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

作　　者：Xingjian DONG Shuo WANG Anshuai WANG Liang WANG Zhaozhan ZHANG Yuanhao TIE Qingyu LIN Yongtao SUN 

机构地区：[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

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第10期1841-1856,共16页应用数学和力学（英文版）

基　　金：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 Traffic Engineering Structures of China(No.SKLTESKF1901);the Aeronautical Science Foundation of China(No.ASFC-201915048001)。

摘　　要：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 ofθ,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 reducingθis 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.

关 键 词：wave propagation vibration suppression METAMATERIAL low-frequency bandgap 

分 类 号：O321[理学—一般力学与力学基础]