| Quadratic Residue Diffuser (QRD) was proposed by Professor Manfred Schroeder in 1970 based on the theory of Maximum Length Sequences. The structure is also called "Diffsorber" because of its good diffusion property and low frequency absorber property. It has been widely used in the places where require a good acoustic environment, such as the opera house, concert hall, conference room and studio. However, at present, the engineering applications of the structure are still confined to empirical design. Accurate and effective theoretical/numerical predictions for its diffusion and absorber properties remain to be very much required, especially for the low frequency diffusion properties, so as to provide theoretical guidance and reference for further engineering application.Based on the existing research, the thesis focuses on diffusion modelling of QRD structures by combining theoretical, numerical and experimental modelling techniques. The study was supported by the National Natural Science Foundation (No.51175300) and a co-research project "Acoustic Prediction and Optimization of Quadratic Residue Diffuser Composite Structures" between Shandong University and Shanghai Jiaotong University.In this paper, first, a comprehensive literature review is presented in which the main research progress achieved both previously and currently on acoustic modelling of QRD structures are summarized, with the major modelling techniques, etc., theoretical, numerical and experimental, being introduced. Then, in respect of the acoustic modelling of QRD structures, such as the surface scattering theory, acoustics polar response distributions, diffusion coefficient modelling, etc, the inherent relationship between diffusion uniformity of QRD structure and the visualization of structure surface velocity distribution, polar response curves, diffusion coefficients were analyzed theoretically. By the AES-4id-2001, which is the international test standard for the diffusion coefficients, a virtual test platform for measuring the diffusion coefficients of QRD structures was set up which allows a set of virtual tests for the acoustic performance of QRD to be conducted in an efficient way. The validity of the virtual testing platform was verified by comparing with the experimental results measured in acoustic chambers. Finally, based on the validated virtual platform, the influences of some structural parameters of QRD structures on affecting their diffusion performances were investigated and assessed, and parts of simulation results were consistent with the relevant existing conclusions.Main contents in this thesis include:(1) Theoretical analysis. Main theories on acoustic analysis of QRD structures were introduced. The definition of QRDs was reviewed which are structures formed according to the quadratic residue sequences generated as a pseudo random sequence by the difference of number sequences. A numerical model of a typical QRD structure was then constructed. Through the analysis of groove surface vibration velocities, the diffusion properties of the structure were illustrated from vibration characteristics; then, structure diffusion uniformity and low frequency sound absorption performance were illustrated by computing far-field polar response distribution curves and the associated diffusion coefficients.(2) Numerical investigations. First, the diffusion uniformity and low frequency sound absorption of QRD structure were illustrated by varying the different structural parameters of QRD, e g, structural geometry sizes and bottom cavity sizes; simulation test platform was established using Virtual. Lab, the influences of QRD parameters (including cavity at the bottom, periodicity and angle of incidence) on structure surface diffusion sound absorption performance were discussed respectively.(3) Generalization. The influences of the bottom cavity size, periodicity and angle of incidence on diffusion properties of generic QRD structures were further investigated by setting up new QRD simulating models with different dimensional sizes. |
