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Experimental study on electro-rheological material with grooved electrode surfaces
Materials and Design 22 Ž2001. 277᎐283
Experimental study on electro-rheological material with grooved electrode surfaces Chun-Ying LeeU , Kuo-Long Jwo Department of Mechanical Engineering, Da-Yeh Uni¨ ersity, Da-Tsuen, Chang-hua, Taiwan, Republic of China Received 8 March 2000; received in revised form 15 August 2000; accepted 25 August 2000
Abstract The dynamically tunable capability of a sandwich beam with embedded electro-rheological material has been proven to be a viable tool for the vibration control of structures. The effectiveness of this technique depends largely on the ER effect caused by the applied electric field. This ER effect is determined by the formation of the chain-like structures between the electrodes. In this study, the surfaces of the electrodes were modified with parallel grooves in different spacing ᎏ 0.5, 1 and 2 mm, respectively. These modified electrodes changed the local electric field distribution. Therefore, the chain-like structures formed by the suspension particles of the ER material upon the application electric field were altered. The dynamic characteristics of both the ER material within the parallel-plate fixture and the ER sandwich beam with modified electrodes were measured. The results showed that with finer spacing of the grooves on the electrodes, the ER material demonstrated greater increases in both the storage modulus and the damping loss factor upon the application of the electric field. Compared to its counterpart with plain electrodes, a 20% greater increment in the first two modes’ resonance frequencies was achieved with the proposed surface modification on the ER sandwich beam at an applied electric field strength of 1.0 kVrmm. 䊚 2001 Elsevier Science Ltd. All rights reserved. Keywords: Electro-rheological fluid; Shear modulus; Sandwich beam
1. Introduction Electro-rheological ŽER. materials are a potential material for application in the field of intelligent materials and structures w1᎐3x. Due to the controllability of the rheological property of the ER materials by an applied electric field, varieties of its applications have been intensive research topics for researchers and engineers w4᎐6x. The incorporation of the ER material into a structure by Gandhi et al. w7x presents an innovative technique for the distributed vibration control of the structure. Thereafter, many experimental works regarding U Corresponding author. Tel.: q886-4-8528469 Žext. 2109.; fax: q886-4-8536667. E-mail address: [email protected] ŽC. Lee..
the dynamic characteristics of the beam-type structures have been published w8᎐10x. Oyadiji w11x used the sandwich plate with complex flexural stiffness to study the ER effect on the constrained layer damping treatment of a clamped-clamped plate. Lee w12x based on an assumed constitutive relationship for the ER material under quasi-static shearing presented a method for calculating the equivalent complex moduli for the ER material under an oscillating shear. The finite element formulation incorporating material non-linearity for the sandwich beam structure was later verified by a followed experimental measurement w13x. In order to enhance the controllable dynamic characteristics of the sandwich beam, Choi et al. w8x studied several specimens with different surface modifications on the electrode surfaces. They showed that the specimen with electrode surfaces roughened by sandpaper
0261-3069r01r$ - see front matter 䊚 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 1 - 3 0 6 9 Ž 0 0 . 0 0 0 9 0 - X
278
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
demonstrated a greater ER effect than its counterpart with original surfaces. On the other hand, the specimens with attached circular or rectangular polyvinyl patches on the electrode surfaces did not significantly show a difference from the original specimen. No discussion regarding the difference was given in their study. Abu-Jdayil and Brunn w14x investigated the effects of electrode morphology on the slit flow of an electro-rheological fluid. Both oblique and corrugated electrodes were used in their study. They demonstrated an average factor of 2.0 and 2.5 in the increase of the ER effect for the oblique and corrugated electrodes, respectively, in the voltage range 1᎐5 kV. The enhancement in the ER effect due to different electrode morphology should be related to the formation of the thicker chain-like structures upon the influence of the applied electric field w15x. The dependence of the ER effect on the morphology of the chain-like structures has been pointed out theoretically by researchers w16,17x. An experimental study regarding the ER effect in different electrode morphology was conducted in this paper with special emphasis on the dynamic characteristics of the ER sandwich beams. According to the deformation pattern of the ER material embedded in the sandwich structure, a parallelplate fixture with machined grooves on the electrode surfaces, combined with an apparatus for ordinary vibration testing, was used to perform dynamic measurement on the ER material. In the meanwhile, the ER sandwich beam specimens fabricated by using aluminum electrodes with rolled grooves on the surfaces were tested to demonstrate the effect of electrode surface modification on their dynamic characteristics.
