Archives of Acoustics, 37, 4, pp. 489–498, 2012

Noise Elimination of a Multi-tone Broadband Noise with Hybrid Helmholtz Mufflers Using a Simulated Annealing Method

Min-Chie CHIU
Department of Mechanical and Automation Engineering, Chung Chou University of Science and Technology

Noise control is essential in an enclosed machine room where the noise level has to comply with
the occupational safety and health act. In order to overcome a pure tone noise with a high peak value
that is harmful to human hearing, a traditional reactive muffler has been used. However, the traditional
method for designing a reactive muffler has proven to be time-consuming and insufficient. In order to
efficiently reduce the peak noise level, interest in shape optimization of a Helmholtz muffler is coming to
the forefront.
Helmholtz mufflers that deal with a pure tone have been adequately researched. However, the shape
optimization of multi-chamber Helmholtz mufflers that deal with a broadband noise hybridized with
multiple tones within a constrained space has been mostly ignored. Therefore, this study analyzes the
sound transmission loss (STL) and the best optimized design for a hybrid Helmholtz muffler under a space-
constrained situation. On the basis of the plane wave theory, the four-pole system matrix used to evaluate
the acoustic performance of a multi-tone hybrid Helmholtz muffler is presented. Two numerical cases for
eliminating one/two tone noises emitted from a machine room using six kinds of mufflers (muffler AF)
is also introduced. To find the best acoustical performance of a space-constrained muffler, a numerical
assessment using a simulated annealing (SA) method is adopted. Before the SA operation can be carried
out, the accuracy of the mathematical model has been checked using the experimental data. Eliminating a
broadband noise hybridized with a pure tone (130 Hz) in Case I reveals that muffler C composed of a one-
chamber Helmholtz Resonator and a one-chamber dissipative element has a noise reduction of 54.9 (dB).
Moreover, as indicated in Case II, muffler F, a two-chamber Helmholtz Resonator and a one-chamber
dissipative element, has a noise reduction of 69.7 (dB). Obviously, the peak values of the pure tones in
Case I and Case II are efficiently reduced after the muffler is added.
Consequently, a successful approach in eliminating a broadband noise hybridized with multiple tones
using optimally shaped hybrid Helmholtz mufflers and a simulated annealing method within a constrained
space is demonstrated.
Keywords: multiple tones; hybrid; Helmholtz; four-pole transfer matrix method; SA method
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