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
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.
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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