Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

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1 Bidisperse Magnetorheological Fluids using Fe Particles at Nanometer and Micron Scale N. M. WERELEY, 1, *A.CHAUDHURI, 1 J.-H. YOO, 1 S. JOHN, 1 S. KOTHA, 2 A. SUGGS, 2 R. RADHAKRISHNAN, 2 B. J. LOVE 3 AND T. S. SUDARSHAN 2 1 Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA 2 Materials Modification Inc., 2721-D Merrilee Drive, Fairfax, VA 22031, USA 3 Department of Materials Science and Engineering Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA ABSTRACT: Conventional magnetorheological (MR) fluids are suspensions of micron-sized particles in a hydraulic or silicone oil carrier fluid. Recently, research has been conducted on the advantages of using bidisperse fluids, which are mixtures of two different powder sizes in the MR suspension. The MR fluids investigated here use a mixture of conventional micronsized particles and nanometer-sized particles. The settling rate of such bidisperse fluids using nanometer-sized particles is reduced because the nanoparticles fill pores created between the larger particles, thereby reducing fluid transport during creeping flow. This reduction in the settling rate comes at a cost of a reduction in the maximum yield stress that can be manifested by such an MR fluid at its saturation magnetization. There is a measurable and predictable variation in rheological properties as the weight percent (wt%) of the nanometer-sized particles is increased relative to the weight percent (wt%) of micron-sized particles, while maintaining a constant solids loading in the MR fluid samples. All bidisperse fluids tested in this study have a solids loading of 60 wt% of iron (Fe) particles. This study investigates the effect of increasing the wt% of 30 nm (nominal) Fe particles relative to 30 mm (nominal) Fe particles on rheological characteristics, such as yield stress and postyield viscosity. The goal of this study is to find an optimal composition of the bidisperse fluid that provides the best combination of high yield stress and low settling rate based on empirical measurements. The applicability of the Bingham-plastic rheological model to the measured flow curves of these MR fluids is also presented. Key Words: magnetorheological fluids, yield stress, sedimentation rate, nanoparticles. INTRODUCTION MAGNETORHEOLOGICAL (MR) fluids are suspensions of soft magnetic particles, such as iron or cobalt, in a carrier fluid. The important characteristics of an MR fluid are its yield stress, viscosity, and settling rate (Kordonski et al., 1998; Phule and Ginder, 1998a, b, 1999; Rosenfeld et al., 2002). The benefits of such fluids are that these properties can be varied by applying a magnetic field. Therefore, MR fluids have been used in numerous types of smart actuation systems, such as dampers, clutches, and isolators (Stanway et al., 1996). Magnetorheological fluids are achieving success as hydraulic fluids in damping applications for military, civil, and especially automotive systems. Most MR fluids in use today utilize powders composed of micronsized particles. These micron powder-based MR fluids *Author to whom correspondence should be addressed. wereley@aero.umd.edu present a high yield stress ( kpa), but they are susceptible to settling in the absence of frequent remixing. The effects of particle size and volume or weight fraction have also been studied by numerous researchers (Taketomi et al., 1993; Rosenfeld et al., 2002). Thixotropic additives have been proven to be effective at minimizing particle settling in an MR fluid (Weiss et al., 1997). An alternative to this approach is the introduction of nanometer-scale particles into MR fluids (Kormann et al., 1996; Rosenfeld et al., 2002), where the settling problem can be mitigated due to the predominance of the thermodynamic forces (Rosensweig, 1996), but the yield stress is reduced. This study focuses on the introduction of nanometerscale particles in small concentrations to enhance the yield stress and to reduce the particle settling rate. In Figure 1, the chain formations in three different lightly loaded MR fluids can be observed under the influence of magnetic field. In these optical micrographs taken at a magnification of 120, the nature of the JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 17 May X/06/ $10.00/0 DOI: / X ß 2006 SAGE Publications

