvesting by Combining Transverse Galloping and Parametric Instability Phenomena

This paper aims to numerically investigate the effects of parametric instability on piezoelectric energy harvesting from the transverse galloping of a square prism. A two degrees-of-freedom reduced-order model for this problem is proposed and numerically integrated. A usual quasi-steady galloping model is applied, where the transverse force coefficient is adopted as a cubic polynomial function with respect to the angle of attack. Time-histories of nondimensional prism displacement, electric voltage and power dissipated at both the dashpot and the electrical resistance are obtained as functions of the reduced velocity. Both, oscillation amplitude and electric voltage, increased with the reduced velocity for all parametric excitation conditions tested. For low values of reduced velocity, 2:1 parametric excitation enhances the electric voltage. On the other hand, for higher reduced velocities, a 1:1 parametric excitation(i.e., the same as the natural frequency) enhances both oscillation amplitude and electric voltage. It has been also found that, depending on the parametric excitation frequency, the harvested electrical power can be amplified in 70% when compared to the case under no parametric excitation.

Nonlinear numerical simulation method for galloping of iced conductor

Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.

The Role of Relative Spinal Motion during Feline Galloping for Speed Performance

Felines use their spinal column to increase their running speed at rapid locomotion performance. However, its motion profile behavior during fast gait locomotion has little attention. The goal of this study is to examine the relative spinal motion profile during two different galloping gait speeds. To understand this dynamic behavior trend, a dynamic motion of the feline animal （Felis catus domestica） was measured and analyzed by motion capture devices. Based on the experiments at two different galloping gaits, we observed a significant increase in speed （from 3.2 m.s-1 to 4.33 m.s-1） during the relative motion profile synchronization between the spinal （range： 118.86~ to 168.00~） and pelvic segments （range： 46.35~ to 91.13~） during the hindlimb stance phase （time interval： 0.495 s to 0.600 s）. Based on this discovery, the relative angular speed profile was applied to understand the possibility that the role of the relative motion match during high speed locomotion generates bigger ground reaction force.

Energy Harvesting in the Wake of An Inverted C-Shaped Bluff Body

This paper proposes a novel wake-induced vibration(WIV)-based energy harvesting system consisting of two bluff bodies.An inverted C-shaped bluff body is stationary installed at the upstream position to generate an interference wake street,and a cylinder bluff body equipped with a transducer is elastically suspended at the downstream position to harness WIV energy.The hydrodynamics and energy harvesting(EH)performance of the proposed system are investigated via experimental studies.The reduced velocity(U*)ranging from 2 to 14(the corresponding Reynolds number ranging from 15100 to 106200)is considered in the present study.It is found that the wake generated by the inverted C-shaped bluff body significantly affects the EH performance.Enlarging the opening angle(α)of the C-shaped bluff body increases the vibration amplitude of the downstream cylinder,thereby increasing the harvested power.When the spacing(L)between two bluff bodies is two times the cylinder diameter(D),the wake-induced vibration(WIV)mode is observed,while the combined WIV and wake galloping(WG)mode occurs whenαis 150°,and L equals 3D or 4D.The average drag coefficient becomes negative when L is 2D,3D,or 4D.By carefully configuring a C-shaped bluff body,the wake generated by it can bring an augmenting effect on the vibration of the downstream EH cylinder.For example,the RMS power output of the proposed EH system reaches a maximum of 0.31 W at U*=8 and L=4D,which is 300%greater than that of its traditional counterpart.Furthermore,after a number of case stud-ies,it is identified that the proposed EH system can achieve the best performance whenαis 150°and L=2D.

Design,modeling and experiments of broadband tristable galloping piezoelectric energy harvester

Galloping based piezoelectric energy harvester is a kind of micro-environmental energy harvesting device based on flowinduced vibrations.A novel tristable galloping-based piezoelectric energy harvester is constructed by introducing a nonlinear magnetic force on the traditional galloping-based piezoelectric energy harvester.Based on Euler-Bernoulli beam theory and Kirchhoff’s law,the corresponding aero-electromechanical model is proposed and validated by a series of wind tunnel experiments.The parametric study is performed to analyse the response of the tristable galloping-based piezoelectric energy harvester.Numerical results show that comparing with the galloping-based piezoelectric energy harvester,the mechanism of the tristable galloping-based piezoelectric energy harvester is more complex.With the increase of a wind speed,the vibration of the bluff body passes through three branches:intra-well oscillations,chaotic oscillations,and inter-well oscillations.The threshold wind speed of the presented harvester for efficiently harvesting energy is 1.0 m/s,which is decreased by 33% compared with the galloping-based piezoelectric energy harvester.The maximum output power of the presented harvester is 0.73 mW at 7.0 m/s wind speed,which is increased by 35.3%.Compared with the traditional galloping-based piezoelectric energy harvester,the presented tristable galloping-based piezoelectric energy harvester has a better energy harvesting performance from flow-induced vibrations.