Fig. 1. Schematic diagram of the test set-up for the ER fluid under oscillating shear using parallel-plate fixture.
in-plane and transverse motions of the central plate. This in turn would assure the pure shear straining on the ER material filled in the gaps. The electric field was established by applying voltage to these parallel plates. There were three types of electrode surface geometry investigated herein, namely, plain, 2-mm and 0.5-mm spaced grooves, respectively, as shown in Fig. 2 for the photomicrographs. It can be seen in this figure that the electrode with 2-mm-spacing grooves had been
2. Experimental measurement and discussions The ER material used in this study consisted of cornstarch suspensions in silicone oil. The carrier fluid had a viscosity of 20 cS. The weight fraction of the suspensions was 50%. In order to study directly the ER effect with different electrode surface modifications, the dynamic measurement using parallel-plate fixture by Lee and Cheng w18x was adopted in this study. 2.1. Parallel-plate fixture setup The schematic diagram of the fixture and the associated testing apparatus is shown in Fig. 1. The fixed part of the fixture mainly consisted of two parallel plates on a base. These two parallel plates formed a rectangular cavity with a height of 6 mm. A 3-mm thick, 140-cm2 area plate attached on the shaker head was inserted into the space between the two parallel plates with an equal gap height from them. This symmetric arrangement should avoid the unwanted coupling between the
Fig. 2. Photomicrographs of electrodes used in parallel-plate fixture: Ža. top view of the 2-mm spacing grooved electrode; Žb. cross-sectional view of the electrodes; Žc. top view of the 0.5-mm spacing grooved electrode.
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
279
Fig. 3. The schematic diagram of the cantilevered ER sandwich beam specimen. Fig. 4. Photomicrograph of the cross-section of the aluminium faceplates used in ER sandwich specimens.
machined deeper than their 0.5-mm counterparts due to the difficulties in obtaining the same machining process. This consequently resulted in a sharper surface peak for the 2-mm-grooved electrode. Since the electrode surfaces surrounding the inner cavity were machined with parallel grooves, the electric field was locally disturbed by these surface modifications. The 0᎐5-kV high-voltage power supply furnished the required voltage that was equivalent to a range of 0᎐3.3 kVrmm nominal field strength on the ER material. During the test, the power amplifier activated the electro-magnetic shaker with the sinusoidal source generated from the dynamic signal analyzer. The eddy current probe monitored the axial motion of the shaker head, and therefore the central plate. This axial motion of the central plate provided the shear straining on the ER material filled between the plates. The force transducer measured the corresponding reacted axial force on the fixed plates. The input axial displacement signal and the reacted force signal were recorded in the dynamic signal analyzer. Thus, the associated shear strain and shear stress on the ER material could be calculated accordingly.
For all specimens, the top and bottom were aluminum faceplates while the mid-layer was filled with ER material confined by the rubber dam on the edges. The aluminum faceplates also served as electrodes for applying an electric field. At the end of the specimen where the boundary constraints applied, a glassrepoxy pad was used as the mid-layer to provide the rigidity for the clamping force. The only difference among the specimens was that the inner surface of the aluminum faceplates was rolled with grooves in different spacing ᎏ none, 0.5, 1 and 2 mm, respectively. Fig. 4 presents a photomicrography of the cross-sections of the different electrodes. The dimensions of the specimens are listed in Table 1. The experimental setup for the measurement of dynamic characteristics of the sandwich specimen is shown in Fig. 5. The cantilever fixture for supporting the specimen was mounted on an electro-magnetic shaker. During the measurement, the shaker provided the desired motion of the fixture base and this motion was measured by an accelerometer. The vibrating response of the specimen under the base excitation was picked up by a non-contacting eddy current probe. The probe was placed at the free end for measuring the displacement of interested mode shape. With the output vibrating response and the input base excitation, the dynamic transmissibility of the specimen in the frequency domain could be obtained by the dynamic signal analyzer.
2.2. Sandwich beam specimen setup For the experimental measurements of the ER sandwich beams in a cantilevered boundary condition, four types of specimens were fabricated in this study. The schematic diagram of the specimens is shown in Fig. 3. Table 1 Dimensions of the ER sandwich beam specimens a Specimen
Span Ž L.
Width Ž b.
Dam width Ž br .
Thickness of faceplates Ž h1 .
Spacing of rolled grooves
Thickness of midlayer Ž h2 .
A B C D
170 170 170 170
25.0 25.0 25.0 25.0
4.0 4.0 4.0 4.0
0.5 0.5 0.5 0.5
None 0.5 1 2
2.6 2.6 2.6 2.6
a
Unit: mm.
280
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
Fig. 5. The schematic diagram of the experimental set-up for the dynamic measurement of the ER sandwich beam.