2 394 N. M. WERELEY ET AL. Figure 1. Fluid chain formation in magnetorheological fluids. (a) Micron (b) Nano (c) Bidisperse chain formation changes as a function of the particle dispersion. In each optical micrograph, the north magnetic pole is on top, and the south magnetic pole is at the bottom. In Figure 1(a), the lightly loaded MR fluid utilizing micron-sized particles develops a relatively coarse, yet highly networked, chain or sheet structure. In contrast, the MR fluid with the nanometer-sized particles, shown in Figure 1(b), has a relatively fine, yet highly networked structure, suggesting a substantial MR effect, but with a reduced yield stress. We have also considered a bidisperse fluid containing a mixture of both nanoparticles and microparticles. In Figure 1(c), the chain formation of a bidisperse MR fluid is shown, the nature of which is quite different from that of the micron or nanometer particle-based fluids. In this case, distinct chains are formed, where the nanoparticles appear to fill in the interparticle spaces that are clearly evident in the networked sheet structures manifested in the monodisperse fluids. These distinct chains suggest the possibility that a bidisperse fluid can be synthesized with a yield stress that is substantial. In addition, the nanopowders in the MR fluids will tend to redisperse themselves by thermal convection. This suggests that an MR fluid can be synthesized having a yield stress comparable to that of a monodisperse micron powder MR fluid, but with the low settling rates of a nanopowder-based MR fluid. To address this trade-off, two key experiments were conducted in this study: (a) settling tests were conducted using a laser scattering device (Hoffman et al., 2002; Maciborski et al., 2002) to track mudline formation in a column of MR fluid in the absence of field, and (b) rheological tests were conducted using a parallel disk rheometer to characterize key rheological properties including Bingham yield stress, post-yield viscosity, and elastic limit yield stress. MAGNETORHEOLOGICAL FLUIDS Materials Modification Inc. developed a patented microwave-based process (Sethuram and Kalyanaraman, 2002) for efficient synthesis of nanopowders. The microwave plasma synthesis process utilized microwave energy to generate plasma by ionization, disassociation, and recombination of gas molecules. The high temperature vaporized the precursors, which promoted chemical reactions at the molecular level in the presence of microwaves. These vapors were rapidly cooled in an inert atmosphere to form powders. Iron powder was synthesized from iron carbonyl precursors according to FeðCOÞ 5! Ar=N 2 FeðÞþ5CO s "ðgþ ð1þ The average particle diameter in this pure Fe powder was nominally 28 nm. Additional Fe powder were purchased commercially, having 30 mm diameter (nominal). One of the major technical challenges in the formulation of MR fluids is to overcome the attractive Van der Waals forces between the particles and to form stable uniform dispersions (Rosensweig, 1996). A key goal is to improve flow characteristics, reduce particle-settling rates, and reduce agglomeration. Numerous additives and coatings have been used in an attempt to resolve the stability problem in MR fluids. Polymer-coated nanoparticles (Kormann et al., 1996), nanoscale additives (Phule and Ginder, 1999), and viscoplastic media (Rankin et al., 1999) have been investigated as a means of maintaining the metallic particles in suspension. The key to prevent particle clustering or agglomeration is to introduce an interparticle force between the particles by either (1) electrostatic, or (2) steric means. In our study, we added surfactants to form stable suspensions as it is a very effective steric means of producing a stable MR fluid. To prepare stable MR fluids, hydraulic oil was chosen as a carrier fluid. Mobil DTE20 series is used extensively in high-pressure systems including industrial, marine, and mobile service, especially in servovalves and robotics, because of their excellent antiwear properties, multimetal compatibility, and corrosion resistance. Lecithin was utilized as a surfactant for producing nanofluidic dispersions. Lecithin (2 wt% optimized) was mixed in hydraulic oil using a high speed emulsifier

3 Bidisperse Magnetorheological Fluids using Fe Particles 395 Table 1. MR fluid compositions are all 60 wt% iron powder. ID 16-B 17-A 17-B 17-C 18-A 18-B 18-C 18-D 19-A 19-B 19-C Micropowder % Nanopowder % at speeds close to 11,000 rpm. Iron nanopowder obtained from the microwave plasma synthesis technique, or commercially available micron-sized powder, were added to the oil and the mixing was continued. The mixing speed was kept constant at 11,000 rpm for a constant mixing time of 30 min for all the MR fluid specimens. The majority of samples were bidisperse MR fluids. One sample was a micron particle-based MR fluid having 60 wt% of Fe powder. All bidisperse MR fluid samples had a 60 wt% solids loading of Fe powder. Each sample was prepared with g of particles, 1.5 g of lecithin used as the surfactant, and 50 g of hydraulic