0
Research Papers

Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators

[+] Author and Article Information
Yong Xiao

e-mail: xiaoy@vip.sina.com

Jihong Wen

e-mail: wenjihong@vip.sina.com

Gang Wang

e-mail: wangg@nudt.edu.cn

Xisen Wen

e-mail: wenxs@vip.sina.com
Vibration and Acoustics Research Group,
Laboratory of Science and Technology on Integrated Logistics Support,
College of Mechatronics and Automation,
National University of Defense Technology,
Changsha 410073, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 6, 2012; final manuscript received April 8, 2013; published online June 6, 2013. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 135(4), 041006 (Jun 06, 2013) (17 pages) Paper No: VIB-12-1140; doi: 10.1115/1.4024214 History: Received May 06, 2012; Revised April 08, 2013

In this paper, we present a design of locally resonant (LR) beams using periodic arrays of beam-like resonators (or beam-like vibration absorbers) attached to a thin homogeneous beam. The main purpose of this work is twofold: (i) providing a theoretical characterization of the proposed LR beams, including the band gap behavior of infinite systems and the vibration transmittance of finite structures, and (ii) providing experimental evidence of the associated band gap properties, especially the coexistence of LR and Bragg band gaps, and their evolution with tuned local resonance. For the first purpose, an analytical method based on the spectral element formulations is presented, and then an in-depth numerical study is performed to examine the band gap effects. In particular, explicit formulas are provided to enable an exact calculation of band gaps and an approximate prediction of band gap edges. For the second purpose, we fabricate several LR beam specimens by mounting 16 equally spaced resonators onto a free-free host beam. These specimens use the same host beam, but the resonance frequencies of the resonators on each beam are different. We further measure the vibration transmittances of these specimens, which give evidence of three interesting band gap phenomena: (i) transition between LR and Bragg band gaps; (ii) near-coupling effect of the local resonance and Bragg scattering; and (iii) resonance frequency of local resonators outside of the LR band gap.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

(a) Schematic diagram of the designed LR beam structure. (b) Simplified physical model.

Grahic Jump Location
Fig. 2

Schematic diagram of the separated beam-like resonator

Grahic Jump Location
Fig. 3

The approximate lumped system of the cantilever beam segment shown in Fig. 2

Grahic Jump Location
Fig. 4

One unit cell of the LR beam shown in Fig. 1(b)

Grahic Jump Location
Fig. 5

(a) Schematic diagram of a finite LR beam. (b) Numbering of the spectral beam elements and nodes.

Grahic Jump Location
Fig. 6

The driving-point dynamic stiffness of the beam-like resonator tuned at fr = 777 Hz

Grahic Jump Location
Fig. 7

(a) Schematic and (b) photograph of the experimental setup

Grahic Jump Location
Fig. 8

Complex band structure for the LR beam with resonators tuned at fr = 869 Hz. (a) 200–2000 Hz; (b) 900–960 Hz.

Grahic Jump Location
Fig. 9

The smaller attenuation constant for the LR beam with resonators tuned at fr = 869 Hz

Grahic Jump Location
Fig. 10

(a) Evolution of band gap behavior with changing total length of the beam-like resonator: 2l. (b) Closer view of the area denoted by the pane in (a).

Grahic Jump Location
Fig. 11

Attenuation constants for the LR beam with resonators tuned at fr = 1269 Hz

Grahic Jump Location
Fig. 12

(a) Analytically predicted band edge frequency curves. (b) Closer view of the area denoted by the pane in (a).

Grahic Jump Location
Fig. 13

Configuration of the finite LR beam model adopted for the finite element simulation

Grahic Jump Location
Fig. 14

Comparison between the analytically predicted (SEM) and numerically simulated (FEM) vibration transmittance FRF of the finite LR beam with resonators tuned at fr = 869 Hz

Grahic Jump Location
Fig. 15

Steady-state vibration profiles (in x–z plane) at the frequencies denoted by the points (a) A, (b) B, (c) C, and (d) D in Fig. 14

Grahic Jump Location
Fig. 16

Influence of (a) the structural length and (b) the global resonator location on the vibration transmittance of finite LR beams with resonators tuned at fr = 869 Hz

Grahic Jump Location
Fig. 17

Effects of (a) the host-beam damping and (b) the resonator damping on the band gap behavior (upper panel) and vibration transmittance (lower panel) of LR beams with resonators tuned at fr = 869 Hz

Grahic Jump Location
Fig. 18

(a) Vibration transmittance FRF and (b) smaller attenuation constant for the LR beam with resonators tuned at fr = 777 Hz

Grahic Jump Location
Fig. 19

(a) Vibration transmittance FRF and (b) smaller attenuation constant for the LR beam with resonators tuned at fr = 869 Hz

Grahic Jump Location
Fig. 20

(a) Vibration transmittance FRF and (b) smaller attenuation constant for the LR beam with resonators tuned at fr = 978 Hz

Grahic Jump Location
Fig. 21

(a) Vibration transmittance FRF and (b) smaller attenuation constant for the LR beam with resonators tuned at fr = 1110 Hz

Grahic Jump Location
Fig. 22

(a) Vibration transmittance FRF and (b) smaller attenuation constant for the LR beam with resonators tuned at fr = 1269 Hz

Grahic Jump Location
Fig. 23

Comparison of vibration transmittances for two cases of placement of the load

Grahic Jump Location
Fig. 24

Numerical and experimental vibration transmittance FRF for the modified version (aL = 105 mm) of the LR beam with resonators tuned at fr = 869 Hz

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In