The high-voltage power supply provided the required electric field during the test. The resonance frequencies of the specimen were found by locating the peaks of the frequency response function while the damping loss factor was calculated by the half-power-pointbandwidth method at the peak. 2.3. Effects of electrode modification on the ER effect Fig. 6 presents a typical measured result of the stress amplitude with respect to the strain amplitude at different applied nominal electric field strengths for the ER material under parallel-plate testing configuration. Without the influence of an electric field, the ER material behaved as a Newtonian fluid, i.e. the stress amplitude was proportional to the strain amplitude under constant sinusoidal excitation of frequency 20 Hz. With the applied electric field, the ER material showed the transition from a pre-yield to post-yield phenomenon as the strain amplitude was increasing monotonously. In the pre-yield region where the strain was small, the ER material demonstrated a nearly linear elastic property. Hence, the slope of the curve was taken as the infinitesimal shear modulus of the activated ER material. It is clearly seen that the shear modulus increased as the electric field strength was raised. The measured shear moduli with different modified electrode surfaces are shown in Fig. 7. The results show that the ER effect was enhanced with surface modification on the electrode. There was a 30% increment at 1.0 kVrmm for the modified electrode over the plain one. However, the measured shear modulus for the ER material using electrodes with 0.5-mm-spacing grooves did not present more increment than its 2-mm counterparts. This should be due to the sharper peak profile for the 2-mm-spacing grooves on the electrode. Although the lower groove density for the 2-mm elec-
Fig. 6. The typical shear stress᎐shear strain curves for the ER fluid tested using the parallel-plate fixture with 2-mm spacing grooves on the electrode surfaces.
trode could not raise more the ER effect than its 0.5-mm counterpart, its sharper groove peaks intensified the local field strength. Those, in turn, caused the formation of stronger chain structures in the ER material. Therefore, a greater ER effect was not seen from the measurement of the specimens. It was suspected that, if under the same groove’s profile, the electrode with the higher groove density should provide a greater ER effect under the same nominal electric field strength. Fig. 8 presents the measured current density of the ER fluid tested in the parallel-plate fixture with different surface modifications on the electrodes. There are two groups of measurements: static and dynamic. The static one denotes the measurement with the central plate of the fixture remains quiescent while the dynamic one has the central plate in a sinusoidal oscillation of amplitude 0.03 mm. For each pattern of surface modification on the electrode, the current density of
Fig. 7. The typical shear modulus of the ER fluid using the parallelplate fixture with different surface modifications on the electrodes.
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
Fig. 8. The measured current density of the ER fluid tested in the parallel-plate fixture with different surface modifications on the electrodes.
the ER fluid in static measurement is less than its dynamic counterpart. This should be due to the temperature effect caused by the dissipated nature of the ER fluid under oscillating shearing. The internal friction of the ER fluid causes the slight temperature rise and, therefore, the decrease in electrical resistance. On the other hand, the ER fluid tested in the fixture with denser grooves on the surface of the electrodes shows more current density both in static and dynamic measurements. It is seen that the greater ER effect, obtained by the surface modification on the electrode, as shown in Fig. 7, is paid by the increased supply of electrical power. 2.4. Effects of electrode modification on the dynamic characteristics of ER sandwich beams
According to the aforementioned experimental technique used in this study, all the dynamic characteristics of the sandwich beam were obtained from the frequency response function. Fig. 9 presents the relative increment of the first mode’s resonance frequency of the specimens under the influence of applied electric field. The percentage increment of the resonance frey0 quency was calculated as = 100 where and 0 0 were the corresponding resonance frequencies with and without an applied electric field, respectively. The measured first mode’s resonance frequency of the cantilevered ER beam without applying electric field was approximately 20 Hz. It is clearly seen that the resonance frequency monotonously increased as the applied electric field strength was raised for each ER beam under consideration. However, the specimen with denser rolled grooves on the electrode showed more
281
Fig. 9. The relative increment in the first mode’s resonance frequency of the ER sandwich beams with different surface modifications on the electrodes.
distinct increments in the resonance frequency from the unmodified specimen. There was nearly a 20% greater ER effect for the specimen with 0.5-mm-spacing rolled grooves than that of plain specimen at the applied electric field strength of 1.0 kVrmm. The less increment in the resonance frequency for the 0.5-mm specimen under small electric field strength should be owed to the frequency shift caused by the increase in damping. The corresponding modal damping loss factors for the first mode of the specimens are presented in Fig. 10. The lines in the figure are the approximately fitted trends from measured data points. In contrast to the change in resonance frequency, the modal damping for each specimen first increased and then decreased as the applied electric field strength was raised. With the rolled grooves on the electrode surfaces, the modified specimens showed that the peak for maximum damping
Fig. 10. The modal damping loss factor for the first mode of the ER sandwich beams with different modifications on the face-plates.
