| The impact of vibration and noise problems on military,aerospace,construction and other fields as well as human health is becoming more and more significant.It is increasingly urgent to meet the needs of multi-functional materials for vibration and noise reduction and better mechanical properties,while it is difficult for conventional materials to achieve these properties at the same time.The emergence of acoustic metamaterials has attracted the attention of scientists.Metamaterials are artificial materials with extraordinary physical properties,and their unique structure and properties,especially their bandgap characteristics,can modulate and suppress the propagation of elastic waves for the purpose of reducing vibration and noise.In this thesis,a fractal structure metamaterial based on the traditional honeycomb structure is designed to address vibration and noise problems in the engineering field,and its band-gap characteristics,transmission losses and acoustic properties are analysed through theoretical calculations,simulations and experimental tests,mainly as follows:Firstly,a new fractal structure acoustic metamatertial is proposed based on the conventional honeycomb structure.Using Bloch’s theorem and finite element method,the energy band structure and band gap of different orders of the fractal structure are calculated and optimised to obtain the new fractal structure acoustic metamaterials,and the mechanism of band gap generation is also analysed by vibrational modes.The results show that the second order fractal structure has the best band gap,with a single band gap covering up to3005 Hz and the total band gap accounting for 58.7% of the frequency range.The proportion of the directional band gap gradually increases with the fractal,from 34.1% to 84.1% and finally to 90.5%,indicating that the optimised fractal structure has good sound insulation properties in the Γ-X direction.The bandgap control of the fractal structure is also investigated using finite element software and the influence of geometric and material parameters on the bandgap is mainly analysed.The fractal ratio,wall thickness and concave angle of the structure increase gradually with the increase of the parameters,and the effect of local defects on the band gap distribution is not obvious.The density,elastic modulus and Poisson’s ratio of structural materials decrease,increase and increase with the increase of material parameters.The result of optimising the design so that the structural band gap achieves a low frequency broadband result,improving vibration and noise reduction performance.Secondly,the beam-bar unit of the fractal structure is disassembled and reassembled using the spectral element method to derive the dynamic stiffness matrix to solve the dynamic response,and the transmittance of the structure is calculated using Matlab software.The results of the spectral element method are compared with the results of the finite element calculation of the energy band structure to verify the correctness and validity of the results of the spectral element method.Thirdly,the acoustic properties of fractal structures are investigated with a view to their acoustic applications.The effect on the transmission characteristics is analysed by varying the effective length and width of the fractal structure channel.To verify the stability of the fractal structure,the robustness of different orders of the fractal structure was investigated.The results show that increasing the channel length and width of the fractal structure leads to a significant increase in sound loss;the different orders of fractal structure have good robustness in the horizontal direction,vertical direction and rotation angle,which can be better applied in practical engineering fields.Finally,the band gap of the fractal structure was verified experimentally,the frequency response curve of the structure was measured,and the experimental results were compared with the simulation results to verify the correctness of the simulation calculation. |
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