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Mathematical Problems in Engineering
Volume 2016, Article ID 1740236, 11 pages
Research Article

Sound Attenuation of Membranes Loaded with Square Frame-Shaped Masses

1Department of Engineering Science, National Cheng Kung University, No. 1, University Road, Tainan City 701, Taiwan
2Missile and Rocket Systems Research Division, National Chung-Shan Institute of Science and Technology, No. 481, Sec. Jia’an, Zhongzheng Road, Longtan District, Taoyuan City 32546, Taiwan

Received 4 February 2016; Accepted 5 April 2016

Academic Editor: Gregory Chagnon

Copyright © 2016 J. S. Chen and D. W. Kao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study examines sound transmission of thin membranes with square frame-shaped masses. Numerical results indicate that multiple transmission loss peaks can be generated by adding more frame mass inclusions. The number and the location of the peaks are controlled by the number of frames, the frame distribution, and the frame width. Near the transmission loss peak frequencies, the dynamic effective mass density turns from positive to negative. The validity of the present model has been verified by comparing the analytical results with FE results. Two types of cell arrangements are also considered in this study, namely, cells in series and cells in array. It is seen that either the stacked or array configurations can produce better sound attenuation than single-celled structures. Moreover, the frequency band where sound wave is blocked can be broadened by stacking more layers with different mass magnitudes. Furthermore, additional frequency bands due to the periodicity of the structure are found in the stacked configurations.