Experimental investigation on vibration characteristics ... - Springer Link

J. Cent. South Univ. Technol. (2008) 15(s1): 239−242 DOI: 10.1007/s11771−008−354−7

Experimental investigation on vibration characteristics of sandwich beams with magnetorheological elastomers cores WEI Ke-xiang(魏克湘)1, 2, MENG Guang(孟光)2, ZHANG Wen-ming(张文明)2, ZHU Shi-sha(朱石沙)3 (1. Department of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan 411101, China; 2. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, China; 3. School of Mechanical Engineering, Xiangtan University, Xiangtan 411105, China) Abstract: A sandwich beam specimen was fabricated by treating with MR elastomers between two thin aluminum face-plates. Experiment was carried out to investigate the vibration responses of the sandwich beam with respect to the intensity of the magnetic field and excitation frequencies. The results show that the sandwich beams with MR elastomers cores have the capabilities of shifting natural frequencies and the vibration amplitudes decrease with the variation of the intensity of external magnetic field. Key words: magnetorheological (MR) elastomer; sandwich beam; vibration response; dynamical characteristic

1 Introduction Magnetorheological (MR) materials are smart materials whose physical properties can undergo instantaneous and reversible change when different intensities of the magnetic field are subjected. MR fluids, MR foams and MR elastomers were developed[1]. As a new class of the magnetorheological materials, MR elastomers are composed of micrometer-sized ferrous particles dispersed in a polymer medium. Typically, magnetic fields are applied to the polymer composite during crosslinking so that particles form chainlike or columnar structures, which are fixed in the matrix after curing. When MR elastomers are exposed to an applied magnetic field which is parallel to their particle-formed chainlike structures, the shear modulus changes with the applied magnetic field due to magnetic interactions between those ferrous particles[2]. This makes the MR elastomers have wide applications such as adaptive tuned vibration absorbers (TVAs), stiffness tunable mounts and suspensions, and variable impedance surfaces[3−10]. So far, many research fabrication, theoretical modeling and engineering application of MR elastomers were studied. However, there are few studies on the applications of MR elastomers to the vibration control of flexible beams or plates. In this paper, the vibration characteristics of sandwich beams with MR elastomers cores were

presented and discussed experimentally. A sandwich beam specimen, which is treated with MR elastomers between two separate elastic layers, was constructed and applied. The vibration responses and control capabilities of the test beam subjected to different magnetic fields and excitation frequencies were demonstrated and discussed.

2 Experimental MR elastomers beam specimen, as shown in Fig.1, was treated with an MR elastomers layer sandwiched between two thin aluminum face-plates. Thin aluminum plates were chosen for elastic surface plates due to its low damping properties and relatively high stiffness properties compared to those of MR elastomers. Additionally, aluminum’s relative magnetic permeability equals to 0, which indicates that it does not affect the distribution and strength of the magnetic field[11−12]. The beam is L=250 mm in length and b=30 mm in width. The aluminum elastic surface layer thickness is h1=h3=1 mm, and the MR elastomers layer thickness is h2 =3 mm. In order to have a uniform MR elastomers layer, 2 mm×3 mm plastic spacers were uniformly bonded onto two long edges of one of the aluminum plates. MR elastomers materials used in this study is composed of silicone rubber (Liyang Silicone Rubber Adhesives Factory, China, Model 704) and carbonyl iron particles (BASF company, Germany, model CM) with an

Foundation item: Project(10602033) supported by the National Natural Science Foundation of China; Project(07B012) supported by Scientific Research Fund of Education Department of Hunan Province; Project(VSN-2007-01) supported the Research Fund of State Key Laboratory of Mechanical System and Vibration Received date: 2008−06−25; Accepted date: 2008−08−05 Corresponding author: WEI Ke-xiang, Associate professor; Tel: +86−732−8688949; E-mail: wei_kx@163.com

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Fig.1 Configuration of MR elastomers beam

average particle diameter of 3−5 µm. The volume fraction of the iron particles is 25%. At first, all ingredients were thoroughly blended with an agitator. Then the mixture was packed into the hollow of the above-mentioned sandwich beam and placed in a magnetic field until it was cured. In this test, the MR elastomers beam was clamped at a fixed platform using a cantilever configuration. Fig.2 presents a schematic configuration and photograph of the experimental set-up, which is integrated with sensing, actuation and signal analysis equipment. The instruments used in the experiments include accelerometer, shaker, amplifier, function generator and dynamic analyzer. An accelerometer produced by B&K Inc. with model number BK4382 was used to measure the vibration

J. Cent. South Univ. Technol. (2008) 15(s1): 239−242

displacement at a single location. The excitation force applied in the MR elastomers beam was produced by a shaker. The shaker was driven by an amplified voltages signal generated by a function generator. A dynamic signal analyzer, produced by Data Physics Corporation with model number SignalCalc430, was used for the fast Fourier transformation of the acquired analog signals from the accelerometer. Vibration responses in frequency domain, natural frequencies and amplitudes of the vibration were presented from the output of the analysis results. Permanent magnets were used to generate magnetic field over the test beam. The magnetic field was applied in the vertical direction of the beam surface. Variations in the magnetic field level were obtained by changing the distance between the permanent magnets with a simple screw mechanism. The shaker tip was glued to the beam at the actuation location which was 20 mm from the fixed-end of the beam. The accelerometer was located at the position of 10 mm from the free-end of the beam. The experimental procedure is carried out as follows: the signal output from the function generator is sent to the shaker through the amplifier. The shaker provides the external vibration over the test beam. The vibration data of the test beam is acquired by the accelerometer and sends to the dynamic signal analyzer. The dynamic signal analyzer processes the input signal. Then, the vibration characteristics of the test beam are obtained and analyzed.