oil as the carrier fluid. The final sample was a nanometer sized powder-based MR fluid with a 40 wt% solids loading. It was necessary to reduce the solids loading in the nanoparticle-based fluid because higher wt% compositions would not mix properly due to the high surface area nanopowders. The ratio between the micron-and the nanometer-sized powders is also by wt% of powder. The eleven bidisperse samples prepared as shown in Table 1 all had 60 wt% of Fe powder. SEDIMENTATION RATE Settling behavior in MR fluids has been a longstanding obstacle to their application in damping devices (Chin et al., 2001). Magnetorheological suspensions have a tendency to settle due to the density difference between the particles and the fluid. When MR fluids settle out of suspension, the particles often form a hard cake substance consisting of magnetized, and therefore tightly bound, primary particles (Chin et al., 2001). Because of the residual magnetism of the particles, solids formed as a result of the Fe powder settling are difficult to redisperse, so that the MR behavior of a redispersed MR fluid is less predictable. The dynamic shear stress of MR fluids is directly related to the volume fraction of dispersed particles in the suspension. Therefore, if the particles settle out and must be redispersed, the effectiveness of the redispersion dictates the rheological properties. An effective means of producing a stable MR fluid is by the addition of surfactants as described above. Two methods have been suggested for measuring sedimentation rates in MR fluids: (i) measuring the rate of change of magnetic permeability of the upper layer of the MR fluid to get a measure of the sedimentation velocity of particles (Gorodkin et al., 2000) and (ii) by Figure 2. Schematic of ZATLLS instrument, which is a z-axis settling rate characterization instrument. laser light transmission through a column of MR fluid. In our study, the instrument used to observe the settling behavior of MR fluids is a z-axis translating laser light scattering device (ZATLLS) designed and fabricated at Virginia Tech (Hoffman et al., 2002). This settling device transmits a 5 mw red laser at 635 nm through the glass sedimentation column to a silicon photodiode. The photodiode reports light transmission in voltage. The photodiode and laser system translate on its z-axis using a motor mounted on threaded rods. The threaded rods are spun by a motor, so that the stage can be translated along the z-axis on which the laser and the photodiode are mounted. Labview software is used to control the entire apparatus. A simplified schematic of the device is shown in Figure 2. The ZATLLS instrument is capable of accurately measuring all expected settling regimes, as well as instances of partial settling where the formation of a distinct mudline is not apparent (Hoffman et al., 2002). The time to mudline formation was also recorded for each of the fluids. A correlation was observed between the time to mudline formation and the wt% of nanoparticles as evident in Figure 3. This plot shows that increasing the wt% of nanoparticles in the MR fluid increases the time to mudline formation, showing that the bidisperse fluids are capable of maintaining the suspension for longer periods of time. Thus, measuring the settling rate of the various bidisperse MR fluid samples led to the conclusion that even replacing only 15 20% of microparticles with nanoparticles drastically improved the homogeneity of the dispersion. The micron particle-based fluid manifested a mudline in just over 20 min as measured by the laser scattering device. In contrast, the bidisperse fluid with only 15% of the microparticles replaced with nanoparticles exhibited

4 396 N. M. WERELEY ET AL. Figure 3. Measurement of particulate settling rate in MR fluids using a z-axis translating laser light scattering device to measure mudline formation in a column of MR fluid in the absence of magnetic field. Figure 4. Calibration of magnetic flux density (B, T) as a function of the input current at the gap between the parallel disks of the viscometer. mudline formation in over 190 min, which is an order of magnitude improvement. In addition, there was no measurable settling rate (over a period of 2 months) for MR fluids composed solely of 30 nm diameter Fe particles. RHEOLOGICAL TESTING The rheological results obtained in this study were obtained using a Paar Physica MCR300 parallel disk rheometer. In this study, a standard gap of 1 mm was used to separate the parallel disks. The magnetic circuit is designed so that the magnetic field lines are perpendicular to the parallel disks. The MR cell (TEK 70 MR) is capable of continuously varying the magnetic field applied to the MR fluid sample. The MR