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3. Conclusions
Fig. 11. The relative increment in the second mode’s resonance frequency of the ER sandwich beams with different surface modifications on the face-plates.
shifted to a lower electric field strength and attained a higher magnitude. This was because the chain structure formed between grooved electrodes had a higher strength than the plain electrodes at the same electric field, as shown in Fig. 7. In the absence of the applied electric field, the ER material was within the post-yield status. The strength of the chain structure developed upon the applied electric field determined its transition from post-yield to pre-yield status. Therefore, with the same deformation amplitude of excitation, the ER material reached the pre-yield status at lower electric field strength for the grooved specimen. In addition, the ER material demonstrated maximum loss modulus at the transition from post-yield to pre-yield straining. Thus, the peak for maximum damping occurred at a lower electric field for the modified specimen compared to the unmodified specimen. Moreover, it should be noted that at higher electric field, where the ER materials were all under pre-yield straining, the specimen with 0.5-mm-spacing grooves presented the least damping due to its highest strength of the chain structure. A similar measurement was also performed on the second mode of the specimens. The results for the percentage increment of the resonance frequency and damping loss factor are shown in Figs. 11 and 12, respectively. Fig. 11 shows that the frequency at the 1.0-kVrmm field strength could be further increased by 20% from the plain specimen by using the surface modification proposed in this study. In Fig. 12, there are several data points missing near the peaks of maximum damping. This was because the big increase in damping blunted the resonance peak of the frequency response function so much that the half-power-point method failed to determine its value. Hence, it is clearly seen that the surface modification proposed could effectively raise the damping effect of the ER sandwich beam.
In this study, the dynamic characteristics of the ER material under the influence of the electric field established between electrodes with grooved surfaces were investigated experimentally. The measured shear modulus of the ER material using a parallel-plate fixture showed that, by modifying the electrode surfaces with parallel machined grooves, there was a 30% greater increment in the modulus at the applied electric field strength of 1.3 kVrmm compared to its counterpart without surface modification. However, an associated increment in the electrical power supply is demanded. The geometrical modification on the electrode surface altered the local electric field, and thereby, the chain structures of the activated ER material between the electrodes. The more agglomerated particle chains demonstrated greater strength and ER effect as they deformed. A similar technique was used in modifying the electrode surfaces of the ER sandwich beam. For the specimens tested, it was found that the denser the rolled grooves on the electrode surfaces, the more the enhanced ER effect on the increment of the resonance frequency and the damping loss factor could be obtained. More than 20% enhancement both in resonance frequency and damping loss factor was achieved in this study. Hence, it could be an effective method for improving the performance of this class of smart structures incorporating ER materials.
Acknowledgements The authors thank the partial financial support from the National Science Council of Taiwan through Contract No. NSC 88-2212-E-212-004.
Fig. 12. The modal damping loss factor for the second mode of the ER sandwich beams with different surface modifications on the face-plates.
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
References w1x Gandhi MV, Thompson BS. Smart materials and structures. London: Chapman and Hall, 1992. w2x Crowson A. Smart materials and structures: an army perspective. In: Recent advances in adaptive and sensory materials and their applications. Lancaster: Technomic, 1988:811᎐821. w3x Joeger CA, Rogers CA. An overview of smart materials & structures. In: Recent advances in adaptive and sensory materials and their applications. Lancaster: Technomic, 1992:1᎐21. w4x Shulman ZP, Gorodkin RG, Korobko EV, Gleb VK. The electrorheological effect and its possible uses. J Non-Newtonian Fluid Mech 1981;8:29᎐41. w5x Stevens NG, Sproston JL, Stanway R. An experimental study of electro-rheological torque transmission. J Mech Transmissions Automat Des 1988;110:182᎐188. w6x Moaishita S, Ura T. ER fluid applications to vibration control devices and their adaptive neural-net controller. In: Recent advances in adaptive and sensory materials and their applications. Lancaster: Technomic, 1992:537᎐546. w7x Gandhi MV, Thompson BS, Choi SB. A new generation of innovative ultra-advanced intelligent composite materials featuring electro-rheological fluids: an experimental investigation. J Compos Mater 1989;23:1232᎐1255. w8x Choi SB, Thompson BS, Gandhi MV. An experimental investigation on smart laminated composite structures featuring embedded electro-rheological fluid domains for vibration-control applications. Compos Eng 1992;2:543᎐559.
