Estimating the Validity of Statistical Energy Analysis Using Dynamical Energy Analysis: A Preliminary Study

Abstract

Dynamical energy analysis was recently introduced as a new approach toward determining the distribution of mechanical and acoustic wave energy in complex built up structures (Tanner 2009). The technique interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. Statistical energy analysis (SEA) is a highly efficient method for analyzing energy distributions in large scale industrial problems, but remains an expert tool since explicit bounds on its validity are generally difficult to establish. In this work we aim to address this problem through a study of the spectral properties of the transfer operator arising in dynamical energy analysis. Through this study one can estimate escape and correlation decay rates for SEA subsystems and use these quantities to indicate the validity of an SEA approach.