Single-phase multi-resonant metabeam for broadband reduction of multi-polarization low-frequency vibration

doi:10.1007/s10483-025-3322-9

Abstract

Abstract:

Reducing the vibration transmission in beams is of significant interest, as beams are among the most widely used basic structures in numerous practical engineering applications. However, achieving broadband suppression of multi-polarization low-frequency vibration in beams presents a challenge. This study proposes a single-phase multi-resonant metabeam, which consists of a host beam with subwavelength arrays of tunable local resonators. These resonators exhibit adjustable multi-polarization resonant modes that strongly couple with the host beam, enabling simultaneous suppression of multi-type waves over a broad frequency range. The theoretical analysis demonstrates that under the fixed total added-mass ratio ( $γ total = 1.5$ ), the tailored frequency spacing ( $δ = 25$ –50 Hz) and the controlled loss factor ( $η = 0.03$ –0.07) act synergistically to broaden bandgaps through resonant zone overlapping and attenuation peak smoothing. The experimental validation with monolithic three-dimensional (3D)-printed specimens confirms the efficacy of this design in multi-polarization vibration control within a deep-subwavelength bandgap, opening a new avenue for designing multi-polarization vibration suppression structures.

Key words: metastructure, vibration suppression, metabeam, bandgap, multi-polarization

2010 MSC Number:

O421⁺.5

Yongzhe LI, Yongqiang LI, Gaoge LIANG, Quanxing LIU, Yong XIAO. Single-phase multi-resonant metabeam for broadband reduction of multi-polarization low-frequency vibration. Applied Mathematics and Mechanics (English Edition), 2025, 46(12): 2265-2280.

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Figures/Tables 11

Fig. 1

Fig. 2

Table 1

Mechanical properties of the resin (3D-printing material)"

$E$ /GA	$ρ$ / $(kg ⋅ m − 3)$	$ν$
2.6	1 120	0.4

Table 1

Table 2

Geometric parameters of an example metabeam"

Number	$h 1$ /mm	$h 2$ /mm	$θ$ /(°)	$d 1$ /mm	$d 2$ /mm	$f F$ /Hz	$f L$ /Hz
1	13.1	12.3	34.8	2.4	2.4	170	240
2	12.9	11.1	28	2.4	2.4	207	271
3	13.5	10.4	12	2.4	2.4	265	315
4	12.7	8.9	9.6	2.4	2.4	330	367
5	12.2	5.7	8	2.4	2.4	525	437

Table 2

Fig. 3

Fig. 4

Table 3

Parameters of three configurations with different frequency spacings"

Configuration	Mass ratio $γ i = m i / (ρ A a)$	Frequency rule (radial/axial)	$γ total$
$δ = 0$ Hz	(0.300, 0.300, 0.300, 0.300, 0.300)	$f F i = f L i = 300$ (all resonators)	1.5
$δ = 25$ Hz	(0.105, 0.165, 0.240, 0.390, 0.600)	$f F i = f L i = 325 + 25 (i − 3)$	1.5
$δ = 50$ Hz	Same as $δ = 25$ Hz	$f F i = f L i = 325 + 50 (i − 3)$	1.5

Table 3

Fig. 5

Fig. 6

Fig. 7

Fig. 8

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