3 Results and discussion

Fig.2 Experimental set-up for MR Elastomers beam: (a) Schematic; (b) Photograph

Firstly, the function generator was set using a swept sine actuation at a range of 0−200 Hz with 1 Hz increment. Fig.3 displays effects of the magnetic field on the vibration response of the MR elastomers beam, and Fig.4 shows the discrepancy of natural frequencies with or without magnetic field. From Figs.3−4 it can be seen that the natural frequencies increase as the magnetic field strength increases, and the vibration amplitude of each mode except for the third mode decreases when the magnetic field is applied. At the same time, these variations are more obvious at the lower frequencies. The results demonstrate that the MR elastomers beams have the capabilities of shifting natural frequencies toward the higher ones and the vibration amplitudes decrease, especially at the low frequencies. In order to further validate the vibration suppression capability of the MR elastomers beam, the responses of the MR elastomers beam were investigated under the control of an on-off magnetic field at different excitation


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Fig.3 Frequency responses of MR elastomers beam with and without magnetic field: (a) Without magnetic field; (b) With magnetic field

Fig.4 Natural frequencies of MR elastomers beam with and without magnetic field

frequencies. The vibration control responses of the MR elastomers beam at different excitation frequencies are shown in Fig.5. Figs.5(a) and 5(c) show the vibration responses when excitation frequencies equal to the first and third natural frequency, respectively. It can be seen that when a magnetic field is applied, the vibration amplitudes reduce obviously. But the relative reductions

Fig.5 Responses of MR elastomers beam under control of on-off magnetic field at different excitation frequencies: (a) f=12.08 Hz (the first natural frequency); (b) f=40 Hz; (c) f= 62.94 Hz (the third natural frequency); (d) f=80 Hz


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are variable for different excitation frequencies. For example, the amplitude reduces about 25% at 12.08 Hz when the magnetic field is applied, while the amplitude reduces less than 20% at 40 Hz. It means that the MR elastomers beam has an optimum vibration control effect for one excitation frequency by applied magnetic field. In the next study, it needs to be furtherly investigated.

4 Conclusions 1) The natural frequencies increase and the vibration amplitude of each mode decreases when the magnetic field is applied to the MR elastomers beam. 2) The MR elastomers beam can shift the natural frequencies and decrease the vibration amplitudes when the magnetic field is applied. Therefore, the MR elastomers can be used to vibration suppression of beam structures.

References [1] [2]

[3]

CARLSON J D, JOLLY M R. MR fluid, foam and elastomer devices[J]. Mechatronics, 2000, 10(4/5): 555−569. GINDER J M, NICHOLS M E, ELIE L D, et al. Magnetorheological elastomers: properties and applications[C]// Proceedings of SPIE: Smart Materials Technologies, 1999, 3675: 131−138. DAVIS L C. Model of magnetorheological elastomers[J]. Journal of Applied Physics, 1999, 85(6): 3348−3351.

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

ZHOU G Y. Complex shear modulus of a magnetorheological elastomers[J]. Smart Materials and Structures, 2004, 13(5): 1203−1210. KALLIO M, LINDROOS T, AALTO S, et al. Dynamic compression testing of a tunable spring element consisting of a magnetorheological elastomer[J]. Smart Materials and Structures, 2007, 16(2): 506−514 DAVID Y, WANG Xiao-jie, FARAMARZ G. A new MR fluid-elastomer vibration isolator[J]. Journal of Intelligent Material Systems and Structures, 2007, 18(12): 1221−1225. DENG H X, GONG X L. Adaptive tuned vibration absorber based on magnetorheological elastomer[J]. Journal of Intelligent Material Systems and Structures, 2007, 18(12): 1205−1210. LERNER A A, CUNEFARE K A. Performance of MRE-based vibration absorbers[J]. Journal of Intelligent Material Systems and Structures, 2008, 19(5): 551−563. DENG Hua-xia, GONG Xing-long. Application of magnetorheological elastomers to vibration absorber[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13(9): 1938−1947. ZHOU G Y, WANG Q. Study on the adjustable rigidity of magnetorheological-elastomer-based sandwich beams[J]. Smart Materials and Structures, 2006, 15(1): 59−74. SUN Qing, ZHOU Jin-xiong, ZHANG Ling. An adaptive beam model and dynamic characteristics of magnetorheological materials[J]. Journal of Sound and Vibration, 2003, 261: 465−481. MELEK Y, DAI He-ming. Vibration suppression capabilities of magnetorheological materials based adaptive structures[J]. Smart Materials and Structures, 2004, 13(1): 1−11. (Edited by CHEN Can-hua)