Dynamical energy analysis for built-up acoustic systems at high frequencies

Area of Science:

• Acoustics and Mechanical Engineering
• Computational Physics
• Wave Propagation

Background:

• Standard methods for wave field intensity analysis include statistical energy analysis (SEA) and ray tracing.
• These methods have limitations, especially in complex, multi-component systems and at high frequencies.
• Dynamical energy analysis (DEA) offers an intermediate approach, bridging SEA and ray tracing.

Purpose of the Study:

• To introduce a novel version of dynamical energy analysis (DEA).
• To utilize a Chebyshev basis expansion of the Perron-Frobenius operator for ray dynamics.
• To address limitations of existing methods in describing wave field intensity distributions.

Main Methods:

• Development of a DEA framework based on Chebyshev basis expansion.
• Application of the Perron-Frobenius operator to model ray dynamics.
• Comparison with hp-adaptive discontinuous Galerkin finite element simulations.

Main Results:

• The proposed DEA method efficiently handles multi-component systems.
• It overcomes geometrical limitations inherent in standard statistical energy analysis.
• The technique provides accurate results comparable to advanced finite element methods.

Conclusions:

• The Chebyshev-based DEA offers a powerful and efficient tool for wave field analysis.
• This method extends the applicability of DEA to more complex vibro-acoustic and architectural acoustics scenarios.
• It represents a significant advancement over traditional statistical energy analysis and ray tracing.