An origami-inspired nonlinear energy sink: design, modeling, and analysis

doi:10.1007/s10483-025-3239-6

Abstract

Abstract:

Designing, modeling, and analyzing novel nonlinear elastic elements for the nonlinear energy sink (NES) have long been an attractive research topic. Since gravity is difficult to overcome, previous NES research mainly focused on horizontal vibration suppression. This study proposes an origami-inspired NES. A stacked Miura-origami (SMO) structure, consisting of two Miura-ori sheets, is adopted to construct a nonlinear elastic element. By adjusting the initial angle and the connecting crease torsional stiffness, the quasi-zero stiffness (QZS) and load-bearing capacity can be customized to match the corresponding mass, establishing the vertical SMO-NES. The dynamic model of the SMO-NES coupled with a linear oscillator (LO) is derived for vibrations in the vertical direction. The approximate analytical solutions of the dynamic equation are obtained by the harmonic balance method (HBM), and the solutions are verified numerically. The parameter design principle of the SMO-NES is provided. Finally, the vibration reduction performance of the SMO-NES is studied. The results show that the proposed SMO-NES can overcome gravity and achieve quasi-zero nonlinear restoring force. Therefore, the SMO-NES has the ability of wide-frequency vibration reduction, and can effectively suppress vertical vibrations. By adjusting the initial angle and connecting the crease torsional stiffness of the SMO, the SMO-NES can be achieved with different loading weights, effectively suppressing the vibrations with different primary system masses and excitation amplitudes. In conclusion, with the help of popular origami structures, this study proposes a novel NES, and starts the research of combining origami and NES.

Key words: nonlinear energy sink (NES), stacked Miura-origami (SMO), vertical vibration, quasi-zero stiffness (QZS)

2010 MSC Number:

O322

Youcheng ZENG, Hu DING, J. C. JI. An origami-inspired nonlinear energy sink: design, modeling, and analysis. Applied Mathematics and Mechanics (English Edition), 2025, 46(4): 601-616.

TrendMD

Figures/Tables 16

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Table 1

Five different initial angles θA0 and the corresponding crease torsional stiffness kC and loading weight G"

$θ A 0$	$− 30 π / 180$	$− 40 π / 180$	$− 50 π / 180$	$− 60 π / 180$	$− 70 π / 180$
$k C$ /( $N ⋅ rad − 1 ⋅ m − 1$ )	0.122	0.296	0.538	0.863	1.378
$G$ /N	0.515	1.366	2.932	5.556	10.21
Schematic diagram

Table 1

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Table A1

Geometric parameters of the SMO[44]"

Parameter	Value	Unit
$a A$	38	mm
$a B$	73.4	mm
$b$	38	mm
$γ A$	$π / 3$	rad
$γ B$	$5 π / 12$	rad
$k A$	0.03	$N ⋅ rad − 1 ⋅ m − 1$
$k B$	1	$N ⋅ rad − 1 ⋅ m − 1$
$k C$	0.865	$N ⋅ rad − 1 ⋅ m − 1$

Table A1

Table A2

Results of the polynomial fitting for the nonlinear restoring force coefficients"

Symbol	Value	Unit
$G$	5.556	N
$B 1$	3.727	$N ⋅ m − 1$
$B 2$	$− 61.650$	$N ⋅ m − 2$
$B 3$	$3.392 × 104$	$N ⋅ m − 3$
$B 4$	$1.218 × 106$	$N ⋅ m − 4$
$B 5$	$6.599 × 108$	$N ⋅ m − 5$
$B 6$	$3.370 × 1010$	$N ⋅ m − 6$
$B 7$	$5.297 × 1011$	$N ⋅ m − 7$

Table A2

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