Low-frequency vibration suppression of meta-beam withsoftening nonlinearity

doi:10.1007/s10483-025-3258-9

Abstract

Abstract:

In order to obtain a lower frequency band gap, this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor. An improved cam-roller structure is designed in this meta-beam to achieve the softening nonlinear stiffness of the local oscillators. Firstly, based on Hamilton's principle and the Galerkin method, the control equations for the coupled system are established. The theoretical band gap boundary is then derived with the modal analysis method. The theoretical results reveal that the band gap of the meta-beam shifts towards lower frequencies due to the presence of a softening nonlinear factor, distinguishing it from both linear metamaterials and those with hardening nonlinear characteristics. Then, the vibration attenuation characteristics of a finite size meta-beam are investigated through numerical calculation, and are verified by the theoretical results. Furthermore, parameter studies indicate that the reasonable design of the local oscillator parameters based on lightweight principles helps to achieve further broadband and efficient vibration reduction in the low-frequency region. Finally, a prototype of the meta-beam is fabricated and assembled, and the formations of the low-frequency band gap and the amplitude-induced band gap phenomenon are verified through experiments.

Key words: softening nonlinearity, nonlinear band gap, meta-beam, low-frequency, vibration attenuation

2010 MSC Number:

O327

Weixing ZHANG, Dongshuo YANG, Xiangying GUO. Low-frequency vibration suppression of meta-beam withsoftening nonlinearity. Applied Mathematics and Mechanics (English Edition), 2025, 46(6): 1011-1028.

TrendMD

Figures/Tables 18

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Table 1

Material parameters of the primary beam"

Item	Notation	Value
Beam length/m	$L$	0.8
Young's modulus/GPa	$E$	210
Beam density/ $(kg ⋅ m − 3)$	$ρ$	7 850
Area moment of inertia/m⁴	$I$	$2.67 × 10 − 11$
Cross-sectional area/m²	$S$	$8 × 10 − 5$

Table 1

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