Analysis and optimization of bandgaps in plate-type metastructures with different configurations

doi:10.1007/s10483-026-3374-8

Abstract

Abstract:

Several types of acoustic metamaterial (AM) plates have been developed to achieve low-frequency and wide bandgaps, which are adjusted by their geometric configurations and material properties. This paper combines the classical plate theory and the characteristics of piezoelectric materials, and uses the plane wave expansion method (PWEM) to derive the bandgap theoretical model of plate-type metastructures. The dispersion curves of the structures composed of elastic materials, piezoelectric materials, and functionally graded (FG) materials are compared and studied, and verified with the finite element simulation results. Then, the effects of temperatures, piezoelectric parameters, scatterer shapes, scatterer distributions, scatterer tapers, rubber layers, and spiral groove configurations on the bandgap of plate-type metastructures are discussed, and the material and geometric parameters are optimized with the genetic algorithm (GA). This study provides a reference for the design of low-frequency broadband structures.

Key words: plate-type metastructure, plane wave expansion method (PWEM), bandgap, optimization

2010 MSC Number:

O347

Fenglian LI, Yin ZHU, Junhui YAN. Analysis and optimization of bandgaps in plate-type metastructures with different configurations. Applied Mathematics and Mechanics (English Edition), 2026, 47(4): 839-858.

TrendMD

Figures/Tables 25

Fig. 1

Table 1

Parameters of different elastic materials"

Matrix				Scatterer
Material	$ρ / (kg ⋅ m − 3)$	E/Pa	μ	Material	$ρ / (kg ⋅ m − 3)$	E/Pa	μ
Polytetrafluoroethylene	2 200	$0.4 × 109$	0.39	Aurum	19 500	$8.75 × 1010$	0.30
Epoxy	1 180	$0.432 × 109$	0.368	Titanium	4 500	$11.6 × 1010$	0.32
Nylon	1 160	$3 × 109$	0.31	Molybdenum	10 280	$33 × 1010$	0.25
Polyethylene	960	$0.6 × 109$	0.43	Chromium	7 190	$27.9 × 1010$	0.30

Table 1

Fig. 2

Fig. 3

Fig. 4

Table 2

Piezoelectric material parameters"

Material	$ρ / (kg ⋅ m − 3)$	$s 11 / Pa − 1$	$s 12 / Pa − 1$	$d 31 / (C ⋅ N − 1)$	$ε 33$
Matrix (PZT-5J)	7 400	$1.62 × 10 − 11$	$− 4.54 × 10 − 12$	$− 2.2 × 10 − 10$	$2.3 × 10 − 8$
Scatterer (PZT-5A)	7 750	$1.64 × 10 − 11$	$− 5.74 × 10 − 12$	$− 1.71 × 10 − 10$	$1.5 × 10 − 8$

Table 2

Fig. 5

Fig. 6

Fig. 7

Table 3

Variations of piezoelectric material parameters for the matrix and scatterer"

Material	Parameter	Group 1	Group 2	Group 3	Group 4	Group 5
Scatterer	$s 11 / Pa − 1$	$1.62 × 10 − 13$	$1.62 × 10 − 12$	$1.62 × 10 − 11$	$1.62 × 10 − 10$	$1.62 × 10 − 9$
Scatterer	$s 12 / Pa − 1$	$− 5.74 × 10 − 14$	$− 5.74 × 10 − 13$	$− 5.74 × 10 − 12$	$− 5.74 × 10 − 11$	$− 5.74 × 10 − 10$
Matrix	$s 11 / Pa − 1$	$1.22 × 10 − 11$	$1.42 × 10 − 11$	$1.62 × 10 − 11$	$1.82 × 10 − 11$	$2.02 × 10 − 11$
	$s 12 / Pa − 1$	$− 4.14 × 10 − 12$	$− 4.34 × 10 − 12$	$− 4.54 × 10 − 12$	$− 4.74 × 10 − 12$	$− 4.94 × 10 − 12$

Table 3

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Table 4

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Fig. 17

Table 5

Fig. 18

Table 6

Material parameter optimization"

Parameter	$ρ 1 / (kg ⋅ m − 3)$	$ρ 2 / (kg ⋅ m − 3)$	E₁/Pa	E₂/Pa
Optimization range	[15 000, 25 000]	[500, 3 000]	$[8, 800] × 109$	$[0.4, 40] × 109$
After optimization	25 000	3 000	$8 × 109$	$0.4 × 109$

Table 6

Fig. 19

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Scatter taper
Band structure
Bandgap coverage/%	18.05	16.48	2.07