图  1  超材料带隙形成机制

a—Unit cell length; M₁ and M₂—Mass of the matrix and the heavy core, respectively; u and w—Displacements; k—Equivalent spring stiffness; α—Wave incidence angle

Figure  1.  Mechanism of metamaterial bandgap formation

图  2  超材料混凝土单胞示意图

Figure  2.  Schematic diagram of metaconcrete unit cell

图  3  超材料混凝土的一维有效质量模型图

j—One-dimensional unit cell number

Figure  3.  Diagram of the one-dimensional effective mass model for metaconcrete

图  4  超材料混凝土的有效质量与频率函数图

m_eff/m_st—Ratio of effective mass m_eff to the actual total mass m_st; ω/ω₀—Ratio of excitation frequency ω to nature frequency ω₀

Figure  4.  Effective mass-frequency relationships of metaconcrete

图  5  超材料混凝土的有效质量和有效刚度的等效模型图

k_eff—Equivalent effective stiffness

Figure  5.  Equivalent model diagram for effective mass and effective stiffness of metaconcrete

图  6  超材料混凝土三维振动模型示意图^{[14, 45]}

l—Equivalent spring length; Δl and θ—Displacement deflection and angular deflection of the transverse equivalent spring, respectively; y—Axial displacement of the heavy core; c—Damping

Figure  6.  Three-dimensional vibration model of metaconcrete^{[14, 45]}

图  7  有序排列的超材料混凝土板模型^[9]

L—Thickness of the plate; b—Width of the selected section

Figure  7.  Sequentially arranged metaconcrete slab model^[9]

图  8  超材料混凝土单胞的边界条件

PBC—Periodic boundary condition

Figure  8.  Boundary condition setting for metaconcrete unit cell

图  9  几何参数、材料属性对超材料混凝土带隙的影响^[50]

Figure  9.  Effect of geometric parameters and material properties on bandgap in metaconcrete^[50]

图  10  具有双质量涂层骨料的超材料混凝土单胞示意图

Figure  10.  Schematic diagram of the metaconcrete unit cell with dual mass coated aggregates

图  11  双质量涂层骨料的超材料混凝土模型示意图^[59]

M_m—Total mass of the mortar matrix

Figure  11.  Schematic diagram of the metaconcrete model with dual mass coated aggregates^[59]

图  12  超材料混凝土中人工骨料的结构示意图^[71-72]

Figure  12.  Structural diagram of artificial aggregates in metaconcrete^[71-72]

图  13  超材料混凝土试件示意图^[71-72]

Figure  13.  Schematic diagram of metaconcrete specimens^[71-72]

图  14  超材料混凝土试件的抗压强度和弹性模量

Figure  14.  Compressive strength and modulus of elasticity for metaconcrete specimens