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

TL;DR

This paper introduces a dynamical energy analysis method based on Chebyshev basis expansion for high-frequency acoustic systems, bridging statistical energy analysis and ray tracing, and demonstrating improved efficiency in complex multi-component systems.

Contribution

It presents a novel Chebyshev basis expansion approach to dynamical energy analysis, enabling efficient handling of multi-component systems beyond traditional geometrical constraints.

Findings

Method effectively interpolates between statistical energy analysis and ray tracing.

It overcomes geometrical limitations of standard statistical energy analysis.

Results align well with hp-adaptive discontinuous Galerkin finite element simulations.

Abstract

Standard methods for describing the intensity distribution of mechanical and acoustic wave fields in the high frequency asymptotic limit are often based on flow transport equations. Common techniques are statistical energy analysis, employed mostly in the context of vibro-acoustics, and ray tracing, a popular tool in architectural acoustics. Dynamical energy analysis makes it possible to interpolate between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. In this work a version of dynamical energy analysis based on a Chebyshev basis expansion of the Perron-Frobenius operator governing the ray dynamics is introduced. It is shown that the technique can efficiently deal with multi-component systems overcoming typical geometrical limitations present in statistical energy analysis. Results are compared with state-of-the-art hp-adaptive discontinuous Galerkin finite element simulations.