A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are per...A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.展开更多
The capacity of energy absorption by fault bands after rock burst wascalculated quantitatively according to shear stress-shear deformation curves considering theinteractions and interplaying among microstructures due ...The capacity of energy absorption by fault bands after rock burst wascalculated quantitatively according to shear stress-shear deformation curves considering theinteractions and interplaying among microstructures due to the heterogeneity of strain softeningrock materials. The post-peak stiffness of rock specimens subjected to direct shear was derivedstrictly based on gradient-dependent plasticity, which can not be obtained from the classicalelastoplastic theory. Analytical solutions for the dissipated energy of rock burst were proposedwhether the slope of the post-peak shear stress-shear deformation curve is positive or not. Theanalytical solutions show that shear stress level, confining pressure, shear strength, brittleness,strain rate and heterogeneity of rock materials have important influence on the dissipated energy.The larger value of the dissipated energy means that the capacity of energy dissipation in the formof shear bands is superior and a lower magnitude of rock burst is expected under the condition ofthe same work done by external shear force. The possibility of rock burst is reduced for a lowersoftening modulus or a larger thickness of shear bands.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12122206,52175125,12272129,12304309,and 12302039)the Zhejiang Provincial Natural Science Foundation of China(No.LQ24A020006)+1 种基金the Hong Kong Scholars Program of China(No.XJ2022012)the Natural Science Foundation of Hunan Province of China(No.2024JJ4004)。
文摘A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.
基金This work was financially supported by the National Natural Science Foundation of China (No.50309004).
文摘The capacity of energy absorption by fault bands after rock burst wascalculated quantitatively according to shear stress-shear deformation curves considering theinteractions and interplaying among microstructures due to the heterogeneity of strain softeningrock materials. The post-peak stiffness of rock specimens subjected to direct shear was derivedstrictly based on gradient-dependent plasticity, which can not be obtained from the classicalelastoplastic theory. Analytical solutions for the dissipated energy of rock burst were proposedwhether the slope of the post-peak shear stress-shear deformation curve is positive or not. Theanalytical solutions show that shear stress level, confining pressure, shear strength, brittleness,strain rate and heterogeneity of rock materials have important influence on the dissipated energy.The larger value of the dissipated energy means that the capacity of energy dissipation in the formof shear bands is superior and a lower magnitude of rock burst is expected under the condition ofthe same work done by external shear force. The possibility of rock burst is reduced for a lowersoftening modulus or a larger thickness of shear bands.
