Study On Mechanics Properties Of One-dimensional Acoustic Black Hole Structure

Vibration and noise suppression of mechanical structures play a very important role in the design of industrial systems.The Acoustic Black Hole(ABH)effect is caused by the infinitely small material attenuation of the medium,such as the wedge-shaped beam,whose thickness is diminished to zero according to the power-law h(x)=?x~m with m?2,giving rise to the reduction in the bending wave speed and no wave reflections in the tip.Therefore,the waves will be trapped in the edge portion,which resulting in the ABH effect.As a potential intelligent structure,which is capable of concentrating energy into local area,the ABH structure has high potential of applications for vibration and noise control and piezoelectric energy harvesting.Taking the beam with one-dimensional ABH effect as the research object in the thesis,the control characteristics of ABH effect on bending waves were studied by theoretical analysis,numerical simulation and experimental verification.The purposes are to suppress the broadband vibration and noise more efficiently through a simple and lightweight structure,and to improve the efficiency of vibration energy harvesting.The results of this research will have significant theoretical guidance value for accelerating the application of ABHs in the engineering.1.Based on the Transfer Matrix Method(TMM),the concept of Edge Energy Ratio(EER)was proposed at first from the perspective of energy,i.e.,the ratio of the energy trapped within the edge portion to that of the whole structure,to illustrate the capture of wave energy by the ABH effect.Analyses show that both the strain energy ratio and kinetic energy ratio of the edge achieve the minimum when the wedge is in resonances,although these two kinds of energy come to peaks at this case.However,in the case of small length of the edge portion,the strain energy ratio reaches the highest peaks at the second and higher resonances.Generally,the best effect of energy concentration occurs when m ranges from 2.5 to 3.Reducing the truncation thickness and increasing the maximum thickness can improve the energy concentration efficiency.2.Considering the effects of structural strain rate damping and viscous air damping,the acoustic radiation performance of the beam with ABH effect was analyzed by the acoustic radiation modes.It was found that the ABH effect could effectively suppress the acoustic radiation of structures.The physical mechanism is that the ABH can convert the supersonic waves into subsonic waves by reducing the propagation velocity of the waves in the structure.Due to the energy concentration effect,the wave energy can be dissipated more effectively by sticking the absorbing material in the high energy density region of the structure.In addition,the low frequency acoustic radiation can be effectively reduced by adjusting the structural parameter to enhance the interaction between the ABH element and low frequency waves.The compression of bending waves at the edge portion with variable thickness is enhanced with the reduction of the truncation thickness,which results in the large deformation of the edge and induces the geometric nonlinear effect of the ABH structure.The nonlinear dynamic responses of the ABH beam were analyzed by using the TMM and multiple scales method in the thesis.The results show that the system will exhibit obvious nonlinear characteristics only when the truncation thickness is reduced to a certain value.In the geometric nonlinearity,the response curves show inclination and jump phenomena,which results in a large reduction in the maximum amplitude of the low frequency vibration responses over a wide frequency range.However,the nonlinear jump phenomena can be eliminated in a certain frequency rang by sticking absorbing material on the surface of the structure.In addition,the nonlinear dynamic responses of the one-dimensional ABH beam with a uniform extended platform were also analyzed.The results show that due to the extended platform,the system has a significant nonlinearity even with a large truncation thickness,therefore the requirements for the ABH manufacturing process can be reduced.In order to study the effect of ABH to the piezoelectric energy harvesting efficiency,the distribution parameter model of cantilever piezoelectric energy harvesting device with ABH effect is established based on TMM,and the mechanical and electrical responses of the system under harmonic excitation were obtained.By comparison with the traditional piezoelectric energy harvester,the ABH effect can significantly improve the efficiency of energy harvesting.Therefore,it is verified the ABH effect has great application potential in the field of piezoelectric energy harvesting.In conclusion,we study the manipulation of bending waves by one-dimensional ABH effect and its application in vibration and noise reduction and piezoelectric energy harvesting.This research provides theoretical methods and new ideas for the further exploration of the ABH behavior.The results also provide theoretical guidance for the practical application of the ABH effect.