Low frequency acoustic method to measure the complex bulk modulus of porous materials

In this work, an acoustic lumped element technique has been developed to measure the dynamic bulk modulus of porous materials in the low frequency range ( f<500 Hz). Based on the electroacoustic analogy of wave propagation inside a porous medium, an analytical derivation of the measurement method is given. Unlike other techniques, it requires the use of only two microphones placed in the cavity containing the sample being tested and in the loudspeaker box. The proposed method provides reliable results when the longitudinal viscous impedance within the medium is negligible with respect to the transversal thermal impedance. The upper limit of the frequency validity range can be determined from the relationship absk̃d≈0.5, where k̃ is the acoustic wavenumber of the porous material and d is the sample thickness. Furthermore, some practical aspects related to the measure are also reported. To validate the methodology, experimental campaigns have been performed on different typologies of materials (fibrous, uniform cross-section geometries, additive manufactured sample, and foam) in two laboratories. The experimental results show good agreement with the theoretical results within the frequency validity range.