Fig.?1

Schematic diagram of wave propagation through a TPMS-SCS with radius R, thickness h, and core thickness hc under the excitation of an acoustic wave at an incident angle (color online)"

Fig.?2

Front view of acoustic propagation on different architectures of a TPMS lattice structure, including (a) G, (b) P, and (c) IWP, incorporated into a sandwich cylinder (color online)"

Table?1

Mechanical properties of different architectures of a TPMS lattice structure"

TPMS unit cell	TPMS property
	E=E^{\text{m}}\{\begin{array}{l}0.317V^{1.264}\mathrm{,}V⩽0.25\hfill \\ 1.007V^{2.006}-\mathrm{0.007,}V>0.25\hfill \end{array}
	G=G^{\text{m}}\{\begin{array}{l}0.705V^{1.189}\mathrm{,}V⩽0.25\hfill \\ 0.953V^{1.715}+\mathrm{0.047,}V>0.25\hfill \end{array}
	\nu =\{\begin{array}{l}0.314{\text{e}}^{-1.004V}+\mathrm{0.119,}V⩽0.55\hfill \\ 0.152V^2-0.235V+\mathrm{0.383,}V>0.55\hfill \end{array}
	E=E^{\text{m}}\{\begin{array}{l}0.596V^{1.467}\mathrm{,}V⩽0.45\hfill \\ 0.962V^{2.006}+\mathrm{0.038,}V>0.45\hfill \end{array}
	G=G^{\text{m}}\{\begin{array}{l}0.777V^{1.544}\mathrm{,}V⩽0.45\hfill \\ 0.973V^{1.982}+\mathrm{0.027,}V>0.45\hfill \end{array}
	\nu =\{\begin{array}{l}0.192{\text{e}}^{-1.349V}+\mathrm{0.202,}V⩽0.50\hfill \\ 0.402V^2-0.603V+\mathrm{0.501,}V>0.50\hfill \end{array}
	E=E^{\text{m}}\{\begin{array}{l}0.597V^{1.225}\mathrm{,}V⩽0.35\hfill \\ 0.987V^{1.782}+\mathrm{0.013,}V>0.35\hfill \end{array}
	G=G^{\text{m}}\{\begin{array}{l}0.529V^{1.287}\mathrm{,}V⩽0.35\hfill \\ 0.960V^{2.188}+\mathrm{0.040,}V>0.35\hfill \end{array}
	\nu =\{\begin{array}{l}2.597{\text{e}}^{-0.157V}-\mathrm{2.244,}V⩽0.13\hfill \\ 0.201V^2-0.227V+\mathrm{0.326,}V>0.13\hfill \end{array}

Fig.?3

Convergence checking diagram for determining the acoustic response of a TPMS-SCS"

Fig.?4

Analytical and numerical vibroacoustic responses of the current approach based on a sandwich cylinder without a TPMS core, compared with the acoustic results of Ref. [65] (color online)"

Fig.?5

Analytical and numerical vibroacoustic responses of the current approach based on a sandwich cylinder without a TPMS core, compared with the acoustic results of Refs. [66]–[68] (color online)"

Table?2

Frequency responses (unit: Hz) of a single-layer cylinder based on the analytical (FSDT and TSDT) and numerical (FE) analyses compared with those provided by Ref. [69], considering E=200 GPa, ρ=7 760 kg/m3, ν=0.3, and R=1"

Table?3

Frequency responses of a single-layer cylinder based on the analytical (FSDT and TSDT) and numerical (FE) analyses compared with those provided by Ref. [70], considering E=72 GPa, ρ=2 760 kg/m3, ν=0.3, and R=1"

Table?4

Frequency responses (unit: Hz) of a TPMS-SCS with respect to various modes and TPMS architectures based on the analytical (FSDT and TSDT) analyses compared with those provided by the numerical FE approach, considering E=70 GPa, ρ=2 760 kg/m3, ν=0.33, R=1.5 m, hc=0.01 m, h=0.012 m, and dr=35%"

Fig.?6

Effects of different architectures of a TPMS-based lattice foam on the acoustic behavior of a TPMS-SCS, showing (a) the entire and (b) specific frequency domains (color online)"

Fig.?7

Analytical STL results of the G-type sandwich cylindrical system against its corresponding numerical outcomes and position illustration of some important frequencies (color online)"

Fig.?8

Analytical STL results of the P-type sandwich cylindrical system against its corresponding numerical outcomes (color online)"

Fig.?9

Analytical STL results of the IWP-type sandwich cylindrical system against its corresponding numerical outcomes (color online)"

Fig.?10

A sandwich cylinder exposed to different mesh illustrations of a TPMS-based lattice metamaterial according to its COMSOL model (color online)"

Fig.?11

The COMSOL acoustic model of a sandwich cylinder exposed to a TPMS core (color online)"

Fig.?12

Illustrating the varying impact of the RD ratio on the sound insulation performance of a TPMS-SCS with respect to (a) G-type, (b) P-type, and (c) IWP-type TPMS lattice structures (color online)"

Fig.?13

Vibroacoustic responses of a TPMS-based sandwich cylinder subject to (a) G-type, (b) P-type, and (c) IWP-type TPMS architectures against the STL spectra of a simple cylinder without a core based on the equal mass and a TPMS-SCS with increased core thickness (color online)"