Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

doi:10.1007/s10483-024-3168-7

Applied Mathematics and Mechanics (English Edition) ›› 2024, Vol. 45 ›› Issue (10): 1841-1856.doi: https://doi.org/10.1007/s10483-024-3168-7

• • 上一篇

收稿日期:2024-03-29 出版日期:2024-10-03 发布日期:2024-09-27

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

Xingjian DONG¹^,*(), Shuo WANG²^,³, Anshuai WANG²^,³, Liang WANG²^,³, Zhaozhan ZHANG²^,³, Yuanhao TIE⁴, Qingyu LIN²^,³, Yongtao SUN²^,³

¹ State Key Laboratory of Mechanical Systems and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China
² Department of Mechanics, Tianjin University, Tianjin 300350, China
³ Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin University, Tianjin 300350, China
⁴ School of Mechanical and Automotive Engineering, Guangxi University of Science and Technology, Liuzhou 545006, Guangxi Zhuang Autonomous Region, China

Received:2024-03-29 Online:2024-10-03 Published:2024-09-27
Contact: Xingjian DONG E-mail:donxij@sjtu.edu.cn
Supported by:
the National Natural Science Foundation of China(12272219);the National Natural Science Foundation of China(12372019);the National Natural Science Foundation of China(12072222);the National Natural Science Foundation of China(12132010);the National Natural Science Foundation of China(12021002);the National Natural Science Foundation of China(11991032);the Open Projects of State Key Laboratory for Strength and Structural Integrity of China(ASSIKFJJ202303002);the State Key Laboratory of Mechanical Behavior and System Safety of Tra–c Engineering Structures of China(SKLTESKF1901);the Aeronautical Science Foundation of China(ASFC-201915048001);Project supported by the National Natural Science Foundation of China (Nos. 12272219, 12372019, 12072222, 12132010, 12021002, and 11991032), the Open Projects of State Key Laboratory for Strength and Structural Integrity of China (No. ASSIKFJJ202303002), the State Key Laboratory of Mechanical Behavior and System Safety of Tra–c Engineering Structures of China (No. SKLTESKF1901), and the Aeronautical Science Foundation of China (No. ASFC-201915048001)

摘要/Abstract

Abstract:

The suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch's theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169. 57 Hz to 216. 42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure's two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i. e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure's excellent low-frequency vibration suppression capability.

Key words: wave propagation, vibration suppression, metamaterial, low-frequency bandgap

中图分类号:

70J50

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(10): 1841-1856.

Xingjian DONG, Shuo WANG, Anshuai WANG, Liang WANG, Zhaozhan ZHANG, Yuanhao TIE, Qingyu LIN, Yongtao SUN. Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(10): 1841-1856.

图/表 14

参考文献 43

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Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

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