Abstract
The acoustic muffler development depends on optimizing its volume for high performance, it is of great importance in the industrial field to obtain a reduction in duct noise economically and efficiently. The main aim of this work is to optimize analytically the acoustic transmission loss (\({\text{TL}}\)) of the Basalt Fiber Reinforced Polymer laminated composite Double-Chamber Mufflers (BFRP-CDCM) because \({\text{TL}}\) is an essential characteristic of the muffler and is not based on the source or the termination impedances. The power transmission coefficient (\({\text{PTC}}\)) and the \({\text{TL}}\) of a muffler will be calculated. The method used to optimize the length of the acoustic muffler is the genetic algorithms (\({\text{GA}}\)) method. The sound pressure data is obtained from the exact solution of the governing equations of the muffler model in Matlab® software. Many mathematical simulations were performed of varying muffler lengths at multiple frequency ranges simultaneously. The results indicate that the \({\text{TL}}\) is optimized at the desired zone of frequency. This research supports the quick and active approach towards optimal design for BFRP-CDCM in a space constrains.
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Appendix: The Table of Acronyms and Mathematical Notation
Appendix: The Table of Acronyms and Mathematical Notation
\({\text{B }}/{\text{L}}\) | Muffler length ratio |
|---|---|
\({\text{B }}\left( {\text{m}} \right)\) | Muffler Length |
\({\text{L }}\left( {\text{m}} \right)\) | Length of chamber |
\({\text{Freq}}.{ }\left( {{\text{Hz}}} \right)\) | Frequency |
\({\text{TL}}\) | Transmission Loss |
\({\text{PTC}}\) | power transmission coefficient |
\({\text{GA}}\) | genetic algorithms |
\(A_{i}\) | standing pressure propagating wave amplitude |
\(B_{i}\) | reflected pressure propagating wave amplitude |
\(P_{i}\) | standing pressure |
\(P_{r}\) | reflected pressure |
\(j\) | junction number |
\(K\) | wavenumber ratio |
\(k\) | the wavenumber |
\(\omega\) | angular frequency |
\(c\) | sound speed |
\(k_{b}\) | bending wavenumber |
\(m\) | area ratio |
\(D_{ij}\) | bending stiffness |
\(\overline{Q}_{ij}\) | transformed reduced stiffness coefficients |
\(E_{x}\), \(E_{y}\),\(E_{z}\) | The elastic modulus in the ‘x’, ‘y’ and ‘z’ directions |
\(G_{xy}\), \(G_{xz}\),\(G_{yz}\) | The shear modulus in the ‘xy’, ‘xz’ and ‘yz’ plane |
\(\nu_{xy}\), \(\nu_{xz}\),\(\nu_{yz}\) | The Poisson's ratio in the ‘xy’, ‘xz’ and ‘yz’ plane |
\(i\) | the imaginary unit |
\(\mu\) | the fluid density |
FRP | fiber reinforced polymer |
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Altabey, W.A., Noori, M. (2024). A Mathematical Modeling of BFRP Laminated Composite Double-Chamber Mufflers Based Acoustic Transmission Loss Optimization. In: Benaissa, B., Capozucca, R., Khatir, S., Milani, G. (eds) Proceedings of the International Conference of Steel and Composite for Engineering Structures. ICSCES 2023. Lecture Notes in Civil Engineering, vol 486. Springer, Cham. https://doi.org/10.1007/978-3-031-57224-1_6
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