Toward a theory of diffuse energy transport in large irregular structures

Statistical energy analysis;diffusion;Acoustics;vibrations

Wolff, Nicholas L.

关键词: Statistical energy analysis;    diffusion;    Acoustics;    vibrations;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16815/1_Wolff_Nicholas.pdf?sequence=2&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We develop a "concatenation ansatz" of energy flow in large,complex structures to predict the response of a nominally diffusivesystem.The concatenation ansatz is inspired by statistical energyanalysis (SEA) which is, in turn, based on an analogy to diffusiveheat transfer.Where in heat transfer, thermal energy flows fromareas of hot temperature to those of cold temperature, in SEAvibrational or acoustic energy is assumed to flow from structures orvolumes with high energy density to those with low energy density.The word "ansatz" refers to a "starting assumption." Here wemake the ansatz that transport of diffuse vibrational energy overshort-time intervals contains all information needed for estimatesof energy flow over long times, and that these estimates can beextracted by concatenating successive copies of transport overshort-time intervals.Though not based directly on an assumption ofdiffusion, the ansatz contains the same phase-neglecting principleas SEA and implies a diffusion limit equivalent to SEA.In this thesis, the concatenation ansatz is tested on variousbenchmark systems, some typically studied using SEA, other not. Wecarry 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.