Investigation of the vibrational modes of edge-constrained fibrous samples placed in a standing wave tube.

In earlier work it was suggested that the frictional constraint of a porous sample around its circumference in a standing wave tube resulted in shearing resonances of the sample. In the present work that effect has been confirmed by direct measurement of the spatial distribution of the velocity of the solid phase of a fibrous sample placed in a rigidly terminated standing wave tube and driven into motion by a plane, incident sound field. The measurements were performed using a standing wave tube to which a transparent downstream section was attached. A laser Doppler velocimeter was then used to measure the velocity of the solid phase of acoustically driven samples. The materials considered here were two types of aviation-grade glass fiber. A poroelastic finite element model was used to simulate the response of the constrained fibrous samples. Good agreement between measured and predicted mode shapes was found both when the samples were constrained only around their edges, and when an additional constraint plane was inserted axially through the samples. The present results confirm that glass fiber samples placed in a standing wave tube exhibit shearing modes and that those modes are associated with previously observed transmission loss minima.