Galloping Vibration Monitoring of Overhead Transmission Lines by Chirped FBG Array

A distributed online fiber sensing system based on the phase-sensitive optical time domain reflectometer(Φ-OTDR)enhanced by the drawing tower fiber Bragg grating(FBG)array is presented and investigated experimentally for monitoring the galloping of overhead transmission lines.The chirped FBG array enhanced Φ-OTDR sensing system can be used to measure the galloping behavior of the overhead transmission lines(optical phase conductor or optical power ground wire),which are helpful for monitoring the frequency response characteristics of the ice-induced galloping,evaluating the motion tendencies of these cables,and avoiding the risk of flashover during galloping.The feasibility of the proposed online monitoring system is demonstrated through a series of experiments at the Special Optical Fiber Cable Laboratory of State Grid Corporation of China(Beijing,China).Results show that the proposed system is effective and reliable for the monitoring of galloping shape and characteristic frequency,which can predict the trend of destructive vibration behavior and avoid the occurrence of cable breaking and tower toppling accidents,and these features are essential for the safety operation in smart grids.

Optimal Center-of-Mass Pivot Effect of Spinal Motion in Feline Galloping

In this paper,we studied the acceleration behavior of a quadruped animal during a galloping motion.Because the development of many quadruped robotic systems has been focused on dynamic movements,it is obvious that guidance from the dynamic behavior of quadruped animals is needed for robotics engineers.To fulfill this demand,this paper deals with analysis of the galloping motions of a domestic cat,which is well known for its excellent acceleration performance among four-legged animals.Based on the planar motion capture environment,the movement data of a galloping feline was acquired and the dynamic motions were estimated using a spring-mass system.In particular,the effects of the position and angle of the center-of-mass of the cat,angular displacement of the spine,and angular velocity of the spine were analyzed and are discussed below.Through this process,it was possible to understand the dynamic movement characteristics of the cat,and to understand the relationships between,and the influences of,these parameters.From this analysis,we provide significant data applicable to the design of joint movements in quadruped robot systems.

Phenomenological model for torsional galloping of an elastic flat plate due to hydrodynamic loads

This study investigates the torsional galloping phenomenon, an instability type flow-induced oscillation, in an elastic stru-cture due to hydrodynamic loads into the water current. The structure applied here is a rectangular flat plate with an elastic axis in its mid-chord length. The elasticity is provided by torsion spring. The flat plate has only one degree of freedom which is rotation in pure yaw about its axis. It is observed that as the current speed is higher than a critical velocity, the flat plate becomes unstable. The instability leads to torsional galloping occurrence, as a result of which the flat plate begins to yaw about the elastic axis. By testing two different chord lengths each with several torsion spring rates, the flat plate behavior is investigated and three different responses are recognized. Then, a phenomenological model is developed with the original kernel in the form of the van der Pol-Duffing equa-tion. The model explains these three responses observed experimentally.

Learning Control of Quadruped Robot Galloping

Achieving galloping gait in quadruped robots is challenging, because the galloping gait exhibits complex dynamical behaviors of a hybrid nonlinear under-actuated dynamic system. This paper presents a learning approach to quadruped robot galloping control. The control function is obtained through directly approximating real gait data by learning algorithm, without consideration of robot＇s model and environment where the robot is located. Three motion control parameters are chosen to determine the galloping process, and the deduced control function is learned iteratively with modified Locally Weighted Projection Regression （LWPR） algorithm. Experiments conducted upon the bioinspired quadruped robot, AgiDog, indicate that the robot can improve running performance continuously along the learning process, and adapt itself to model and environment uncertainties.

Numerical Analysis of the Influence of Turbulence Intensity on Iced Conductors Gallop Phenomena

Turbulence is expected to play a relevant role in the so-called conductor gallop phenomena,namely,the high-amplitude,low-frequency oscillation of overhead power lines due to the formation of ice structures and the ensu-ing effect that wind can have on these.In this work,the galloping time history of a wire with distorted(fixed in time)shape due to the formation of ice is analyzed numerically in the frame of afluid-solid coupling method for different wind speeds and levels of turbulence.The results show that the turbulence intensity has a moderate effect on the increase of the conductor’s aerodynamic lift and drag coefficients due to ice accretion;nevertheless,the corresponding changes in the torsion coefficient are very significant and complicated.A high turbulence intensity can affect the torsion coefficient in a certain range of attack angles and increase the torsion angle of the conductor.Through comparison of the galloping phenomena for different wind velocities,it is found that the related amplitude grows significantly with an increase of the wind speed.For a relatively large wind speed,the galloping amplitude is more sensitive to the turbulence intensity.Moreover,the larger the turbulence intensity,the larger the conductor’s vertical and horizontal galloping amplitudes after icing.The torsion angle also increases with an increase in the wind speed and turbulence intensity.