The configuration of the flexible thin ER layer is shown in Figure 15(a). It includes two sheets of plastic film (0.1 mm thickness), whose inner surfaces are painted with a thin layer of conducting glue respectively so as to serve as electrodes, ER fluid, PMMA spacer and fixtures. The supple plastic sheets are adhered to fixtures on sides, keeping a slight tension in the sheet surface. ER fluid is sandwiched between the two plastic sheets. The size of the ER layer is 90×90 mm with a total thickness of 1.2 mm.
(a) (b)
Figure 15. (a) Configuration of the thin electrorheological fluid layer and (b) schematic diagram of the measurement setup
A speaker (7 cm of diameter size) connected with an acoustic signal generator (XFS-8, Tianjin 11th radio factory, China) is fixed at the focus of a parabolic reflector, which makes the sound an approximately collimated beam towards the ER layer. The parabolic reflector and the speaker form a sound-generating cavity. The parabolic reflector is packed around with plastic foam material outside in order to reduce the sound radiation from its surface. The ER layer is laid horizontally on the rim of the reflector. A microphone (CR523, Beijing 797 Audio, China) is positioned close to the upper side of the ER layer in order to detect changes in the received sound pressure. Signal from the microphone is amplified by an amplifier (Amoisonic 777, China) and then inputted to channel (CH) X of an oscilloscope (GOS-620, Goodwill, Taiwan). The input voltage for the speaker is also connected to CH Y so as to observe the change in Lissajous figures. The experimental setup is shown in figure 15(b). The ER fluid used in experiment is a suspension of corn-starch powder in silicone oil. The corn starch powder is dehydrated at 60 for 3 hours in order to reduce the leak current in ER fluid.
The sound frequency is tuned manually from 75 Hz to 240 Hz with a progressing step of 5 Hz or 10 Hz. At each frequency, the SPL under different external electric field strength is obtained, and then the data are plotted as figure 16. It should be pointed out that as we change the strength of electric field at a measuring frequency point, the voltage for the speaker is kept at a same value. The sound pressure amplitude is expressed as P V/S, where V is the reading of voltage amplitude from oscilloscope and S represents the microphone sensitivity.
The formula of SPL is
0
log
20 P
SPL P, where P0 is reference sound pressure and P0 20PPa. The uncertainty of SPL can be deduced as
V SPL 'V
' ln10
) 20
( , where ǻV is the uncertainty of V. We set V as the average value of voltage amplitude for five times measurements andǻVis the difference between the measuring value and the average one. ǻV /V can reach 10%. So the maximalǻ(SPL) is about 0.9dB. The experiment errors may come from the influence of measuring environment and the precision limit of experiment apparatus. The relative changes ofSPL at the presence of electric field are mainly concerned and verified qualitatively from the data.
(a) (b)
(c)
Figure 16. Transmitted sound pressure level as a function of frequency for three volume fractions ɮ : (a)ɮ=31%, (b) ɮ=23%, and (c) ɮ=16%. Data with same electric field E are linked by means of cubic B-spline in order to guide eyes and their error bars are marked.
As shown in Figures 16(a), 16(b), and 16(c), with increase in the applied electric-field strength E, the SPL increases generally in frequency range of 80-150 Hz except several frequency points, which are different for the different starch volume fraction ij. At these frequencies the SPL exhibits somewhat abnormal changing behaviors (see 95Hz and 160Hz in figure 16(a), 150Hz in figure 16(b)). A hump within 80-150Hz at each E appears and the ordinate of the hump increases accordingly with E. Whenijis low, see figure 17, the increasing tendency of SPL with electric field is mild. But the increasing tendency steepens with a higher ij.
We denote the frequency band in which the SPL can be tuned electrically as responding frequency band Ƚ, the SPL difference between the electric-present one to the electric-absent one as D and its maximal value withinȽ is Dm. As shown in table 3, whenij increases from 16% to 31%, Ƚ moves from 75-140Hz or so to 90-170Hz or so, and Dm increases approximately from 4dB to 15dB. It implies that the tunability of SPL with high volume fraction is higher than that with low volume fraction.
Figure 17. Sound pressure level as a function of electric field E at the sound frequency of 120 Hz (Ŷɮ=16%,Ɣɮ=23%, Ÿɮ=31%).
