soft porous silicone rubbers with ultra-low sound speeds in acoustic metamaterials

by:Keyuan     2020-07-18
The soft porous silicone rubber has been shown to exhibit a very low sound speed of tens of meters/second for these dense materials, even for a few percent low hole rate.
Our ultrasonic experiments show that the longitudinal speed of sound suddenly drops with the increase of the air holes, while the transverse speed of sound remains unchanged.
For this porous elastic material, we propose a simple analytical expression for these two kinds of sound speeds derived under the framework of Kuster and toköz, the good consistency between the theoretical prediction of longitudinal and shear waves and the experimental results is revealed.
The acoustic attenuation measurement also completes the representation of these soft porous materials.
The soft porous silicone rubber used in this work is synthesized by emulsion
Template program.
The silicone network is formed by a multi-addition reaction in the mixture of SiH and SiVi with Platinumbased catalyst.
All products are from Blue Star silicone. Water-in-
Silicone rubber emulsion prepared by mechanical stirring with silica gel
Surface active substance of Silube (Siltech).
Pour the emulsion into 35mm-diameter disk-
Store in the room like a mold
Temperature before the reaction is completed (
About four hours).
The drying of the sample results in a soft porous silicone rubber with a pore diameter ranging from 1 to 30 µm, which corresponds to the size of the initial emulsion droplets.
Therefore, the hole rate of the final material is controlled by adjusting the volume of the dispersed water phase in the emulsion.
The large pore structure of all samples was confirmed by scanning electron microscope pictures (TM-1000, Hitachi)as shown in .
The mass density of various voids was determined from the mass and volume of the sample, and it was found that the mixture rule Eq was satisfied. 1a.
Please note that the mechanical properties-
Silicone rubber is characterized by direct static automatic measurement, providing . . . . . . = 1040 kg/m, will . . . . . . = u2009 1. 2u2009GPa and u2009=u20090.
For mass density, the volume and shear modulus are 3mpa mpa, respectively.
These values are consistent with the values reported in the literature for polyzhengdione, a rubber elastic polymer.
The soft porous silicone rubber materials were characterized by ultrasonic waves of various pore sizes from 0 to 35%.
For a large overall sample given (
35mm diameter)
Prepared with two millimeters of different thickness.
Each sample is then placed between two identical large broadband ultrasound (US)transducers (
Transmitter and receiver)
25mm in diameter ,.
, Less than the diameter of the sample.
For longitudinal waves, we use two immersion sensors (Olympus V301)
And two cuts.
Wave sensor (Sonaxis CMP79)
Used to generate and detect lateral waves.
S. sensors are placed face-to-face and mounted on a linear manual platform, allowing accurate measurement of sample thickness with an uncertainty of about 10 µm.
Each sample is first slightly pre-used, rather than using a coupled fluid between a US sensor and a sample capable of penetrating its porous structure
Apply pressure through the sensor and then relax before each measurement to ensure good mechanical contact.
The emission sensor is short excited (broadband)
Pulse generated by the pulse generator/receiver (Olympus, 5077PR)
This is also used to amplify the electrical signals recorded by the receiving sensor before being collected on the computer through the waveform digitizer (
AlazarTech at ATS460).
And the typical experimental results are shown, where longitudinal and transverse waves propagating in soft-porous silicone rubber materials with a SFP = 35 35% are obtained.
In this case, the thickness of the sample is 2. 2u2009mm and 3. 7u2009mm.
First, the transmitted signal is filtered in time and only two first oscillations are maintained to remove multiple reflections between the pulse observed in a short time and the surface of the two American sensors (
See and Echo). Such a cut-
The Off Protocol is appropriate because the signal waveform has no significant distortion during material propagation, as shown in and.
Then, the fast Fourier transform (FFTs)
Execute on these two selected communication numbers to extract the corresponding phase and amplitude spectrum (and and ).
Know the thickness difference between the two samples (=u20091. 5u2009mm)
, The phase velocity and attenuation coefficient are derived as functions of the frequency, as shown in and.
It is found that the phase velocity of longitudinal and transverse waves is constant (
~ u2009 40 u2009 m/s and will . . . . . . ~ 201715. 0m/s)
Within the entire width-
Half of the maximum bandwidth (
View gray areas in middle).
Therefore, within this frequency range, the scattering effect is negligible and then the described cut-outs are used
The procedure here is reasonable.
Finally, it is worth noting that the heat
The phase velocity of the cured rubber considered here is twice lower than that of the soft porous silicone rubber material previously aggregated with UV (
~ 80 µm/s and 40 m/s).
These experiments were performed ten times under the same experimental conditions to test the repeatability and obtain the error bars on the phase
Speed and attenuation measurements, as shown in and.
The phase velocity is extracted using the same experimental scheme and the phase velocity of all other samples with various gaps is extracted.
Please note that it is impossible to measure the lateral phase velocity as non-
Porous Materials (=u20090%)
The wave attenuation in these materials is much more than that of the longitudinal wave.
Despite the use of the shear wave sensor, the longitudinal mode is actually generated and completely dominates the shear mode, so the longitudinal mode cannot be detected.
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