cell also included a water-based heating/cooling system, so that a temperature of 25 C was maintained for all data reported here. As the top disk rotates above the stationary bottom disk or platen, a load cell measures the torque and a shaft encoder measures the angular rate. The MCR300 software then computes the shear stress versus shear rate flow curve for the MR fluid sample consisting of 0.31 ml from each sample. Two classes of tests were performed as a function of magnetic field: (a) constant RPM tests to measure the flow curve (shear stress vs. shear rate) and (b) oscillatory tests where the amplitude of oscillation varied and the complex modulus was measured. Several practical difficulties were encountered in performing these tests: (a) lack of a fluid container, (b) expulsion of fluid from the MR cell at high shear rates, and (c) sedimentation. Since the rheometer uses a parallel disk configuration, there was no fluid container, and the fluid remained between the disks only as the result of surface tension around the circumference of the disks. Magnetorheological fluids with a low wt% ratio of nanopowder tended to spill out, and fluids tended to be expelled from between the disks at higher RPM. One difficulty was the rapid settling of the particles in the MR fluid, especially for low nanoparticle wt% fluids in the absence of field. When the sample was placed between the two disks of the rheometer, the sedimentation process begins immediately so that the homogeneity of the MR fluid, and, thus, the consistency of the rheological characterization, was problematic. To ensure as much as possible that homogeneous MR fluid samples were tested, an MR fluid sample bottle was placed in an ultrasonic mixing device and agitated for 15 min. A sample was then taken from the center of the bottle volume. The rheometer test was begun immediately after preparation. When rheometer tests were conducted under a magnetic field, sedimentation was prevented by applying a low magnetic field until the start of the test. Applying magnetic field in this way was efficient at mitigating sedimentation, but utilization of this strategy was not possible when testing in the zero field condition. When more than 17.5 wt% of the dispersed powder was composed of nanoparticles, the sedimentation rate was much lower and the MR fluid composition much more stable. Thus, MR fluid samples with higher wt% of nanoparticles had more consistent results when their properties were measured in the rheometer. Figure 4 shows a calibration curve for the input current to the viscometer and the magnetic flux

5 Bidisperse Magnetorheological Fluids using Fe Particles 397 density at the gap. A thin Hall sensor (F.W. Bell FH301) was placed in the MR fluid between the plate and the upper disk while current was applied. Similar calibration data were obtained for all of the MR fluid samples. A nominal applied current of 2 A (near the maximum allowable current applied to the electromagnet in the rheometer) corresponds to a magnetic flux density of 0.3 T. RHEOLOGICAL FLOW CURVES Using the parallel disk rheometer, rheological flow curves of shear stress versus shear rate were measured. In these tests, approximately a 0.31 ml sample of MR fluid was placed between the base platen disk and upper disk, where rotation of the upper disk was accomplished via shear rate control. The range of shear rates tested was from 0.1 to 1500 s 1. The maximum shear rate was 1500 s 1, because the fluid was expelled from between the disks at higher RPM. For each fluid sample, 20 measurements were taken from 0.1 to 10 s 1, 20 points from 10 to 100 s 1, 20 points from 100 to 1000 s 1, and 10 points from 1000 to 1500 s 1. The only exception was for a relatively low current of 0.2 A, when the fluid was expelled from between the disks for shear rates above 1300 s 1. For each test, the shear rate was held constant for 5 s until the measured shear stress reached a steady-state value, to ensure consistency in the measurements. These measurements were taken over a range of current from 0.2 to 2.0 A, in increments of 0.2 A. Also, during these tests, a temperature control system consisting of a chilled water system maintained a constant temperature of 25 C. Figure 5 shows typical flow curves for four of the tested fluid compositions. In each case, the measurements are shown as circles. For these constant RPM rotational tests, a steadystate flow curve, or a shear stress,, versus shear rate, _, is measured by the rheometer. From these results, the rheological properties of each fluid in Table 1 can be characterized with respect to a rheological model. In this study, the Bingham-plastic model was used to Figure 5. Experimental data with Bingham-plastic model superimposed.

