In the study, energy flow analysis is performed to predict the performance of silencers. To date, deterministic approaches such as finite element method have been widely used for silencer analysis. However, they have limitations in analyzing large structures and mid-high frequency ranges due to unreasonable computational costs and errors. However, silencers used for ships and off-shore plants are much larger than those used in other engineering fields. Hence, energy governing equation, which is significantly efficient for systems with high modal density, is solved for silencers in ships and off-shore plants. The silencer is divided into two different acoustic media, air and absorption materials. The discontinuity of energy density at interfaces is solved via hypersingular integrals for the 3-D modified Helmholtz equation to analyze multi-domain problems with the energy flow boundary element method. The method is verified by comparing the measurements and analysis results for ship silencers over mid–high frequency ranges. The comparisons confirm good agreement between the measurement and analysis results. We confirm that the applied analysis method is useful for large silencers in mid-high frequency ranges. With the proven procedures, energy flow analysis can be performed for various types of silencer used in ships and off-shore plants in the first stage of the design.

Abstract
1. Introduction
2. Theory
    2.1 Energy governing equation
    2.2 Hypersingular boundary integral equation
    2.3 Energy flow boundary integral equation for the multidomain problem
3. Validation for the performance of ship silencers
    3.1 Experiment
    3.2 Simulation
    3.3 Results
4. Conclusions
References

• Tae-Gyoung Kim(Department of Naval Architecture and Ocean Engineering, Seoul National University)
• Jee-Hun Song(Department of Naval Architecture and Ocean Engineering, Chonnam National University) Corresponding Author
• Suk-Yoon Hong(Department of Naval Architecture and Ocean Engineering, Seoul National University)