Recovery of airflow resistivity of poroelastic beams submitted to transient mechanical stress

Abstract

The airflow resistivities of air-saturated poroelastic slender beams submitted to transient mechanical stress are recovered using fluid and solid borne compressional mode phase velocity expressions drawn from a modified Biot theory. A point where the two dilatational modes intersect and their phase velocities equal is first sought. This point also corresponds to the Biot transitional frequency indicating the frequency at which the solid and the pore fluid start disassociating due to the weakening of the viscous forces by the thinning of the viscous boundary layer in the pores. A bilinear time–frequency (TF) distribution is used to represent on the time–frequency plane, the captured transient mechanical stress waves from which the point of intersection/separation of the two modes is located. The projection of the Eigenfrequencies obtained from a simple 3D finite element modeling of the thin poroelastic beam, on a (TF) diagram, facilitates the identification of the modes. The transition frequencies for the poroelastic beams thus retrieved are verified through the use of variable frequency, single cycle sine wave bursts. The anisotropy of the foams are also revealed by analyzing the transient responses of the poroelastic beam specimens cut from the same panel but in two perpendicular directions in orientation to each other.