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w9x Choi Y, Sprecher AF, Conrad H. Response of electrorheological fluid-filled laminate composites to forced vibration. J Intelligent Mater Sys Struct 1992;3:17᎐29. w10x Berg CD, Evans LF, Kermode PR. Composite structure analysis of a hollow cantilever beam filled with electro-rheological fluid. J Intelligent Mater Sys Struct 1996;7Ž5.:494᎐502. w11x Oyadiji SO. Applications of electro-rheological fluids for constrained layer damping treatment of structures. J Intelligent Mater Sys Struct 1996;7Ž5.:541᎐549. w12x Lee CY. Finite element formulation of a sandwich beam with embedded electro-rheological fluids. J Intelligent Mater Sys Struct 1995;6Ž5.:718᎐728. w13x Lee CY, Cheng CC. Dynamic characteristics of sandwich beam with embedded electro-rheological fluid. J Intelligent Mater Sys Struct 1998;9Ž1.:60᎐68. w14x Abu-Jdayil B, Brunn PO. Effects of electrode morphology on the slit flow of an electrorheological fluid. J Non-Newtonian Fluid Mech 1996;63:45᎐61. w15x Otsubo Y. Effect of electrode pattern on the column structure and yield stress of electrorheological fluids. J Colloid Interf Sci 1997;190:466᎐471. w16x Gulley GL, Tao R. Static shear stress of electrorheological fluids. Phys Rev E 1993;48Ž4.:2744᎐2751. w17x Clercx HJH, Bossis G. Static yield stresses and shear moduli in electrorheological fluids. J Chem Phys 1995;103Ž21.:9426᎐9437. w18x Lee CY, Cheng CC. Complex moduli of electro-rheological fluid under oscillating shear. Int J Mech Sci 2000;42Ž3.:561᎐574.
Experimental study on electro-rheological material with grooved electrode surfaces Chun-Ying LeeU , Kuo-Long Jwo Department of Mechanical Engineering, Da-Yeh Uni¨ ersity, Da-Tsuen, Chang-hua, Taiwan, Republic of China Received 8 March 2000; received in revised form 15 August 2000; accepted 25 August 2000
Abstract The dynamically tunable capability of a sandwich beam with embedded electro-rheological material has been proven to be a viable tool for the vibration control of structures. The effectiveness of this technique depends largely on the ER effect caused by the applied electric field. This ER effect is determined by the formation of the chain-like structures between the electrodes. In this study, the surfaces of the electrodes were modified with parallel grooves in different spacing ᎏ 0.5, 1 and 2 mm, respectively. These modified electrodes changed the local electric field distribution. Therefore, the chain-like structures formed by the suspension particles of the ER material upon the application electric field were altered. The dynamic characteristics of both the ER material within the parallel-plate fixture and the ER sandwich beam with modified electrodes were measured. The results showed that with finer spacing of the grooves on the electrodes, the ER material demonstrated greater increases in both the storage modulus and the damping loss factor upon the application of the electric field. Compared to its counterpart with plain electrodes, a 20% greater increment in the first two modes’ resonance frequencies was achieved with the proposed surface modification on the ER sandwich beam at an applied electric field strength of 1.0 kVrmm. 䊚 2001 Elsevier Science Ltd. All rights reserved. Keywords: Electro-rheological fluid; Shear modulus; Sandwich beam
1. Introduction Electro-rheological ŽER. materials are a potential material for application in the field of intelligent materials and structures w1᎐3x. Due to the controllability of the rheological property of the ER materials by an applied electric field, varieties of its applications have been intensive research topics for researchers and engineers w4᎐6x. The incorporation of the ER material into a structure by Gandhi et al. w7x presents an innovative technique for the distributed vibration control of the structure. Thereafter, many experimental works regarding U Corresponding author. Tel.: q886-4-8528469 Žext. 2109.; fax: q886-4-8536667. E-mail address: [email protected] ŽC. Lee..
