0
Research Papers

A New Design Strategy for Minimizing Sound Radiation of Vibrating Beam Using Dimples

[+] Author and Article Information
W. N. Cheng

Advanced Institute of Manufacturing for High-Tech Innovations and Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan, R.O.C.

C. C. Cheng

Advanced Institute of Manufacturing for High-Tech Innovations and Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan, R.O.C.imeccc@ccu.edu.tw

G. H. Koopmann

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802

J. Vib. Acoust 133(5), 051008 (Sep 20, 2011) (7 pages) doi:10.1115/1.4003939 History: Received May 24, 2010; Revised December 23, 2010; Published August 31, 2011; Online September 20, 2011

A method is proposed for minimizing the sound radiation of a vibrating beam by patterning the beam with a series of cylindrical dimples such that one or more of the vibration modes have the same shape as the corresponding weak modes. In implementing the proposed approach, the objective is to minimize the shape difference between the vibration mode(s) and the designated weak mode(s) rather than to minimize the radiated sound power at a specific frequency or over a certain bandwidth. The design objective is achieved by calculating the weak modes of the beam using the finite element method and then applying an optimization scheme with the modal assurance criterion (MAC) as the objective function. The optimization results, which cause the vibration mode(s) of the dimpled beam to approach the corresponding weak modes(s), determine the dimple angle and dimple depth. The numerical results show that the radiation efficiency of the optimized dimpled beam using MAC as the objective is generally lower than that of a uniform beam. However, the effectiveness of the proposed design strategy depends on the degree of closeness between the shape of the vibration mode(s) of the dimpled beam and that of the designated weak mode(s).

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic illustration of dimpled beam

Grahic Jump Location
Figure 7

Vibration and weak mode shapes of dimpled beam after modifying third, fourth, and fifth vibration modes to corresponding weak modes

Grahic Jump Location
Figure 8

Schematic illustration of beam after optimization

Grahic Jump Location
Figure 9

Wavenumber spectra of third vibration and weak modes

Grahic Jump Location
Figure 10

Radiation efficiency of uniform beam and dimpled beam after modifying third vibration mode to corresponding weak mode

Grahic Jump Location
Figure 11

Weak and vibration modes of dimpled beam after modifying third, fourth, and fifth vibration modes to corresponding weak modes

Grahic Jump Location
Figure 12

Radiation efficiency of uniform beam and dimpled beam after modifying third, fourth, and fifth vibration modes to corresponding weak modes: (a) radiation efficiency spectra and (b) radiation efficiency spectra but with a frequency normalized to the respective natural frequency

Grahic Jump Location
Figure 2

Vibration and weak modes of uniform beam at 300 Hz; the first column: vibration mode shapes; the second column: weak modes normalized with respect to velocity; the third column: weak modes normalized with respect to strain energy

Grahic Jump Location
Figure 3

Radiation efficiency of vibration modes and acoustic weak modes at 300 Hz

Grahic Jump Location
Figure 4

Variation of weak mode shape with frequency for various weak modes

Grahic Jump Location
Figure 5

Variation of radiation efficiency of weak modes with MAC: (a) first and second weak modes, and (b) third to sixth weak modes

Grahic Jump Location
Figure 6

Sketch of the simply supported beam with dimples

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