Review Paper on Free Vibration Response of Magnetorheological Elastomer-based Sandwich Beam
Abstract
The dynamic analysis of a three-layered symmetric sandwich beam with magneto rheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to a periodic axial load have been carried out under various boundary conditions by researchers. As the skins of the sandwich beam are conductive, magnetic loads are applied to the skins during vibration. Due to the field-dependent shear modulus of MRE material, the stiffness of the MRE embedded sandwich beam can be changed by the application of magnetic fields. Using extended Hamilton’s principle along with generalized Galarkin’s method the governing equation of motion has been derived. The free vibration analysis of the system has been carried out and the results are compared with the published experimental and analytical results which are found to be in good agreement. Here, recently developed magneto rheological elastomer based on natural rubber containing iron particles and carbon blacks have been used. The effects of magnetic field, length of MRE patch, core thickness, percentage of iron particles and carbon blacks on the regions of parametric instability for first three modes of vibration have been studied. These results have been compared with the parametric instability regions of the sandwich beam with fully viscoelastic core to show the passive and active vibration reduction of these structures using MRE and magnetic field.
References
[2] L.Chen, X.l.Gong, W.Q.Jiang, J.J.Yao, H.X.Deng, W.H.Li, Investigation on magneto rheological elastomers based on natural rubber, Journal of material science 42 (2007)5483–5489. [3] L.Chen, X.L.Gong, W.H.Li, Effect of carbonblack on the mechanical performances of magneto rheological elastomers, Journal of Polymer Testing 27 (2008) 340–345. [4] R.A.Ditaranto; Theory of the vibratory bending for elastic and viscoelastic layered finite-length beams, Journal of Applied Mechanics 32 (1965)881–886. [5] D.J. Mead, S. Sivakumaran; The stodola method applied to sandwich beam vibration, Proceedings of the Symposiumon Numerical Methods for Vibration Problems, University of Southampton, UK, 1966. [6] D.J.Mead, S.Markus, Loss factors and resonant frequencies of encastre damped sandwich beams, Journal of Sound and Vibration 12 (1)(1970)99–112.
[7] N.T. Asnani, B.C. Nakra, Vibration analysis of multilayered beams with alternate elastic and viscoelastic layers, Journal of Institution of Engineers (India)—Mechanical Engineering Division 50 (1970)187– 193. [8] D.K. Rao, Frequency and loss factors of sandwich beams under various boundary conditions, Journal of Mechanical Engineering and Science 20 (1978) 271–282. [9] W.P. Howson., A. Zare, Exact dynamic stiffness matrix for flexural vibration of three-layered sandwich beams, Journal of Sound and Vibration 282 (2005) 753–767. [10] J.R. Banerjee, Free vibration of sandwich beams using the dynamic stiffness method, Computers & Structures 81 (2003)1915–1922. [11] J.R.Banerjee,Freevibrationofsandwichbeamsusingthedynamicstiffnessm ethod, Computers &Structures 81 (2003)1915–1922. [12] J.R.Banerjee, C.W.Cheung, R.Morishima, M.Perera, J.Njuguna, Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment, International Journal of Solids and Structures 44 (2007)7543–7563. [13] Q.Sun.,J.-X.Zhou, L.Zhang, An adaptive beam model and dynamic characteristics of magnetorheological materials, Journal of Sound and Vibration 261 (2003) 465–481. [14] A.H.Nayfeh, D.T.Mook, Non-linear Oscillations, Wiley Inter science, NewYork, 1979. [15] R.C.Kar, T.Sujeta, Dynamic stability of a tapered symmetric sandwich beam, Computers & Structures 40 (1991)1441–1449. [16] K.Ray, R.C.Kar, Parametric instability of a sandwich beam with various boundary conditions, Computers & Structures 55 (1995)857–870. [17] K.Ray, R.C.Kar, Parametric in stability of multi-layered sandwich beams, Journal of Sound and Vibration 193 (3)(1996)631–644. [18] H.Boudaoud, E.M.Daya, S.Belouettar, L.Duigou, M.Potier-Ferry, Damping analysis of beams submitted to passive and active control, Journal of Engineering Structure 31 (2009)322–331. [19] T.Shiga, A.Okada, T.Kurauchi, Magneto viscoelastic behavior of composite gels, Journal of Applied Polymer Science 58 (1995)787–792. [20] M.R.Jolly, J.D.Carlson, B.C.Munoz, A.Bullions, The magneto viscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix, Journal of Intelligent material Systems and Structures 7 (1996)613–622. [21] G.Y.Zhou, Shear property of a magneto rheological elastomer, Journal of Smart Materials and Structures 12 (2003)139–146. [22] C.Bellan, G.Bossis, Field dependence of viscoelastic properties of magnetorheological elastomers, International Journal of Modern Physics B 16 (2002) 2447–2453. [23] X.Zhang, W.Li, X.L.Gong, An effective permeability model to predict field-dependent modulus of magnetorheological elastomers, Communications in Non-linear Science and Numerical Simulation 13 (2007)1910–1916.
