An innovative nonlinear bionic X-shaped vibration isolator enhanced by quasi-zero stiffness characteristics: theory and experimental investigation

doi:10.1007/s10483-025-3277-8

Abstract

Abstract:

Bionic X-shaped vibration isolators have been widely employed in aerospace and other industrial fields, but the stiffness properties of classic X-shaped structures limit the vibration isolation ability for low frequencies. An innovative bionic quasi-zero stiffness (QZS) vibration isolator (BQZSVI), which can broaden the QZS range of a classic X-shaped isolator and can bring it closer to the equilibrium position, is proposed. The BQZSVI consists of an X-shaped structure as the bone fabric of lower limbs and a nonlinear magnetic loop device simulating the leg muscle. Based on static calculation, the stiffness characteristic of the structure is confirmed. The governing equations of motion of the BQZSVI structure are established in the framework of the Lagrange equation, and the harmonic balance method (HBM) is adopted to obtain the transmissibility responses. The results show that the BQZSVI can provide a more accessible and broader range of QZS. In the dynamic manifestation, the introduction of the BQZSVI can reduce the amplitude of a classic X-shaped vibration isolator by 65.7%, and bring down the initial vibration isolation frequency from 7.43 Hz to 2.39 Hz. In addition, a BQZSVI prototype is designed and fabricated, and the exactitude of the theoretical analysis method is proven by means of experiments.

Key words: bionic quasi-zero stiffness (QZS), X-shaped structure, magnetic loop device, vibration isolation, dynamic property

2010 MSC Number:

O322

Zeyu CHAI, Zhen ZHANG, Kefan XU, Xuyuan SONG, Yewei ZHANG, Liqun CHEN. An innovative nonlinear bionic X-shaped vibration isolator enhanced by quasi-zero stiffness characteristics: theory and experimental investigation. Applied Mathematics and Mechanics (English Edition), 2025, 46(8): 1475-1492.

TrendMD

Figures/Tables 18

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Table 1

The primary parameters of BQZSVI system"

Parameter	Value	Unit
Bionic connecting rod length $l$	0.2	m
The number of bionic quadrilateral layers $n$	2
The installation angle $θ$	$π / 3$
Equivalent positive stiffness $k 1$	300	N/m
Equivalent nonlinear stiffness $k 2$	$2 × 106$	N/m³
Damping $c 1$	1.5	N·s/m
Vibration isolation object mass $m 1$	2	kg

Table 1

Fig. 8

Table 2

Fig. 9

Table 3

Performance comparison under different masses"

Parameter	Linear isolator	Classic X-shaped isolator	BQZSVI
Resonance peak value (transmissibility, $m 1 = 1$ kg)	35.92	31.11	10.15
Resonance frequency ( $m 1 = 1$ kg)/Hz	8.57	7.42	2.40
Initial vibration isolation frequency ( $m 1 = 1$ kg)/Hz	12.13	10.50	3.38
Resonance peak value (transmissibility, $m 1 = 1.5$ kg)	43.98	38.09	12.65
Resonance frequency ( $m 1 = 1.5$ kg)/Hz	7.00	6.06	2.00
Initial vibration isolation frequency ( $m 1 = 1.5$ kg)/Hz	9.90	8.57	2.75
Resonance peak value (transmissibility, $m 1 = 2$ kg)	50.78	43.97	15.08
Resonance frequency ( $m 1 = 2$ kg)/Hz	6.06	5.25	1.80
Initial vibration isolation frequency ( $m 1 = 2$ kg)/Hz	8.57	7.43	2.39

Table 3

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

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