Improved dynamic anti-resonance vibration isolator based on a Halbach array negative stiffness mechanism

doi:10.1007/s10483-026-3387-9

Abstract

Abstract:

To concurrently achieve low-frequency vibration absorption and high-frequency vibration isolation in high-static-stiffness applications, this study proposes a hybrid passive vibration isolator that integrates a lever mechanism with a Halbach array negative stiffness mechanism. The lever mechanism reduces the natural frequency by increasing the system’s effective mass and introduces an anti-resonance frequency. Additionally, the negative stiffness amplified by the lever counteracts the positive stiffness, leading to the substantial reduction in the dynamic stiffness with only a small amount of negative stiffness required. Both theoretical and experimental results indicate that the synergistic integration facilitates the broad isolation bandwidth and effective low-frequency absorption while keeping the added mass minimal and the negative stiffness low. The comparative analysis of several magnetic array configurations demonstrates that, when the isolator dimensions and added mass are held constant, the Halbach array configuration reduces both resonance and anti-resonance frequencies while preserving high-frequency transmissibility. The integrated strategy enables the development of a compact and lightweight isolator, providing an effective solution for low-frequency vibration suppression in scenarios where mass and space are limited.

Key words: lever mechanism, Halbach array, low-frequency vibration absorption, high-frequency vibration isolation, high-static-stiffness application

2010 MSC Number:

O328

Jialei DENG, Xinhua LONG. Improved dynamic anti-resonance vibration isolator based on a Halbach array negative stiffness mechanism. Applied Mathematics and Mechanics (English Edition), 2026, 47(5): 941-964.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-026-3387-9

https://www.amm.shu.edu.cn/EN/Y2026/V47/I5/941

Figures/Tables 23

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Table 1

Fig. 7

Table 2

Fitting stiffness coefficients"

Array type	$k 1 / (N ⋅ m − 1)$	$k 3 / (N ⋅ m − 3)$	$k 5 / (N ⋅ m − 5)$
Array 1 NSM	$− 4.358 8 × 103$	$6.514 1 × 107$	$− 2.929 3 × 1011$
Array 2 NSM	$− 0.807 3 × 103$	$5.243 9 × 107$	$− 1.945 3 × 1010$
Halbach array NSM	$− 5.889 1 × 103$	$4.277 8 × 107$	$− 1.670 7 × 1011$

Table 2

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Table 3

Calculation parameters"

Parameter	Array 1	Array 2	Halbach
$μ s$	0.025	0.025	0.025
ξ	0.03	0.03	0.03
α	2.12	2.12	2.12
η	$− 0.148$	$− 0.027$	$− 0.200$
γ	$− 1.494 × 104 η$	$− 6.496 × 103 η$	$− 7.264 × 103 η$
δ	$6.721 × 107 η$	$2.410 × 107 η$	$2.837 × 107 η$

Table 3

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Table 4

Fig. 17

Fig. 18

Fig. 19

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Magnet type	Length/mm	Width/mm	Hight/mm	Number
PM 1#	15	15	5	8
PM 2#	15	5	5	12

Magnet type	Length/mm	Width/mm	Hight/mm	Mass/mm	Number
PM 1#	10	10	5	3.7	8
PM 2#	10	5	3	1.1	12