Multidimensional wave propagation in elastic porous materials with applications to sound absorption, transmission and impedance measurement.

摘要

In this thesis, a multi-dimensional model for wave propagation in elastic porous materials is discussed along with its application to the prediction of the absorption coefficient and the transmission loss of foam-lined noise control treatments. In addition, the theory has been used to investigate the effects of edge constraints on the measurement of the surface normal impedance of elastic porous materials in standing wave tubes.;The theoretical model described in this thesis is based on the Biot theory and takes into account all three types of waves known to propagate in an elastic porous material; it can thus be used to predict the acoustical behavior of layers of elastic porous materials when excited by plane waves incident at arbitrary angles. In the present theory, the elastic porous material is characterized by seven macroscopic parameters, including: the bulk density, the in vacuo bulk Young's modulus, the associated loss factor, the Poisson's ratio, the porosity, the structure factor and flow resistivity.;The elastic porous material model has been incorporated into a technique for predicting the absorption coefficients of noise control treatments featuring an impermeable membrane, a porous lining and a hard wall. This absorption model was used to study effects associated with the method of mounting a porous material to a backing or facing material and, at the same time, to identify optimum treatment configurations. Results of this study have indicated that configurations in which a porous lining is separated from a facing membrane by a small air gap generally yield better performance than do those treatments in which a facing material is bonded directly to a porous layer.;The porous material model has also been used in predictions of sound transmission through lined double-panel structures. It was found that configurations in which the lining is not directly attached to the facing panels are to be preferred to those in which the foam is directly bonded to the facing panels. Satisfactory agreement was found between experimental measurements and theoretical predictions of transmission loss, and all significant effects predicted by the theoretical model were found to appear in the experimental results.;The predictions of absorption coefficients and transmission losses confirmed that the acoustical behavior of foam is very sensitive to its mounting. Consequently, it is reasonable to expect that the measurement of surface normal impedance of foam placed in a standing wave tube depends on how the sample is constrained at its edges when it is placed in the tube. Two extreme mounting configurations were investigated theoretically: a sample fully constrained at its edges and a sample that is free to slide at its edges. Comparison of the surface normal impedances of the two configurations has shown that edge constraints may significantly affect impedance measurements, particularly at low frequencies.