Nonlinear Analysis And Experimental Study Of Piezoelectric Energy Harvester Based On Galloping And Vortex-induced Vibration

Galloping and vortex-induced vibrations are two typical types of flow-induced vibration phenomena,which are widely presented in hydrodynamics and oceanic dynamics,and subsequently utilized for the energy harvesting.Piezoelectric energy harvester is a new power generation device which potential to convert the flow-induced vibration energy into electricity.The distributed parameter model can be used to describe the dynamic characteristics of the piezoelectric energy harvester and estimate its performance.However,the nonlinearity has not been clearly investigated by existing studies regarding the distributed parameter model of piezoelectric energy harvester.In addition,previous models is specifically developed for wind energy harvesting with less attention paid to energy harvesting from the low-velocity water flow.Therefore,this paper focus on the piezoelectric energy harvester with galloping and vortex-induced vibration,to carry out the nonlinear analysis of the distribution parameter model of piezoelectric energy harvester and the study of the open channel experiment.Aiming at the problem that the piezoelectric energy harvester without considering the geometric nonlinearity of the cantiever beam,the nonlinear boundary of analytical solution of piezoelectric energy harvester with inductance-resistance circuit is uncertain and the lack of experimental and model research on water energy utilization.The research contents of this paper are as follows.(1)To investigate the effects of structural dimension on the performance of cantilever-beam piezoelectric energy harvesters,a novel distributed parameter model considering the geometric nonlinearity of the cantilever beam is proposed,using the extended Hamilton's principle.Electromechanical decoupling method is utilized to simplify the coupling simulation and facilitate the geometric dimension analysis.The geometric nonlinearity is found to affect the tip displacement and power greatly at high wind speed.The velocity of modal coordinate changes little with the geometric parameters,the power changes with these parameters can be approximately predicted by the electric damping,and the displacement changes with these parameters are opposite to the correction frequency.For higher power with smaller tip displacement,shorter narrower thicker substrate layer fully covered with thicker piezoelectric layer is preferred.For higher power density with smaller tip displacement,shorter wider thicker substrate layer covered with shorter thinner piezoelectric layer is recommended.(2)For nonlinear characterization of the galloping piezoelectric energy harvester with the inductive-resistive circuit,the electromechanical coupled distributed parameter model is briefly derived.A general electromechanical decoupled model is proposed for the series and parallel circuits with different algebraic expressions of the electrical damping and modified frequency.The electrical damping corresponding to Hopf bifurcation(EDHB)is derived and noticed to be linearly and positively varied with the wind speed.Galloping occurs when the electrical damping is smaller than EDHB.To analyze the effects of the electrical circuits on Hopf bifurcation,the inductance corresponding to Hopf bifurcation(IHB)is proposed as a function of the load resistance and EDHB.The stable and galloping regions of the inductance and modified frequency varied with the wind speed are determined and found to be strongly depend on the load resistance.Hopf bifurcation for the small load resistance of the series connection is similar as that for the large load resistance of the parallel case,and vice versa.The time history,phase portrait and power spectrum are introduced to show the differences between the results obtained with the small and large initial conditions.It is found that the large initial condition corresponds to the large electrical damping and the small initial condition relates to the small electrical damping.This is due to the fact that large resistors are more difficult to excite.(3)The piezoelectric energy harvesting experiments at low-velocity water flow are performed in open water channel.Firstly,the energy harvesting with cylinder and triangular prism bluff bodies are studied.It is found that the cylinder exhibits better performance than the prism in the case of vorticity-induced vibration(VIV)due to upstream turbulence at low velocity.As the flow velocity increases,the triangular-prism exceeds the cylinder,and the triangular-prism under the interaction of low-speed galloping while the cylinder only experience VIV.In addition to fluid-solid coupling,electromechanical coupling can also affect the damping,hence the load resistance plays an important role in the power harvesting.Comparing the effects of different bluff bodies,the result shows that the power harvested by the semi-cylinder is significantly better than the other bluff bodies with the same mass and the same flow projection diameter.The cylinder and semi-cylinder energy harvesters are also tested under wakes caused by fixed cylinder.The result indicates that the harvested power increases with the increase of flow velocity,and the semi-cylinder can obtain more energy at a small reduced distance.The harvested power of the cylinder exceeds that of the semi-cylinder at a large reduced distance.(4)To study the piezoelectric energy harvesting from low velocity water flow by ?? and galloping.The piecewise distributed parameter model for the piezoelectric cantilever beam with three types of bluff bodies is proposed.The modified Van der Pol model is established to simulate the ?? force for the cylinder bluff body,and the quasi-steady hypothesis is used to obtain the galloping hydrodynamic force for the tri-prism and semi-cylinder bluff bodies.The added-mass term of the hydrodynamic force is accounted in both the ?? and galloping forces.The approximate analytical solutions of the harvested power for the ?? and galloping models are derived.The analytical solutions is validated by the experimental results in open water channel.After that,the performance of the piezoelectric energy harvester is estimated.The research indicates that the performance of galloping energy harvester is superior to the ?? energy harvester.The ratio of the linear to the cubic hydrodynamic coefficient is crucial in the galloping energy harvesting.