Contents: 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001

2003, 18

Long-Jyi Yeh, Ying-Chun Chang, Min-Chie Chiu

Shape optimization on constrained linearly expanded tubes by using genetic algorithm

language: English

received 09.10.2003, published 19.11.2003

Download article (PDF, 550 kb, ZIP), use browser command "Save Target As..."
To read this document you need Adobe Acrobat © Reader software, which is simple to use and available at no cost. Use version 4.0 or higher. You can download software from Adobe site (


One of the most important practical considerations in muffler design is the constrain problems in a confined place. In addition, to release the pressure drop in a muffler system, a new silencer of linearly expanded tube is proposed and investigated in this paper. The genetic algorithm (GA), a stochastic algorithm, is used as an optimizer by mimicking the genetic drift and Darwinian strife for survival.
To approach this study effectively, the linearly inclined tube is divided into several segments of straight tube with different diameters. Four-pole transfer matrix is then in use, accordingly. Not only the theoretical derivation in sound transmission loss (STL) but also the GA searching technique is discussed. Additionally, a numerical case on the expanded tube is introduced. To achieve the best optimization in terms of STL of a muffler, the GA parameters are on trial in various values.
Results show that when the divided elements of the tube are more than sixteen segments, the modeled segmental tube is similar to the linearly expanded tube. In addition, the STL in muffler becomes to be stable.

Keywords: shape optimization; linearly expanded tube; muffler; transfer matrix method; space constraints; genetic algorithm

11 pages, 11 figures

Сitation: Long-Jyi Yeh, Ying-Chun Chang, Min-Chie Chiu. Shape optimization on constrained linearly expanded tubes by using genetic algorithm. Electronic Journal “Technical Acoustics”,, 2003, 18.


[1] Tracor Inc. Guidelines on Noise. American Petroleum Institute, 1973.
[2] P. L. Timar. Noise and Vibration of Electrical Machines. Elsevier Science, New York, 1989.
[3] L. J. Yeh, M. C. Chiu, G. J. Lay. Computer aided design on single expansion muffler under space constraints. Proceedings of the 19th National Conference on Mechanical Engineering (The Chinese Society of Mechanical Engineers), C7: pp.625–633, Yun Lin, R.O.C., 2002.
[4] Mark E. Schaffer. A Practical Guide to Noise and Vibration Control for HVAC Systems. ASHRAE, 1991.
[5] D. E. Goldberg. Genetic Algorithm in Search, Optimization and Machine Learning. Addison-Wesley, Massachusets, 1988.
[6] M. G. Prasad. A note on acoustic plane waves in a uniform pipe with mean flow. Journal of Sound and Vibration. 1984, 95(2), pp. 284–290.
[7] M. G. Prasad, M. J. Crocker. Studies of acoustical performance of a multi-cylinder engine exhaust muffler system. Journal of Sound and Vibration. 1983, 90(4), pp. 491–508.
[8] M. L. Munjal. Acoustics of Ducts and Mufflers with Application to Exhaust and Ventilation System Design. John Wiley & Sons, New York, 1987.
[9] J. M. Johnson, R. S. Yahya. Genetic algorithm optimization and its application to antenna design. IEEE. 1994, pp. 326–329.


Long-Jyi Yeh Long-Jyi Yeh received his MS and PhD degrees from the Mechanical Engineering Department of Tatung University, Taipei, Taiwan, in 1987 and 1994, respectively. From 1992 to 1995, he jointed Tatung Company as a senior automation engineer, where he developed researches of manufacturing and automation technologies. In 1995, he jointed the faculty of the Department of Mechanical Engineering at Tatung University, Taipei, Taiwan as an Associate Professor.

e-mail: ljyeh(at)

Corresponding author. Mailing address: Department of Mechanical Engineering, Tatung University, 40, Chungshan N. Rd., 3-rd Sec., Taipei, Taiwan 104, R.O.C.


Ying-Chun Chang received his MS degree from the Mechanical Engineering Department of Manhattan College, New York, USA, in 1982. Since 1983, he has been with the Department of Mechanical Engineering, Tatung University, Taipei, Taiwan, where he is engaged in teaching and research in the area of noise and vibration control. His current research interests include computer-aided acoustical filter design, experimental modal analysis and smart structures. He is currently an Assistant Professor at Tatung University.

e-mail: ycchang(at)


Min-Chie Chiu received his MS degree from the Mechanical Engineering Department of Stevens Institute of Technology, New Jersey, USA in 1989. He jointed CTCI, Taipei, Taiwan as an environmental engineer in 1990 where he developed practical design work in noise and vibration control during his employment with the company. He still continues his design work in CTCI and owns seven patents in sound absorber personally. Currently, he is pursuing his PhD degree at Tatung University, Taipei, Taiwan.

e-mail: Min-Chie.Chiu(at)