6 398 N. M. WERELEY ET AL. characterize the flow curves. This is a generalized model for viscoplastic flow with yield stress. The equation for the constitutive behavior is ¼ y þ >0 ð2þ The two parameters of the Bingham-plastic model are the yield stress, y, and the postyield viscosity,. The Bingham-plastic model has also been used to model Poiseuille flow in ER and MR dampers (Gavin et al., 1996; Wereley and Pang, 1998). The Bingham-plastic model was fit to the data using a weighted least squares error minimization by selection of the parameters ( y, ) for each fluid tested at all values of applied field. These results are also shown in Figure 5(a) (d). The measured shear rates were used as the weights and resulted in the model being a better fit to the high shear rate data. Figure 6 shows the trends of the Bingham-plastic yield stress as a function of magnetic field (Figure 6(a)) and nanoparticle concentration (Figure 6(b)). As expected, the dynamic yield stress has a strong dependence on the applied field. At peak values of current (I ¼ 2A, 0.30 T), the dynamic yield stress was just over kpa for the microparticle fluid, increasing up to nearly 11 kpa for the bidisperse fluid with 20 wt% of the microparticles replaced with nanoparticles, and then reduced to levels below the MR fluid composed only of microparticles as the wt% of nanoparticles increased further. On the other hand, the nanoparticles do not appear to have as large an impact on the MR effect at low values of current. Therefore, a key observation is that the bidisperse MR fluid with 20 wt% of the microparticles replaced with nanoparticles showed an increase in the dynamic yield stress at the highest values of current (magnetic field) tested. The trends of the Bingham-plastic (high shear rate) post-yield viscosity as functions of magnetic field (Figure 7(a)) and nanoparticle concentration (Figure 7(b)) are also shown. The variation in the plastic viscosity does not appear to follow any precise trend, and further tests and refinements to our characterization are ongoing. However, at low applied field values (for example, 0.3 T), the plastic viscosity clearly increases as a function of nanoparticle wt%, indicating that the increase in the off-state viscosity as the surface area of nanoparticles increases is a key reason why the settling rate decreases as nanoparticle wt% increases. Thus, there appears to be a favorable trade-off when replacing microparticles with nanoparticles. As shown in Figure 8, replacing 20 wt% of the microparticles with nanoparticles, reducing the settling rate substantially (by an order of magnitude), and the dynamic yield stress at high magnetic field (current) increased by over 15%. Such a trade-off is shown for a moderate level of magnetic field of 0.18 T in Figure 8. Figure 6. Dynamic yield stress with the Bingham-plastic model: (a) yield stress vs field and (b) yield stress vs % nanoparticles. OSCILLATORY RHEOMETRY The second category of rheological tests was an amplitude sweep using oscillatory rheometry. Such a test is used to measure the viscoelastic characteristics of the fluid, which are important to identify the microstructure of the MR suspension in the presence of a magnetic field. A viscoelastic fluid can be modeled by a complex modulus, G* ¼ G 0 þjg 00. G 0 is the in-phase elastic or storage modulus, whereas G 00 is the quadrature or loss modulus. But this characterization is valid only if the complex modulus is measured in the linear viscoelastic (LVE) regime. Thus, the main purpose of the amplitude sweep test is to determine the limits of the LVE range. As shown in Figure 9, the test was initiated for a low value of amplitude, and the amplitude was slowly increased while tracking the storage and loss moduli. The elastic limit yield stress can be determined

7 Bidisperse Magnetorheological Fluids using Fe Particles 399 (a) Coefficient of viscosity, m (Pas) Coefficient of viscosity, m (Pas) (b) Magnetic flux density (T) Figure 8. Trade-off between yield stress and settling time as represented by the time to mudline formation for a 60 wt% MR fluid. Weight of nanoparticles (%) Figure 7. Post-yield viscosity using a Bingham-plastic model: (a) post-yield viscosity vs field and (b) post-yield viscosity vs % nanoparticles. as the point at which G 0 deviates significantly (e.g., 1, 5, 10%) from the plateau value in the LVE range (Mezger, 2002, pp ). In our study, the values of the storage modulus were recorded, and the limit of the LVE range was determined to be 90% of the initial plateau value. At the edge of the LVE, the chain formations are disrupted and begin to break. The shear strain and shear stress at this LVE threshold value are also measured, so that the elastic limit yield stress can be determined (Chen et al., 1998). The yield strain occurs in the range of %, which is comparable to values