Study of Fractal Honeycomb Structural Mechanics Metamaterial Vibration Bandgap Characteristics

PurposeA new mechanical metamaterial with a periodic fractal honeycomb structure was designed and optimized based on the vibration and noise reduction demand in engineering applications.MethodsThe dynamic stiffness matrix of the structure was derived based on the spectral element method, and the frequency response curves were plotted. The feasibility and correctness of the band gap results calculated by the spectral element method were also confirmed by comparison with the finite element method.ResultsBased on the finite element method, the energy band structure and vibration transmission characteristics of different order fractal structures are analyzed and calculated, and the effect of a structural fractal on the vibration band gap of different order structures is investigated. The influence of these factors on the band gap is explored by changing the structural fractal ratio and the internal concave angle when designing the optimized structure.ConclusionsThe feasibility and correctness of the spectral element method are verified by comparing the calculation results of the finite element and spectral element methods. By comparing the band gaps of fractal structures of different orders, it is found that the band gaps generated by the second-order structures are lower frequency and wider frequency, which are more compatible with the current applications in engineering. By varying the fractal ratio and the internal concave angle of the structure, it is found that the larger the value of the fractal ratio, the lower the frequency at which the band gap is generated. At the same time, the increase of the internal concave angle shifts the band gap of the fractal structure toward the high-frequency range. By optimizing the design, the structural band gap is gradually shifted to the position of low-frequency broadband, and the vibration and noise reduction performance is improved.