Table 3. Responding frequency bandȽ and maximal sound pressure level difference Dm for different volume fractionij.
ij (%) Ƚ(Hz-Hz) Dm (dB)
16 75-140 4
23 85-160 6
31 90-170 15
The input signals to the speaker are sinusoidal. The detected signals on oscilloscope are sinusoidal too except for frequencies of 140-150Hz. Within 140-150Hz the signals in CH X for sound pressure are non-sinusoidal. This may be relevant to the complex vibration in the ER layer. Phase angle changes of the measured sound wave can be analyzed from Lissajous figures on the oscilloscope. The phase difference in each Lissajous figure can be calculated as following
y
x y A
A
x0 1 0
1 sin
sin
' M , (1)
where ' M is the phase difference between CH X and CH Y, x0 and y0 are the intercepts of Lissajous figure on axis x and y respectively, and Ax,Ay are the projection lengths of Lissajous figure on axis x,y respectively.
Figure 18 shows the phase difference as a function of E. It can be seen that the absolute value of phase difference increases with the electric field.
The sound energy received by microphone in experiment can come from the following sources. That is the direct transmitted sound wave (DTSW) through the ER layer, the diffracting sound wave (DSW) from the clearance between the ER layer specimen and the reflector, the sound radiation from the ER layer surface (SRER), and the sound radiation from the reflector surface and the packing material (SRRP). Figure 19 is a comparison of the SPLs
between different specimens. It shows that the three curves, representing no-specimen, empty-thin-layer and with-ER-fluid-at-0V/mm respectively, approximately have the same SPL within 90-160 Hz. It implies that the thin ER layer with ER fluid has little influence to the SPL within 90-160 Hz under E=0V/mm. But when the electric field is present, the influence of layer manifestly appears. The SPL increases drastically and a resonant peak appears at frequencies of 80-150Hz. Additionally, DSW and SRRP should not change obviously between without and with electric field. So it implies that the increment of SPL with electric field and the resonant peak are not from the increments of DTSW, DSW and SRRP, but from that of the so-called SRER.
0.0 0.5 1.0 1.5 2.0
0 50 100 150 200 250 300
130Hz 115Hz 105Hz
sound frequency:
Phase difference (Degree)
E (kV/mm)
Figure 18. Phase difference as a function of electric field at volume fraction 31%.
Figure 19. Comparison of the SPL spectrum for different specimen (Ɣno specimen, ×empty layer, Ÿ ER layer at E=0 kV/mm). The data for ER layer at E=0kV/mm is obtained by averaging the corresponding data in figure 17.
Figure 20. Schematic drawings of the ER layer and its Voigt mechanic model
The thin ER layer is excited by the vibrating air in the reflector and also vibrates forcedly. The vibration of the ER layer is complex due to the filled ER fluid. The vibrational characteristics of ER fluid under an electric field are governed by the electric-induced viscoelasticity in the material. The Voigt model that consists of a spring and a parallel dashpot can be adopted to model the ER fluid in the layer approximately [128, 132]. See figure 20. When the electric field is absent, the elasticity in ER fluid is weak and the viscosity is in dominance. Then, the damping in ER fluid attenuates the vibration in the lower plastic film that is directly stimulated by the vibrating air in the reflector. So the vibration in the upper plastic film excited by the ER fluid is weak and results in a low sound radiation from the surface of upper plastic film [133]. This can interpret the approximately same SPL in figure 19. When the electric field is present, the elasticity in ER fluid increases drastically and the viscosity also increases somewhat. The increasing elasticity in ER fluid transmits the vibrational energy from the lower plastic film to the upper one. Thus the coupling vibration in the upper plastic film is enhanced after the electric field is applied. As a result, the sound radiation from the upper plastic film surface is also improved. So the resonant peak appears in the plot of SPL vs frequency. Similarly, as the elasticity in ER fluid increases with the electric field, the phase difference between the vibrations in the upper plastic film and in the lower plastic film changes accordingly. It can explain the observed phase difference changes in Lissajous figures. Generally, the restore modulus in ER fluid with high volume fraction is higher than that with low volume fraction under the same electric field. This may explain the changing characteristics in SPL in term of ij.
In fact, ER fluids are complex in viscoelasticity properties as many investigators addressed [103,104]. Experimental results and theoretical analysis show that the viscoelasticity properties of ER materials are dependent on applied electric field strength, strain amplitude, and strain frequency [104]. In the so-called yield region ER fluids can be treated as a mode of nonlinear viscoelastic (or viscoelastic-plastic). The complex viscoelasticity in ER fluids causes the complexity in the vibrational characteristics in the ER layer. These complex vibrational characteristics in the thin ER layer may lead to the special points in frequency domain, where the SPL changes strangely with the electric field. We just present here a rough sketch of explanation for the experimental results. A precise calculation based on a rational model is desired to reveal the complex mechanism in the thin ER layer under acoustic waves.