the dynamic characteristics of the beam-type structures have been published w8᎐10x. Oyadiji w11x used the sandwich plate with complex flexural stiffness to study the ER effect on the constrained layer damping treatment of a clamped-clamped plate. Lee w12x based on an assumed constitutive relationship for the ER material under quasi-static shearing presented a method for calculating the equivalent complex moduli for the ER material under an oscillating shear. The finite element formulation incorporating material non-linearity for the sandwich beam structure was later verified by a followed experimental measurement w13x. In order to enhance the controllable dynamic characteristics of the sandwich beam, Choi et al. w8x studied several specimens with different surface modifications on the electrode surfaces. They showed that the specimen with electrode surfaces roughened by sandpaper
0261-3069r01r$ - see front matter 䊚 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 1 - 3 0 6 9 Ž 0 0 . 0 0 0 9 0 - X
278
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
demonstrated a greater ER effect than its counterpart with original surfaces. On the other hand, the specimens with attached circular or rectangular polyvinyl patches on the electrode surfaces did not significantly show a difference from the original specimen. No discussion regarding the difference was given in their study. Abu-Jdayil and Brunn w14x investigated the effects of electrode morphology on the slit flow of an electro-rheological fluid. Both oblique and corrugated electrodes were used in their study. They demonstrated an average factor of 2.0 and 2.5 in the increase of the ER effect for the oblique and corrugated electrodes, respectively, in the voltage range 1᎐5 kV. The enhancement in the ER effect due to different electrode morphology should be related to the formation of the thicker chain-like structures upon the influence of the applied electric field w15x. The dependence of the ER effect on the morphology of the chain-like structures has been pointed out theoretically by researchers w16,17x. An experimental study regarding the ER effect in different electrode morphology was conducted in this paper with special emphasis on the dynamic characteristics of the ER sandwich beams. According to the deformation pattern of the ER material embedded in the sandwich structure, a parallelplate fixture with machined grooves on the electrode surfaces, combined with an apparatus for ordinary vibration testing, was used to perform dynamic measurement on the ER material. In the meanwhile, the ER sandwich beam specimens fabricated by using aluminum electrodes with rolled grooves on the surfaces were tested to demonstrate the effect of electrode surface modification on their dynamic characteristics.
Fig. 1. Schematic diagram of the test set-up for the ER fluid under oscillating shear using parallel-plate fixture.
in-plane and transverse motions of the central plate. This in turn would assure the pure shear straining on the ER material filled in the gaps. The electric field was established by applying voltage to these parallel plates. There were three types of electrode surface geometry investigated herein, namely, plain, 2-mm and 0.5-mm spaced grooves, respectively, as shown in Fig. 2 for the photomicrographs. It can be seen in this figure that the electrode with 2-mm-spacing grooves had been
2. Experimental measurement and discussions The ER material used in this study consisted of cornstarch suspensions in silicone oil. The carrier fluid had a viscosity of 20 cS. The weight fraction of the suspensions was 50%. In order to study directly the ER effect with different electrode surface modifications, the dynamic measurement using parallel-plate fixture by Lee and Cheng w18x was adopted in this study. 2.1. Parallel-plate fixture setup The schematic diagram of the fixture and the associated testing apparatus is shown in Fig. 1. The fixed part of the fixture mainly consisted of two parallel plates on a base. These two parallel plates formed a rectangular cavity with a height of 6 mm. A 3-mm thick, 140-cm2 area plate attached on the shaker head was inserted into the space between the two parallel plates with an equal gap height from them. This symmetric arrangement should avoid the unwanted coupling between the
Fig. 2. Photomicrographs of electrodes used in parallel-plate fixture: Ža. top view of the 2-mm spacing grooved electrode; Žb. cross-sectional view of the electrodes; Žc. top view of the 0.5-mm spacing grooved electrode.
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
279
Fig. 3. The schematic diagram of the cantilevered ER sandwich beam specimen. Fig. 4. Photomicrograph of the cross-section of the aluminium faceplates used in ER sandwich specimens.
machined deeper than their 0.5-mm counterparts due to the difficulties in obtaining the same machining process. This consequently resulted in a sharper surface peak for the 2-mm-grooved electrode. Since the electrode surfaces surrounding the inner cavity were machined with parallel grooves, the electric field was locally disturbed by these surface modifications. The 0᎐5-kV high-voltage power supply furnished the required voltage that was equivalent to a range of 0᎐3.3 kVrmm nominal field strength on the ER material. During the test, the power amplifier activated the electro-magnetic shaker with the sinusoidal source generated from the dynamic signal analyzer. The eddy current probe monitored the axial motion of the shaker head, and therefore the central plate. This axial motion of the central plate provided the shear straining on the ER material filled between the plates. The force transducer measured the corresponding reacted axial force on the fixed plates. The input axial displacement signal and the reacted force signal were recorded in the dynamic signal analyzer. Thus, the associated shear strain and shear stress on the ER material could be calculated accordingly.
