J. Stuart Bolton
1077 Ray W. Herrick Labs., School of Mech. Eng., Purdue Univ., West Lafayette, IN 47907-1077
Katholieke Universiteit, Leuven, Celestijnenlaan 300B, 3001 Leuven, Belgium
Ford Motor Co., Dearborn, MI 48121-2053
Previous work has indicated that the acoustical behavior of partially reticulated noise control foams can be sensitive to small mounting details. It is thus reasonable to expect that the surface normal impedance of a foam sample placed in a standing wave tube will depend on the degree to which the sample is constrained at its edges. Here a two-dimensional version of the Biot theory governing wave propagation in elastic porous materials has been used to investigate the effect of such an edge constraint. First, the allowed modes of propagation within a constrained foam layer were identified. Those modes were then used to predict the response of the constrained layer to an incident plane wave. A comparison of that prediction with the surface normal impedance of an unconstrained half-space of the same material has shown that the principal effect of the edge constraints is to stiffen the sample at frequencies below the cut on of the first shearing mode within the constrained layer. A simple criterion based on the shear stiffness of the elastic porous material has been developed to give the frequency below which the edge-stiffening effect may have a significant effect on a sample's surface normal impedance.