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research-article

Elastic wave propagation in hierarchical honeycombs with woodpile-like vertexes

[+] Author and Article Information
Zhiwei Zhu

School of Mechanical Engineering and Mechanics, NingBo University, NingBo 315211, China NingBo, 315211 China zhuzhiwei@nbu.edu.cn

Zichen Deng

127 Youyi Xilu Xi'an, Not Applicable 710072 China dweifan@nwpu.edu.cn

Jianke Du

Fenghua Road No.818 Jiangbei District Ningbo city, Zhengjiang provience 315211 China dujianke@nbu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received April 29, 2018; final manuscript received March 20, 2019; published online xx xx, xxxx. Assoc. Editor: A. Srikantha Phani.

ASME doi:10.1115/1.4043352 History: Received April 29, 2018; Accepted March 26, 2019

Abstract

This paper investigates the dispersion behavior of elastic wave propagation in hierarchical honeycombs using the finite element method in conjunction with Bloch's theorem. The hierarchical honeycomb is constructed by replacing each vertex of a regular hexagonal honeycomb with smaller hexagons stacked in a woodpile pattern. Band structure analysis reveals that, in the considered range of frequency, the maximum band gap for the hierarchical honeycomb is localized in the frequency corresponding to the natural vibration frequency of the cell strut, and moreover, the width of this particular gap is significantly broadened as the order of hierarchy increases. In addition, for the hierarchical honeycombs satisfying an invariable ratio between the thickness and squared length of the cell strut, which is extracted from the expression of the natural frequency of the simply supported element beam, a coincidence among dispersion curves (or contours) for the hierarchical configurations with the same scale order, occurs. The resulting identical band gaps as well as the quasi-static phase wave velocities provide an advantage or the hierarchical honeycombs in the manipulation of vibration and associated multifunction designs.

Copyright © 2019 by ASME
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