For all specimens, the top and bottom were aluminum faceplates while the mid-layer was filled with ER material confined by the rubber dam on the edges. The aluminum faceplates also served as electrodes for applying an electric field. At the end of the specimen where the boundary constraints applied, a glassrepoxy pad was used as the mid-layer to provide the rigidity for the clamping force. The only difference among the specimens was that the inner surface of the aluminum faceplates was rolled with grooves in different spacing ᎏ none, 0.5, 1 and 2 mm, respectively. Fig. 4 presents a photomicrography of the cross-sections of the different electrodes. The dimensions of the specimens are listed in Table 1. The experimental setup for the measurement of dynamic characteristics of the sandwich specimen is shown in Fig. 5. The cantilever fixture for supporting the specimen was mounted on an electro-magnetic shaker. During the measurement, the shaker provided the desired motion of the fixture base and this motion was measured by an accelerometer. The vibrating response of the specimen under the base excitation was picked up by a non-contacting eddy current probe. The probe was placed at the free end for measuring the displacement of interested mode shape. With the output vibrating response and the input base excitation, the dynamic transmissibility of the specimen in the frequency domain could be obtained by the dynamic signal analyzer.
2.2. Sandwich beam specimen setup For the experimental measurements of the ER sandwich beams in a cantilevered boundary condition, four types of specimens were fabricated in this study. The schematic diagram of the specimens is shown in Fig. 3. Table 1 Dimensions of the ER sandwich beam specimens a Specimen
Span Ž L.
Width Ž b.
Dam width Ž br .
Thickness of faceplates Ž h1 .
Spacing of rolled grooves
Thickness of midlayer Ž h2 .
A B C D
170 170 170 170
25.0 25.0 25.0 25.0
4.0 4.0 4.0 4.0
0.5 0.5 0.5 0.5
None 0.5 1 2
2.6 2.6 2.6 2.6
a
Unit: mm.
280
C. Lee, K. Jwo r Materials and Design 22 (2001) 277᎐283
Fig. 5. The schematic diagram of the experimental set-up for the dynamic measurement of the ER sandwich beam.
The high-voltage power supply provided the required electric field during the test. The resonance frequencies of the specimen were found by locating the peaks of the frequency response function while the damping loss factor was calculated by the half-power-pointbandwidth method at the peak. 2.3. Effects of electrode modification on the ER effect Fig. 6 presents a typical measured result of the stress amplitude with respect to the strain amplitude at different applied nominal electric field strengths for the ER material under parallel-plate testing configuration. Without the influence of an electric field, the ER material behaved as a Newtonian fluid, i.e. the stress amplitude was proportional to the strain amplitude under constant sinusoidal excitation of frequency 20 Hz. With the applied electric field, the ER material showed the transition from a pre-yield to post-yield phenomenon as the strain amplitude was increasing monotonously. In the pre-yield region where the strain was small, the ER material demonstrated a nearly linear elastic property. Hence, the slope of the curve was taken as the infinitesimal shear modulus of the activated ER material. It is clearly seen that the shear modulus increased as the electric field strength was raised. The measured shear moduli with different modified electrode surfaces are shown in Fig. 7. The results show that the ER effect was enhanced with surface modification on the electrode. There was a 30% increment at 1.0 kVrmm for the modified electrode over the plain one. However, the measured shear modulus for the ER material using electrodes with 0.5-mm-spacing grooves did not present more increment than its 2-mm counterparts. This should be due to the sharper peak profile for the 2-mm-spacing grooves on the electrode. Although the lower groove density for the 2-mm elec-
Fig. 6. The typical shear stress᎐shear strain curves for the ER fluid tested using the parallel-plate fixture with 2-mm spacing grooves on the electrode surfaces.
trode could not raise more the ER effect than its 0.5-mm counterpart, its sharper groove peaks intensified the local field strength. Those, in turn, caused the formation of stronger chain structures in the ER material. Therefore, a greater ER effect was not seen from the measurement of the specimens. It was suspected that, if under the same groove’s profile, the electrode with the higher groove density should provide a greater ER effect under the same nominal electric field strength. Fig. 8 presents the measured current density of the ER fluid tested in the parallel-plate fixture with different surface modifications on the electrodes. There are two groups of measurements: static and dynamic. The static one denotes the measurement with the central plate of the fixture remains quiescent while the dynamic one has the central plate in a sinusoidal oscillation of amplitude 0.03 mm. For each pattern of surface modification on the electrode, the current density of
Fig. 7. The typical shear modulus of the ER fluid using the parallelplate fixture with different surface modifications on the electrodes.
