Dynamic measurements of the elastic constants of glass wool

Abstract

The sound wave in the air between the fibers of glass wool exerts an oscillatory viscous drag on the fibers and excites a mechanical wave in the fiber skeleton. Accurate calculations of sound attenuation in glass wool must take the mechanical wave in the fiber skeleton into account, and this requires knowledge of the dynamic elastic constants of the fiber skeleton. The mechanical properties of glass wool are highly anisotropic. Previously only one of the elastic constants has been measured dynamically, but here all the elastic constants are reported. The measurement method is well known. But a new mechanical design, which reduces mechanical resonance, is described. The measurements were carried out in atmospheric air at normal pressure, and this causes an oscillatory airflow in the sample. To obtain the elastic constants, the influence of the airflow was subtracted from the data by a new formula. The elastic constants were measured in the frequency range 20-160 Hz for glass wool of mass density 30 kg/ m 3 . The elastic constant C 11 depended on the frequency; at 20 Hz it was 1.5+ 0.01i MPa, and at 160 Hz it was 2.6+ 0.06i MPa. The constant C 33 = 12+ 0.6i kPa did not depend on frequency. The shear constant C 44 =40+2i kPa was constant. The two constants C 12 , C 13 were zero.

Three-dimensional reconstruction of a random fibrous medium: Geometry, transport, and sound absorbing properties

“…The values corresponding to the remaining elastic parameters, and g, are classical for fibrous materials. For glass wool of density 30 kg/m 3 , Tarnow 29 reported a constant complex Young's modulus E 3 * ¼ 12(1 þ 0.05j) kPa in the direction perpendicular to which the fibers are laid (longitudinal direction). In the direction parallel to which the fibers are laid (transverse direction), the complex Young's modulus E 1 * was found to increase with frequency.…”

“…At 20 Hz E 1 * ¼ 1.5(1 þ 0.01j) MPa, and at 160 Hz E 1 * ¼ 2.6(1 þ 0.06j) MPa. 29 Obviously, the real part of the Young's modulus, corresponding to the studied sample mounted in an impedance tube, satisfies the inequality, E 3 < E < E 1 , where E 1 and E 3 , respectively, account for the real parts of E 1 * and E 3 * . This suggests that, when mounted in a tube of small diameter, the longitudinal and transverse elastic coefficients are strongly coupled, which has the effect of shifting the effective longitudinal Young's modulus toward the value of the transverse Young's modulus.…”

Visualizations of sound energy across coupled rooms using a diffusion equation model

“…The cavity is used to simplify the inversion procedure and to limit the effect of air pumping. 3 A circular aluminum plate of 1 mm thickness is bonded on the loudspeaker cone to ensure a planar and unidirectional compression of the porous sample. The association of the plate and the cone is called the diaphragm.…”

Ironless transducer for measuring the mechanical properties of porous materials

“…Classical methods to measure the viscoelastic properties of the frame can be sorted in two groups: 7 the quasistatic methods neglect the inertia effects and give relevant information in the low frequency range before the first resonance of the system [8][9][10][11] ͑usually for f Ͻ 100 Hz͒ and the dynamic methods are based on the vibration study of a porous layer, [12][13][14] or of a structure that includes a porous layer, 15,16 and give information at the resonance frequencies of the structure. Most of the existing methods are carried out in ambient conditions because "in vacuum" conditions lead to some experimental issues: the experimental setup is heavier, the frame of some types of acoustical material can be altered, and the temperature has to be slightly controlled.…”

“…It is shown that both real and imaginary parts of this impedance can be greatly influenced by the presence of air for thin samples or materials having a large airflow resistivity. Tarnow 10 proposed an analytical correction that accounts for this influence on the measurement of the force transmitted by the porous sample to the rigid wall for cylindrical samples. In a previous paper, 20 investigated the feasibility to extend the quasistatic compression method toward higher frequencies by mean of…”