In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metama...In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metamaterials are established using the finite element method,and the dispersion relation is solved using the Bloch’s theorem.The band structures of the lattice metamaterials with different numbers of iterations are studied,and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics.Furthermore,dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials.The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal,and the position of the lowest band gap decreases as the number of iterations increases.The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.展开更多
In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder conditi...In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder condition with exponent and has a 4-adic arithmetic-analytic representation. We will prove that the Koch curve has exact -Hölder 4-adic derivative.展开更多
基金Funding for this work has been provided by the National Natural Science Foundation of China(Nos.11872313 and 11502202)National Key R&D Program of China(2017YFB1102801)Fundamental Research Funds for the Central Universities and Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(CX2020107).
文摘In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metamaterials are established using the finite element method,and the dispersion relation is solved using the Bloch’s theorem.The band structures of the lattice metamaterials with different numbers of iterations are studied,and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics.Furthermore,dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials.The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal,and the position of the lowest band gap decreases as the number of iterations increases.The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.
文摘In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder condition with exponent and has a 4-adic arithmetic-analytic representation. We will prove that the Koch curve has exact -Hölder 4-adic derivative.
