A lattice metamaterial-based sandwich cylindrical system for numerical simulation approach of vibroacoustic transmission considering triply periodic minimal surface

doi:10.1007/s10483-025-3314-9

摘要/Abstract

Abstract:

This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system (TPMS-SCS) for the first time. Although these structures exhibit outstanding physical and mechanical properties, their dynamic and acoustic features have not been reported yet. This study addresses this gap by calculating the sound transmission loss (STL) coefficient within the framework of the wave approach across various architectures, including the primitive (P), Schoen gyroid (G), and wrapped package-graph (IWP) of a TPMS lattice structure. To determine an analytical STL, a third-order approach is used to precisely capture the stress-strain distribution based on the thickness coordinate, thereby providing a simultaneous solution to the general characteristic relations along with fluid-structure coupling. Given the lack of studies for frequency and STL comparisons, the structure is modeled considering a finite element (FE) design, which is a challenging and time-consuming process because of the complex topological TPMS configurations incorporated within a sandwich cylinder. In fact, achieving convincing computational accuracy requires fine mesh discretization, which significantly increases computational costs during vibroacoustic analysis. Using the numerical results from the COMSOL software Multiphysics, the accuracy of the analytical STL spectrum is verified for different configurations, including P, G, and IWP. The effective acoustic specifications of a TPMS-SCS in the frequency domain are examined by the comparison of the STL with that of a simple cylinder of the same mass. In this context, it would also be beneficial to examine the effect of TPMS thickness, which can demonstrate the importance of the present results. The findings of this approach can be beneficial for scholars working on the numerical and analytical sound insulation characteristics of metamaterial-based cylindrical systems.

Key words: lattice structure, vibration transmission, triply periodic minimal surface (TPMS), finite element (FE), wave propagation

中图分类号:

O242

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(11): 2035-2054.

M. R. ZARASTVAND, E. ABDOLI, R. TALEBITOOTI. A lattice metamaterial-based sandwich cylindrical system for numerical simulation approach of vibroacoustic transmission considering triply periodic minimal surface[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(11): 2035-2054.

图/表 17

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

Mode number		$h = 0.1$ m
$n$	$m$	Present (FSDT)	Present (TSDT)	Present (FEM)	Ref. [69]
1	1	72.644 73	72.644 12	76.732	73.677
	2	69.004 88	68.970 36	67.675	72.173
	3	173.617 80	173.402 80	170.430	185.225
2	1	229.302 30	229.308 60	221.580	216.623
	2	120.912 30	120.884 30	120.990	120.913
	3	192.263 70	192.027 00	196.780	199.648
3	1	397.873 80	397.915 80	393.560	–
	2	212.471 80	212.465 10	207.660	204.569
	3	230.810 30	230.556 00	221.900	232.400
4	1	534.628 00	534.772 80	539.320	–
	2	319.144 90	319.186 80	320.790	–
	3	289.775 80	289.519 80	276.000	283.744

Mode number	$h = 0.05$ m
Mode number	Present (FSDT)	Present (TSDT)	Present (FEM)	Ref. [70]
6	12.413 91	12.413 86	–	12.452 6
7	17.560 82	17.558 50	–	17.139 4
8	24.023 92	24.021 90	24.350	22.548 4
9	–	–	–	28.679 2
10	39.630 23	39.628 84	35.075	35.531 7
11	45.108 14	45.108 08	46.378	43.105 6
12	49.335 35	49.319 96	52.688	51.401 4
13	60.580 89	60.565 40	60.203	60.418 5
14	71.758 04	71.743 48	75.372	70.157 0
15	86.546 02	86.533 15	84.580	80.617 4
16	90.883 61	90.833 16	95.924	91.798 4
17	104.273 30	104.262 90	104.880	103.701 3
18	120.135 90	120.139 60	116.050	116.325 7
19	124.154 30	124.147 40	136.940	129.671 2
20	139.935 80	139.937 10	141.500	143.738 3
21	151.424 90	151.432 60	160.810	158.527 8
22	–	–	169.880	174.037 2
23	190.502 50	190.506 00	190.140	190.268 4
24	213.909 50	213.642 90	206.040	207.221 9
25	–	–	225.030	224.895 2

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Mode	TPMS	Present (FSDT)	Present (TSDT)	Present (FEM)	RE/%
(1,1)	G	146.342 60	146.342 60	145.440	0.62
	P	146.342 60	146.342 60	147.040	-0.71
	IWP	146.342 60	146.342 60	146.020	0.22
(1,2)	G	497.599 70	497.599 70	497.330	0.05
	P	497.599 70	497.599 70	496.710	0.17
	IWP	497.599 70	497.599 70	498.800	-0.24
(2,1)	G	46.280 95	46.280 93	49.285	-6.09
	P	46.280 95	46.280 93	49.717	-6.91
	IWP	46.280 95	46.280 93	49.497	-6.49
(2,2)	G	177.689 20	177.689 20	177.880	-0.10
	P	177.689 20	177.689 20	178.310	-0.34
	IWP	177.689 20	177.689 20	176.510	0.66
(1,3)	G	912.756 80	912.756 90	912.170	0.06
	P	912.756 80	912.756 90	912.360	0.04
	IWP	912.756 80	912.756 90	912.340	0.04
(3,1)	G	22.554 70	22.554 68	23.254	-3.00
	P	22.554 70	22.554 68	23.350	-3.40
	IWP	22.554 70	22.554 68	23.299	-3.19