Galloping And Energy Harvesting Study Of Cantilever Structures Considering Fluid-Solid-Electric Coupling

Wind-induced vibration widely exists in various practical engineering,especially in transmission line systerms.This kind of adverse vibration needs to be avoided and weakened for structure safety.If this kind of harmful vibration energy is utilized rationally,it can not only reduce the vibration of the structure but also collect the energy.Galloping has become the focus in the field of small-scale wind energy harvesting in recent years due to its self-excitation,low frequency and large amplitude characteristics.The slender cantilever beam structure is widely used in piezoelectric energy harvesting because of its simple form,low stiffness,easy realization and larger output power at lower frequency and amplitude.The piezoelectric galloping energy harvester is a structural system which can convert the small-scale vibration energy of structure galloping into electric energy.Then self-powed of various sensors can be realized.Galloping can be divided into cross-flow galloping and wake galloping.The Den Hartog galloping model based on quasi-steady assumption is often used in the mechanical model for cross-flow galloping.The Den Hartog model has good applicability in dealing with typical galloping problems.For the aerodynamic load of wake galloping,the existing models are mostly based on quasi-steady assumption,and the formulas are complex and the physical meaning is not clear.Therefore,to make use of the common galloping vibration in Engineering,this paper establishes the models of piezoelectric energy harvester undegoes galloping.In order to improve the energy capture performance of the energy harvester,systematic researches are carried out from the aspects of structure,load and external circuit.The main research contents are as follows:(1)The piezoelectric energy harvester with bluff bodies of different cross sections,such as triangles,squares,rectangles,D-shaped and crescents,were experimentally studied.The effects of cross section of the bluff body and load resistance on the onset speed to galloping,output harvested power and vibration amplitude of the galloping piezoelectric energy harvester are studied.The results show that the onset speed of the energy harvester with square cross section is the smallest,the onset speed of the energy harvester with elliptical(crescent)cross section is the largest,and the energy capture performance of the energy harvester with rectangular cross section is the best.The optimal resistance is about 2×10~6 Ohm for relatively minimum vibration displacement and maximum harvested power.In addition,the smaller the mass of the bluff body,the smaller the vibration displacement as well as larger harvested power can be obtaied.(2)According to Den Hartog single-degree-of-freedom cross-flow galloping machism and the electromechanical conversion principle of piezoelectric materials,a fluid-solid-electric coupling analytical model of galloping piezoelectric energy harvester is established.In order to obtain higher output power,the cantilever beam of the cantilever piezoelectric energy harvester is designed.The section of the cantilever beam is changed from constant section to variable section(tapered design).By decoupling the complex three-phase coupled analytical model,the explicit analytical expressions of onset speed,vibration displacement and harvested power of the tapered piezoelectric energy harvester are derived.The effects of tapered ratio,wind speed and external load resistance on the vibration displacement and output power are discussed.The results show that as the tapered ratio increases,the displacement decreases and the harvested power increases when the wind speed is greater than a certain value.Besides,the highest harvsted power and the smallest vibration displacement are obtained when the tapered ratio of the cantilever beam reaches the optimal value(the strain distribution of the beam is basically uniform).(3)A piezoelectric energy harvester with circular cross section is placed downstreeam of an equal diameter cylinder,and its energy capture characteristics are experimentally studied.By changing the spacing between the two cylinders arranged in tandem or staggered,the influences of the spacing on the vibration displacement and the output power for the piezoelectric energy harvester are discussed.Besides,the effects of cross-section of the bluff body on the vibration displacement and output power of the piezoelectric energy harvester are analyzed.The results show that,under the same spacing ratio,the harvested power of the piezoelectric energy harvester in tandem arrangement is larger than that in staggered arrangement.For the tandem arrangement,the maximum values of the vibration displacement and harvested power are obtained at L/D=3.In addition,the crescent section has the largest vibration displacement and harvested power.(4)The wake galloping of double cylinders in tandem arrangement is simulated by numerical software FLUENT.Based on the simulation results,a theoretical model of wake galloping aerodynamic load is proposed based on Taylor expansion.Accroding to the proposed aerodynamic load model,the fluid-solid-electric coupling distributed parameter model of the wake galloping piezoelectric energy harvester is established.By parameter setting,the harvested power and vibration displacement calculated by the proposed theoretical analytical model are compared with the wind tunnel test results,which verify the correctness of the proposed model.The results show that the smaller the mass of the bluff body,the better the energy capture performance of the energy harvester.When the external resistance is about 10~5 Ohm?R?10~7 Ohm,the vibration displacement of the energy harvester is relatively small with relatively larger harvested power,i.e.,its energy capture performance is relatively better.(5)Based on Hamilton's principle and Gauss's law,the fluid-solid-electric coupling distributed parameter model of the galloping piezoelectric energy harvester with the standard direct-current(standard DC),synchronous charge extraction(SCE),parallel or series synchronized switch harvesting on inductor(P-SSHI or SSSHI)circuit is proposed.The Hopf bifurcation,beam displacement,and harvested power are generalized to the same expressions of the aerodynamic,structural and electrical dampings,modal frequency and shape with different formulas of the electrical damping and modified natural frequency for different DC circuits.The results show that the maximum harvested power can always be achieved by the two SSHI circuits by tuning the external resistance.Additionally,the maximum power of the two SSHI circuits is detected to be the upper boundary of the maximum powers yielded by the four circuits.