A nonlinear damping absorber for broadband and multi-directional vibration suppression

doi:10.1007/s10483-026-3395-9

摘要/Abstract

Abstract:

Most existing vibration absorbers are limited by the need for precise tuning, and are difficult to suppress broadband vibration. A nonlinear damping absorber (NDA) is proposed in this paper to control the vibrations of structures in multiple modes, providing nonlinear damping in multiple directions and enabling broadband and multi-directional vibration suppression. A pipe is selected as the research object to analyze its dynamic behaviors and vibration suppression mechanisms. The vibration reduction performance of the NDA on the in-plane vibration and out-of-plane vibration of the pipe is studied through experimentation and theory. First, the configuration of the NDA is designed, and its mechanical model is established. An experimental platform is built for the parameter identification and multi-directional vibration reduction test of the absorber. Second, based on the generalized Hamilton’s principle, the mechanical model describing the in-plane vibration and out-of-plane vibration of the pipe with the NDAs is derived. The approximate solution of the nonlinear response is derived and numerically validated. The multi-directional and multi-modal vibration reduction efficiency of the NDAs for the structures is analyzed. The research results show that the proposed absorber can significantly control the multi-directional vibration. Nonlinear damping effectively broadens the vibration reduction bandwidth, and improves the damping efficiency, with the cubic term playing the dominant role. Finally, a concept of multi-modal weighted optimization is proposed. The absorber parameters are optimized through the particle swarm optimization (PSO) algorithm. This paper provides a new type of absorbers for the vibration control of multiple directions in broadband.

Key words: absorber, nonlinear damping, multi-directional vibration, vibration control

中图分类号:

O322

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(6): 1301-1322.

Haiting ZHENG, Hu DING, J. C. JI. A nonlinear damping absorber for broadband and multi-directional vibration suppression[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(6): 1301-1322.

图/表 19

Parameter	Symbol	Value	Unit
Mass of the oscillator	m	0.3	kg
Linear stiffness	k₁	$1.14 × 105$	N/m
Linear damping	c₁	6.6	N·s/m
Square nonlinear damping	c₂	$− 453.3$	N·s²/m²
Cubic nonlinear damping	c₃	$− 4.8 × 105$	N·s³/m³

Parameter	Symbol	Value	Unit
Mass of the oscillator	m	0.3	kg
Linear stiffness	K₁	$1.40 × 106$	N/m
Linear damping	C₁	7.62	N·s/m
Square nonlinear damping	C₂	$− 434.9$	N·s²/m²
Cubic nonlinear damping	C₃	$1.44 × 105$	N·s³/m³

Parameter	Symbol	Value	Unit
Pipe length	L	2.2	m
Inner diameter	d	$5 × 10 − 2$	m
Outer diameter	D	$6 × 10 − 2$	m
Pipe density	ρ	7 850	kg/m³
Young’s modulus	E	210	GPa
Damping coefficient of in-plane vibration	c_w	5	N·s/m
Damping coefficient of out-of-plane vibration	c_v	5	N·s/m
Spring stiffness	K	$1 × 106$	N/m
Acceleration amplitude	A_a	1.6	m/s²
Angle of inclination	θ	45	°

Parameter	Symbol	Value	Unit
Mass of the oscillator	m	0.3	kg
Linear stiffness	k₁	$1.14 × 105$	N/m
Linear damping	c₁	6.6	N·s/m
Square nonlinear damping	c₂	0	N·s²/m²
Cubic nonlinear damping	c₃	0	N·s³/m³

Parameter	Symbol	Value	Unit
Mass of the oscillator	m	0.3	kg
Linear stiffness	K₁	$1.40 × 106$	N/m
Linear damping	C₁	7.62	N·s/m
Square nonlinear damping	C₂	0	N·s²/m²
Cubic nonlinear damping	C₃	0	N·s³/m³

Parameter	Symbol	Value
Population size	M	40
Maximum iteration	$n iter, max$	70
Maximum inertia weight	$ω max$	0.9
Minimum inertia weight	$ω min$	0.4
Individual learning factor	$γ 1$	1.5
Group learning factor	$γ 2$	1.7
Penalty coefficient	α	1

Parameter	Symbol	Value	Unit
Linear stiffness of NDA1	k₁	$8.32 × 104$	N/m
Linear damping of NDA1	c₁	7.17	N·s/m
Square nonlinear damping of NDA1	c₂	297.46	N·s²/m²
Cubic nonlinear damping of NDA1	c₃	$5.81 × 105$	N·s³/m³
Linear stiffness of NDA2	K₁	$1.46 × 106$	N/m
Linear damping of NDA2	C₁	8.93	N·s/m
Square nonlinear damping of NDA2	C₂	500.72	N·s²/m²
Cubic nonlinear damping of NDA2	C₃	$1.11 × 105$	N·s³/m³

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