of yield strain reported in the literature (Weiss et al., 1994; Li et al., 1999). The elastic limit yield stress, plotted in Figure 10, is much lower than the measured dynamic yield stress (Figure 6). From Figure 10(a) and (b), it is also clear that the elastic limit yield stress consistently degrades as the wt% of nanoparticles increases. This is also contrary to the measurements of Figure 9. Method of determining the elastic limit yield stress. the Bingham dynamic yield stress from Figure 6(a) and (b). However, it should be noted that the dynamic yield stress is a more appropriate measure of MR fluid performance for practical devices employing higher shear rates. CONCLUSIONS We investigated the influence of nanometer-sized particles in constant solids loading bidisperse magnetorheological (MR) fluids. A key goal was to assess the impact of nanoparticles on bulk rheological properties of MR fluids. An important trade-off was identified when using nanoscale powders in an MR fluid. First, the addition of nanoparticles substantially reduced the

8 400 N. M. WERELEY ET AL. Figure 10. Elastic limit yield stress of bidisperse MR nanofluids using oscillatory rheometry: (a) elastic-limit yield stress vs current and (b) elasticlimit yield stress vs % nanoparticles. sedimentation rate of the MR fluid. Second, replacing microparticles with nanoparticles in small concentrations (<15 wt%) tended to increase the field dependent yield stress. However, adding more than 15 wt% of nanoparticles tended to address this trade-off. Two key experiments were conducted in this study: (a) settling tests were conducted using a laser scattering device to track mudline formation in a column of MR fluid in the absence of field, and (b) rheological tests were conducted using a parallel disk rheometer. Settling tests, as well as qualitative observation, suggested that the addition of nanoparticles greatly reduced the settling rate of the MR fluid based on a preliminary particle sedimentation study. Measuring the settling rate of the various bidisperse MR fluid samples led to the conclusion that even replacing only 15 20% of microparticles with nanoparticles drastically improved the homogeneity of the dispersion. The micron particlebased fluid manifested a mudline in just over 20 min as measured by a laser scattering device. In contrast, the bidisperse fluid with only 15% of the microparticles replaced with nanoparticles exhibited mudline formation in over 190 min, which is an order of magnitude improvement. In addition, it was noted that there was no measurable settling rate for MR fluids composed solely of 30 nm diameter Fe particles. Rheological tests conducted using the parallel disk rheometer also indicated that the nature of the flow curves changed as a function of the ratio of nanoparticle wt% to powder wt%. A key observation was that because of increased shear thinning as nanoparticle wt% increased, comparison of the bulk properties of all of the bidisperse MR fluid samples was problematic. Therefore, a Bingham-plastic model was used to characterize the dynamic yield stress and post-yield viscosity of the MR fluid samples. At peak values of current (I ¼ 2 A), the dynamic yield stress was just over kpa for the microparticle fluid, increasing up to nearly 12 kpa for the bidisperse fluid with 20 wt% of the microparticles replaced with nanoparticles, and then as the wt% of nanoparticles increased further, the yield stress was reduced to levels below that of the microparticle-based MR fluid. In contrast, such a trend was not evident for the elastic limit yield stress as measured using oscillatory rheometry, which instead presented a monotonic decrease in the yield stress as wt% of nanoparticles increased. Thus, there is a favorable trade-off when replacing microparticles with nanoparticles. Replacing 20 wt% of the microparticles with nanoparticles lead to a substantial reduction in the settling rate (by an order of magnitude), and an increase in the dynamic yield stress of over 15% at high magnetic field. ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No Instrumentation supported by the US Army Research Office under a Defense Instrumentation Program grant (DURIP), contract No. DAAH (Dr Gary Anderson, Technical Monitor). REFERENCES Chen, C., Boger, D.V. and Nguyen, Q.D The Yielding of Waxy Crude Oils, Industrial and Engineering Chemistry Research, 37(4): Chin, B.D., Park, J.H., Kwon, M.H. and Park, M.H Rheological Properties and Dispersion Stability of Magnetorheological (MR) Suspensions, Rheologica Acta, 40: Gavin, H.P., Hanson, R.D. and Filisko, F.E Electrorheological Dampers, Part I: Analysis and Design, ASME Journal of Applied Mechanics, 63(3): Gorodkin, S.R., Kordonski, W.I., Medvedeva, E.V., Novikova, Z.A., Shorey, A.B. and Jacobs, S.D A Method and Device for

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