Fig. 1

Conceptual graphs of function for chiral metamaterials in underwater application environment (color online)"

Fig. 2

Conceptual graphs of underwater sound insulation design: (a) scheme; (b) demonstration; (c) process of inverse design for chiral metamaterials using our topology optimization (color online)"

Table 1

Parameters of used materials"

Fig. 3

Configurations of initial solutions in local coordinate system: (a) initial solution 1; (b) initial solution 2; (c) initial solution 3 (color online)"

Fig. 4

Relevant schematic diagrams of optimized chiral lattices S1—S4 and their unit cells C1—C4 (color online)"

Table 2

Relevant parameters and optimization conditions of S1—S4"

Fig. 5

Relevant schematic diagrams of optimized results: (a) comparison of stiffness and acoustic impedance between initial solutions and S1—S4; (b) iterative process of C1; (c) iterative curve of normalized equivalent parameters of S1, where "Iter." represents iteration (color online)"

Fig. 6

Effects of principal direction angles, initial solutions, and stiffness constraints on equivalent parameters of optimized chiral lattices (color online)"

Fig. 7

Schematic diagrams related to simulations: (a) finite element analysis model; (b) M1—M4 (color online)"

Table 3

Relevant parameters of M1—M4"

Fig. 8

Numerical simulation predictions of STL: (a) M1, EHM1, and SQL1; (b) M2, EHM2, and SQL2; (c) M3, EHM3, and SQL3, M4, EHM4, and SQL4; (d) effect of cover plate on STL of M2 (color online)"

Fig. 9

Distributions of acoustic pressure, acoustic pressure field, and particle velocity field with propagation position of sound waves before and after passing through SQL1 and M1 in water domain (color online)"

Fig. 10

Contour maps of STL versus frequency and incident angle θi: (a) SQL1; (b) M1; (c) M3; (d) M4 (color online)"

Table 4

Equivalent elastic constants of L1—L4 Unit: MPa"

Fig. 11

Comparison of equivalent parameters for square lattices and optimized chiral lattices: (a) Zs/Zw; (b) cqL/cw; (c) cqL/cqT; (d) |tan θqL| (color online)"

Fig. 12

Schematic diagrams and STL for scaled-up M1 and M2, as well as photos and relevant experimental results of mechanical specimens (color online)"

Fig. 13

Schematic diagrams of underwater sound insulation test: (a) experimental setup; (b) photo of acoustic specimen 1 and its numerical and experimental results of STL; (c) photo of acoustic specimen 2 and its numerical and experimental results of STL (color online)"