Bandgap characteristics analysis and graded design of a novel metamaterial for flexural wave suppression

doi:10.1007/s10483-025-3204-7

Abstract

Abstract:

A novel elastic metamaterial is proposed with the aim of achieving low-frequency broad bandgaps and bandgap regulation. The band structure of the proposed metamaterial is calculated based on the Floquet-Bloch theorem, and the boundary modes of each bandgap are analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the metamaterials with a low elastic modulus of ligaments can generate flexural wave bandgaps below 300 Hz. Multi-frequency vibrations can be suppressed through the selective manipulation of bandgaps. The dual-graded design of metamaterials that can significantly improve the bandgap width is proposed based on parametric studies. A new way that can regulate the bandgap is revealed by studying the graded elastic modulus in the substrate. The results demonstrate that the nonlinear gradient of the elastic modulus in the substrate offers better bandgap performance. Based on these analyses, the proposed elastic metamaterials can pave the way for multi-frequency vibration control, low-frequency bandgap broadening, and bandgap tuning.

Key words: metamaterial, flexural wave bandgap, local resonance, graded design

2010 MSC Number:

O421⁺.5

Fan YANG, Zhaoyang MA, Xingming GUO. Bandgap characteristics analysis and graded design of a novel metamaterial for flexural wave suppression. Applied Mathematics and Mechanics (English Edition), 2025, 46(1): 1-24.

TrendMD

Figures/Tables 19

Fig. 1

Table 1

Geometric parameters of the unit cell"

Parameter	$l b / m$	$h b / m$	$l e / m$	$h e / m$	$l L / m$	$h L / m$	$R t / m$	$R L / m$
Value	0.055	0.01	0.005	0.01	0.008	0.001	0.005	0.003

Table 1

Table 2

Material parameters of the unit cell"

Material	$ρ / (kg ⋅ m − 3)$	$E / Pa$	$ν$
Substrate	2 700	$7 × 1010$	0.33
Elastic block	100	$2.1 × 106$	0.46
Ligament	100	Varying	0.33

Table 2

Fig. 2

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