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Fig. 8. The measured current density of the ER fluid tested in the parallel-plate fixture with different surface modifications on the electrodes.
the ER fluid in static measurement is less than its dynamic counterpart. This should be due to the temperature effect caused by the dissipated nature of the ER fluid under oscillating shearing. The internal friction of the ER fluid causes the slight temperature rise and, therefore, the decrease in electrical resistance. On the other hand, the ER fluid tested in the fixture with denser grooves on the surface of the electrodes shows more current density both in static and dynamic measurements. It is seen that the greater ER effect, obtained by the surface modification on the electrode, as shown in Fig. 7, is paid by the increased supply of electrical power. 2.4. Effects of electrode modification on the dynamic characteristics of ER sandwich beams
According to the aforementioned experimental technique used in this study, all the dynamic characteristics of the sandwich beam were obtained from the frequency response function. Fig. 9 presents the relative increment of the first mode’s resonance frequency of the specimens under the influence of applied electric field. The percentage increment of the resonance frey0 quency was calculated as = 100 where and 0 0 were the corresponding resonance frequencies with and without an applied electric field, respectively. The measured first mode’s resonance frequency of the cantilevered ER beam without applying electric field was approximately 20 Hz. It is clearly seen that the resonance frequency monotonously increased as the applied electric field strength was raised for each ER beam under consideration. However, the specimen with denser rolled grooves on the electrode showed more
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Fig. 9. The relative increment in the first mode’s resonance frequency of the ER sandwich beams with different surface modifications on the electrodes.
distinct increments in the resonance frequency from the unmodified specimen. There was nearly a 20% greater ER effect for the specimen with 0.5-mm-spacing rolled grooves than that of plain specimen at the applied electric field strength of 1.0 kVrmm. The less increment in the resonance frequency for the 0.5-mm specimen under small electric field strength should be owed to the frequency shift caused by the increase in damping. The corresponding modal damping loss factors for the first mode of the specimens are presented in Fig. 10. The lines in the figure are the approximately fitted trends from measured data points. In contrast to the change in resonance frequency, the modal damping for each specimen first increased and then decreased as the applied electric field strength was raised. With the rolled grooves on the electrode surfaces, the modified specimens showed that the peak for maximum damping
Fig. 10. The modal damping loss factor for the first mode of the ER sandwich beams with different modifications on the face-plates.
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3. Conclusions
Fig. 11. The relative increment in the second mode’s resonance frequency of the ER sandwich beams with different surface modifications on the face-plates.
shifted to a lower electric field strength and attained a higher magnitude. This was because the chain structure formed between grooved electrodes had a higher strength than the plain electrodes at the same electric field, as shown in Fig. 7. In the absence of the applied electric field, the ER material was within the post-yield status. The strength of the chain structure developed upon the applied electric field determined its transition from post-yield to pre-yield status. Therefore, with the same deformation amplitude of excitation, the ER material reached the pre-yield status at lower electric field strength for the grooved specimen. In addition, the ER material demonstrated maximum loss modulus at the transition from post-yield to pre-yield straining. Thus, the peak for maximum damping occurred at a lower electric field for the modified specimen compared to the unmodified specimen. Moreover, it should be noted that at higher electric field, where the ER materials were all under pre-yield straining, the specimen with 0.5-mm-spacing grooves presented the least damping due to its highest strength of the chain structure. A similar measurement was also performed on the second mode of the specimens. The results for the percentage increment of the resonance frequency and damping loss factor are shown in Figs. 11 and 12, respectively. Fig. 11 shows that the frequency at the 1.0-kVrmm field strength could be further increased by 20% from the plain specimen by using the surface modification proposed in this study. In Fig. 12, there are several data points missing near the peaks of maximum damping. This was because the big increase in damping blunted the resonance peak of the frequency response function so much that the half-power-point method failed to determine its value. Hence, it is clearly seen that the surface modification proposed could effectively raise the damping effect of the ER sandwich beam.
In this study, the dynamic characteristics of the ER material under the influence of the electric field established between electrodes with grooved surfaces were investigated experimentally. The measured shear modulus of the ER material using a parallel-plate fixture showed that, by modifying the electrode surfaces with parallel machined grooves, there was a 30% greater increment in the modulus at the applied electric field strength of 1.3 kVrmm compared to its counterpart without surface modification. However, an associated increment in the electrical power supply is demanded. The geometrical modification on the electrode surface altered the local electric field, and thereby, the chain structures of the activated ER material between the electrodes. The more agglomerated particle chains demonstrated greater strength and ER effect as they deformed. A similar technique was used in modifying the electrode surfaces of the ER sandwich beam. For the specimens tested, it was found that the denser the rolled grooves on the electrode surfaces, the more the enhanced ER effect on the increment of the resonance frequency and the damping loss factor could be obtained. More than 20% enhancement both in resonance frequency and damping loss factor was achieved in this study. Hence, it could be an effective method for improving the performance of this class of smart structures incorporating ER materials.
Acknowledgements The authors thank the partial financial support from the National Science Council of Taiwan through Contract No. NSC 88-2212-E-212-004.
Fig. 12. The modal damping loss factor for the second mode of the ER sandwich beams with different surface modifications on the face-plates.
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