To ensure uniformity of treatment among all contributors, other forms may not be substituted for this form, nor may any wording of the form be changed. This form is intended for original material submitted to AJCT and must accompany any such material in order to be published by AJCT. Please read the form carefully.
The undersigned hereby assigns to the Asian Journal of Convergence in Technology Issues ("AJCT") all rights under copyright that may exist in and to the above Work, any revised or expanded derivative works submitted to AJCT by the undersigned based on the Work, and any associated written, audio and/or visual presentations or other enhancements accompanying the Work. The undersigned hereby warrants that the Work is original and that he/she is the author of the Work; to the extent the Work incorporates text passages, figures, data or other material from the works of others, the undersigned has obtained any necessary permission. See Retained Rights, below.
AUTHOR RESPONSIBILITIES
AJCT distributes its technical publications throughout the world and wants to ensure that the material submitted to its publications is properly available to the readership of those publications. Authors must ensure that The Work is their own and is original. It is the responsibility of the authors, not AJCT, to determine whether disclosure of their material requires the prior consent of other parties and, if so, to obtain it.
RETAINED RIGHTS/TERMS AND CONDITIONS
1. Authors/employers retain all proprietary rights in any process, procedure, or article of manufacture described in the Work.
2. Authors/employers may reproduce or authorize others to reproduce The Work and for the author's personal use or for company or organizational use, provided that the source and any AJCT copyright notice are indicated, the copies are not used in any way that implies AJCT endorsement of a product or service of any employer, and the copies themselves are not offered for sale.
3. Authors/employers may make limited distribution of all or portions of the Work prior to publication if they inform AJCT in advance of the nature and extent of such limited distribution.
4. For all uses not covered by items 2 and 3, authors/employers must request permission from AJCT.
5. Although authors are permitted to re-use all or portions of the Work in other works, this does not include granting third-party requests for reprinting, republishing, or other types of re-use.
INFORMATION FOR AUTHORS
AJCT Copyright Ownership
It is the formal policy of AJCT to own the copyrights to all copyrightable material in its technical publications and to the individual contributions contained therein, in order to protect the interests of AJCT, its authors and their employers, and, at the same time, to facilitate the appropriate re-use of this material by others.
Author/Employer Rights
If you are employed and prepared the Work on a subject within the scope of your employment, the copyright in the Work belongs to your employer as a work-for-hire. In that case, AJCT assumes that when you sign this Form, you are authorized to do so by your employer and that your employer has consented to the transfer of copyright, to the representation and warranty of publication rights, and to all other terms and conditions of this Form. If such authorization and consent has not been given to you, an authorized representative of your employer should sign this Form as the Author.
Reprint/Republication Policy
AJCT requires that the consent of the first-named author and employer be sought as a condition to granting reprint or republication rights to others or for permitting use of a Work for promotion or marketing purposes.
GENERAL TERMS
1. The undersigned represents that he/she has the power and authority to make and execute this assignment.
2. The undersigned agrees to indemnify and hold harmless AJCT from any damage or expense that may arise in the event of a breach of any of the warranties set forth above.
3. In the event the above work is accepted and published by AJCT and consequently withdrawn by the author(s), the foregoing copyright transfer shall become null and void and all materials embodying the Work submitted to AJCT will be destroyed.
4. For jointly authored Works, all joint authors should sign, or one of the authors should sign as authorized agent
for the others.
Licenced by :
Creative Commons Attribution 4.0 International License.
