Among the parameters of Biot model, that characterize the acoustic character of porous elastic materials, the system to measure the parameter related to elasticity, Young's modulus and shear modulus is provided. In general, the moduli are characteristic value which represent the difficulty of deformation, as well as a general term of proportional constant between stress and strain. Young's modulus can be defined as a modulus which corresponds to the deformation by pulling (or compressing) force, and the shear modulus as a coefficient against shearing force. Poisson's ratio can be calculated from Young's modulus and the shear modulus. These parameters are used to describe the elastic behaviors of the material. These parameters can be used in our acoustic modeling software, and also in the CAE software such as the Auto SEA.
The transmission of sound in the air (left), and in a porous material (right)
Elastic moduli are related to the structure-borne component.
Although it may be difficult to imagine the elastic behavior of the porous material compared with elastic material like rubber, the Biot model can be considered both air-borne and structure-borne component which is transmitted through the frame structure of the porous material. The elastic moduli are related to this structure-borne component. This componet can be ignored for the single-layered fibrous material. However, materials like urethane foam, it cannot be ignored. Moreover, creating the acoustic model to examine the characteristics of the multi-layered structure, these parameters should not be ignored even if the material is a fibrous one.
Elastic moduli can be categorized into two kinds, the Young's modulus and the shear modulus. From these two elastic moduli, Poisson's ratio can be determined.
When measuring the Young's modulus, the specimen for measurement is put on a shaker and then put the weight on it. After that, the random vertical vibration is provided to the specimen to measure the vibration transmission characteristics. From the frequency response function (FRF) of the vibration, Young's modulus and the attenuation coefficient (loss factor) can be calculated.
To measure the shear modulus, the similar measurement is performed as the Young's modulus case, but the excitation shold be simulated the shear force for this case. Our system provides the shear force by putting a plate for exciting the vibration between two specimens. Similar as the Young's modulus measurement, the modulus and attenuation coefficient (loss factor) is calculated from the frequency response function of the vibration transmission.
| Method (Young's modulus) | Resonance method (assuming one degree of freedom system) |
|---|---|
| Method (shear modulus) | Resonance method (assuming one degree of freedom system) |
| Frequency range | 10 - 400 Hz (typical) |
| Operating condition | Windows 2000 / XP |