Toward a theory of diffuse energy transport in large irregular structures
"We develop a ""concatenation ansatz"" of energy flow in large, complex structures to predict the response of a nominally diffusive system. The concatenation ansatz is inspired by statistical energy analysis (SEA) which is, in turn, based on an analogy to diffusive heat transfer. Where in heat transfer, thermal energy flows from areas of hot temperature to those of cold temperature, in SEA vibrational or acoustic energy is assumed to flow from structures or volumes with high energy density to those with low energy density. The word ""ansatz"" refers to a ""starting assumption."" Here we make the ansatz that transport of diffuse vibrational energy over short-time intervals contains all information needed for estimates of energy flow over long times, and that these estimates can be extracted by concatenating successive copies of transport over short-time intervals. Though not based directly on an assumption of diffusion, the ansatz contains the same phase-neglecting principle as SEA and implies a diffusion limit equivalent to SEA. In this thesis, the concatenation ansatz is tested on various benchmark systems, some typically studied using SEA, other not. We carry out direct numerical simulation (DNS) in the time domain using finite-difference and finite-element methods. We study two- and three-room systems with rooms connected by a window allowing energy to flow between them. We study a torus, a single statistically homogenous structure, which cannot be studied by SEA. We also study plates coupled by springs allowing energy to flow between the plates. This type of system is of interest to the structures community. Finally, we study an interesting ""hybrid"" system consisting of two coupled systems. One system would typically be studied statistically in a framework such as SEA. The other system, not satisfying the assumptions of SEA, would typically be studied deterministically in a framework such as finite-element analysis."
Statistical energy analysis, diffusion, Acoustics, vibrations
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign