Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Free vibration analysis of magneto-rheological smart annular three-layered plates subjected to magnetic field in viscoelastic medium

  • Amir, Saeed (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arshid, Ehsan (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Maraghi, Zahra Khoddami (Faculty of Engineering, Mahallat Institute of Higher Education)
  • Received : 2019.07.01
  • Accepted : 2019.12.08
  • Published : 2020.05.25
⟨ Previous Next ⟩

Abstract

Magneto-rheological fluids and magneto-strictive materials are of the well-known smart materials which are used to control and reduce the vibrations of the structures. Vibration analysis of a smart annular three-layered plate is provided in this work. MR fluids are used as the core's material type and the face sheets are made from MS materials and is assumed they are fully bonded to each other. The structure is rested on visco-Pasternak foundation and also is subjected to a transverse magnetic field. The governing motion equations are derived based on CPT and employing Hamilton's principle and are solved via GDQ as a numerical method for various boundary conditions. Effect of different parameters on the results are considered and discussed in detail. One of the salient features of this work is the consideration of MR fluids as the core, MS materials as the faces, and all of them under magnetic field. The outcomes of this study may be led to design and create smart structures such as sensors, actuators and also dampers.

Keywords

Acknowledgement

The authors would like to thank the reviewers for their valuable comments and suggestions to improve the clarity of this study. The authors are thankful to the University of Kashan for supporting this work by Grant No. 891255/8.

References

  1. Aguib, S., Nour, A., Zahloul, H., Bossis, G., Chevalier, Y. and Lancon, P. (2014), "Dynamic behavior analysis of a magnetorheological elastomer sandwich plate", Int. J. Mech. Sci., 87, 118-136. https://doi.org/10.1016/J.IJMECSCI.2014.05.014
  2. Amir, S. (2019), "Orthotropic patterns of visco-Pasternak foundation in nonlocal vibration of orthotropic graphene sheet under thermo-magnetic fields based on new first-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 233(2), 197-208. https://doi.org/10.1177/1464420716670929
  3. Amir, S., Bidgoli, E.M.-R. and Arshid, E. (2018), "Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT", Mech. Adv. Mater. Struct., 1-15. https://doi.org/10.1080/15376494.2018.1487612
  4. Amir, S., Arshid, E. and Ghorbanpour Arani, M.R. (2019a), "Size-Dependent Magneto-Electro-Elastic Vibration Analysis of FG Saturated Porous Annular/Circular Micro Sandwich Plates Embedded with Nano-Composite Face sheets Subjected to Multi-Physical Pre Loads", Smart Struct. Syst., Int. J., 23(5), 429-447. https://doi.org/10.12989/sss.2019.23.5.429
  5. Amir, S., Arshid, E., Rasti-Alhosseini, S.M.A. and Loghman, A. (2019b), "Quasi-3D tangential shear deformation theory for sizedependent free vibration analysis of three-layered FG porous micro rectangular plate integrated by nano-composite faces in hygrothermal environment", J. Thermal Stress., 1-24. https://doi.org/10.1080/01495739.2019.1660601
  6. Amir, S., Soleimani-Javid, Z. and Arshid, E. (2019c), "Size-dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT", ZAMM - J. Appl. Mathe. Mech. / Zeitschrift Fur Angewandte Mathematik Und Mechanik. https://doi.org/10.1002/zamm.201800334
  7. Anh, V.T.T., Bich, D.H. and Duc, N.D. (2015), "Nonlinear stability analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads", Eur. J. Mech. - A/Solids, 50, 28-38. https://doi.org/10.1016/J.EUROMECHSOL.2014.10.004
  8. Arshid, E. and Khorshidvand, A.R. (2018), "Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin- Wall. Struct., 125, 220-233. https://doi.org/10.1016/j.tws.2018.01.007
  9. Arshid, E., Khorshidvand, A.R. and Khorsandijou, S.M. (2019a), "The Effect of Porosity on Free Vibration of SPFG Circular Plates Resting on visco-Pasternak Elastic Foundation Based on CPT, FSDT and TSDT", Struct. Eng. Mech., Int. J., 70(1), 97-112. http://dx.doi.org/10.12989/sem.2019.70.1.097
  10. Arshid, E., Kiani, A. and Amir, S. (2019b), "Magneto-electroelastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 233(10), 2140-2159. https://doi.org/10.1177/1464420719832626
  11. Arshid, E., Kiani, A., Amir, S. and Zarghami Dehaghani, M. (2019c), "Asymmetric free vibration analysis of first-order shear deformable functionally graded magneto-electro-thermo-elastic circular plates", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(16), 5659-5675. https://doi.org/10.1177/0954406219850598
  12. Babu, V.R. and Vasudevan, R. (2016), "Dynamic analysis of tapered laminated composite magnetorheological elastomer (MRE) sandwich plates", Smart Mater. Struct., 25(3), 035006. https://doi.org/10.1088/0964-1726/25/3/035006
  13. Bayat, R., Jafari, A.A. and Rahmani, O. (2015), "Analytical Solution for Free Vibration of Laminated Curved Beam with Magnetostrictive Layers", Int. J. Appl. Mech., 7(3), 1550050. https://doi.org/10.1142/S1758825115500507
  14. Brush, D.O., Almroth, B.O. and Hutchinson, J.W. (1975), "Buckling of bars, plates, and shells", J. Appl. Mech., 42, 911.
  15. Bui, T.Q. and Nguyen, M.N. (2011), "A moving Kriging interpolation-based meshfree method for free vibration analysis of Kirchhoff plates", Comput. Struct., 89(3-4), 380-394. https://doi.org/10.1016/j.compstruc.2010.11.006
  16. Bui, T.Q., Nguyen, T.N. and Nguyen-Dang, H. (2009), "A moving Kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems", Int. J. Numer. Methods Eng., 77(10), 1371-1395. https://doi.org/10.1002/nme.2462
  17. Bui, T.Q., Nguyen, M.N. and Zhang, C. (2011a), "Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method", Eng. Anal. Boundary Elem., 35(9), 1038-1053. https://doi.org/10.1016/J.ENGANABOUND.2011.04.001
  18. Bui, T.Q., Nguyen, M.N. and Zhang, C. (2011b), "An efficient meshfree method for vibration analysis of laminated composite plates", Computat. Mech., 48(2), 175-193. https://doi.org/10.1007/s00466-011-0591-8
  19. Bui, T.Q., Do, T.V., Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B: Eng., 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048
  20. Chakraverty, S., Bhat, R.B. and Stiharu, I. (2001), "Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh-Ritz method", J. Sound Vib., 241(3), 524-539. https://doi.org/10.1006/jsvi.2000.3243
  21. Chan, D.Q., Quan, T.Q., Kim, S.-E. and Duc, N.D. (2019), "Nonlinear dynamic response and vibration of shear deformable piezoelectric functionally graded truncated conical panel in thermal environments", Eur. J. Mech. - A/Solids, 77, 103795. https://doi.org/10.1016/J.EUROMECHSOL.2019.103795
  22. Chen, L. and Hansen, C.H. (2005), "Active vibration control of a magnetorheological sandwich beam", Proceedings Acoustics, 93-98.
  23. Duan, Y., Ni, Y.Q., Zhang, H., Spencer Jr, B.F., Ko, J.M. and Dong, S. (2019), "Design formulas for vibration control of sagged cables using passive MR dampers", Smart Struct. Syst., Int. J., 23(6), 537-551. https://doi.org/10.12989/sss.2019.23.6.537
  24. Duc, N.D. (2014), Nonlinear static and dynamic stability of functionally graded plates and shells, Vietnam National University Press.
  25. Duc, N.D. (2018), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric Sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 20(3), 351-378. https://doi.org/10.1177/1099636216653266
  26. Duc, N.D. and Cong, P.H. (2018), "Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations", J. Sandw. Struct. Mater., 20(2), 191-218. https://doi.org/10.1177/1099636216648488
  27. Duc, N.D., Quan, T.Q. and Luat, V.D. (2015a), "Nonlinear dynamic analysis and vibration of shear deformable piezoelectric FGM double curved shallow shells under damping-thermoelectro-mechanical loads", Compos. Struct., 125, 29-40. https://doi.org/10.1016/J.COMPSTRUCT.2015.01.041
  28. Duc, N.D., Tuan, N.D., Tran, P., Dao, N.T. and Dat, N.T. (2015b), "Nonlinear dynamic analysis of Sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments", Int. J. Mech. Sci., 101, 338-348. https://doi.org/10.1016/J.IJMECSCI.2015.08.018
  29. Duc, N.D., Cong, P.H., Anh, V.M., Quang, V.D., Tran, P., Tuan, N.D. and Thinh, N.H. (2015c), "Mechanical and thermal stability of eccentrically stiffened functionally graded conical shell panels resting on elastic foundations and in thermal environment", Compos. Struct., 132, 597-609. https://doi.org/10.1016/J.COMPSTRUCT.2015.05.072
  30. Duc, N.D., Cong, P.H. and Quang, V.D. (2016a), "Nonlinear dynamic and vibration analysis of piezoelectric eccentrically stiffened FGM plates in thermal environment", Int. J. Mech. Sci., 115, 711-722. https://doi.org/10.1016/J.IJMECSCI.2016.07.010
  31. Duc, N.D., Bich, D.H. and Cong, P.H. (2016b), "Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations", J. Thermal Stress., 39(3), 278-297. https://doi.org/10.1080/01495739.2015.1125194
  32. Duc, N.D., Lee, J., Nguyen-Thoi, T. and Thang, P.T. (2017), "Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations", Aerosp. Sci. Technol., 68, 391-402. https://doi.org/10.1016/J.AST.2017.05.032
  33. Ebrahimi, F. and Dabbagh, A. (2018a), "Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates", Eur. Phys. J. Plus, 133(3), 97. https://doi.org/10.1140/epjp/i2018-11910-7
  34. Ebrahimi, F. and Dabbagh, A. (2018b), "Wave propagation analysis of magnetostrictive sandwich composite nanoplates via nonlocal strain gradient theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(22), 4180-4192. https://doi.org/10.1177/0954406217748687
  35. Eshaghi, M., Sedaghati, R. and Rakheja, S. (2015), "The effect of magneto-rheological fluid on vibration suppression capability of adaptive sandwich plates: Experimental and finite element analysis", J. Intel. Mater. Syst. Struct., 26(14), 1920-1935. https://doi.org/10.1177/1045389X15586449
  36. Ghorbanpour Arani, A. and Abdollahian, M. (2017), "Transient response of FG higher-order nanobeams integrated with magnetostrictive layers using modified couple stress theory", Mech. Adv. Mater. Struct., 26(4), 359-371. https://doi.org/10.1080/15376494.2017.1387326
  37. Ghorbanpour Arani, A. and Khoddami Maraghi, Z. (2016), "A feedback control system for vibration of magnetostrictive plate subjected to follower force using sinusoidal shear deformation theory", Ain Shams Eng. J., 7(1), 361-369. https://doi.org/10.1016/J.ASEJ.2015.04.010
  38. Ghorbanpour Arani, A., BabaAkbar Zarei, H., Eskandari, M. and Pourmousa, P. (2017a), "Vibration behavior of visco-elastically coupled sandwich beams with magnetorheological core and three-phase carbon nanotubes/fiber/polymer composite facesheets subjected to external magnetic field", J. Sandw. Struct. Mater., 21(7), 2194-2218. https://doi.org/10.1177/1099636217743177
  39. Ghorbanpour Arani, A., Khoddami Maraghi, Z. and Khani Arani, H. (2017b), "Vibration control of magnetostrictive plate under multi-physical loads via trigonometric higher order shear deformation theory", J. Vib. Control, 23(19), 3057-3070. https://doi.org/10.1177/1077546315588222
  40. Ghorbanpour Arani, A., Pourjamshidian, M., Arefi, M. and Arani, M.R.G. (2019), "Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) timoshenko nano-beams considering surface effects and residual surface stress", Smart Struct. Syst., Int. J., 23(2), 141-153. https://doi.org/10.12989/sss.2019.23.2.141
  41. Guerroudj, H.Z., Yeghnem, R., Kaci, A., Zaoui, F.Z., Benyoucef, S. and Tounsi, A. (2018), "Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory", Smart Struct. Syst., Int. J., 22(1), 121-132. https://doi.org/10.12989/sss.2018.22.1.121
  42. Huang, H.W., Liu, T.T. and Sun, L.M. (2019), "Multi-mode cable vibration control using MR damper based on nonlinear modeling", Smart Struct. Syst., Int. J., 23(6), 565-577. https://doi.org/10.12989/sss.2019.23.6.565
  43. Karami, B. and Shahsavari, D. (2019), "Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers", Smart Struct. Syst., Int. J., 23(3), 215-225. https://doi.org/10.12989/sss.2019.23.3.215
  44. Lara-Prieto, V., Parkin, R., Jackson, M., Silberschmidt, V. and Kesy, Z. (2010), "Vibration characteristics of MR cantilever sandwich beams: experimental study", Smart Mater. Struct., 19(1), 015005. https://doi.org/10.1088/0964-1726/19/1/015005
  45. MalekzadehFard, K., Gholami, M., Reshadi, F. and Livani, M. (2017), "Free vibration and buckling analyses of cylindrical sandwich panel with magneto rheological fluid layer", J. Sandw. Struct. Mater., 19(4), 397-423. https://doi.org/10.1177/1099636215603034
  46. Manoharan, R., Vasudevan, R. and Jeevanantham, A.K. (2014), "Dynamic characterization of a laminated composite magnetorheological fluid sandwich plate", Smart Mater. Struct., 23(2), 025022. https://doi.org/10.1088/0964-1726/23/2/025022
  47. Minh, P.P. and Duc, N.D. (2019), "The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory", Compos. Part B: Eng., 175, 107086. https://doi.org/10.1016/J.COMPOSITESB.2019.107086
  48. Minh, P.P., Van Do, T., Duc, D.H. and Duc, N.D. (2018), "The stability of cracked rectangular plate with variable thickness using phase field method", Thin-Wall. Struct., 129, 157-165. https://doi.org/10.1016/J.TWS.2018.03.028
  49. Mohammadimehr, M., Arshid, E., Alhosseini, S.M.A.R., Amir, S. and Arani, M.R.G. (2019), "Free vibration analysis of thick cylindrical MEE composite shells reinforced CNTs with temperature-dependent properties resting on viscoelastic foundation", Struct. Eng. Mech., Int. J., 70(6), 683-702. https://doi.org/10.12989/sem.2019.70.6.683
  50. Mohammadrezazadeh, S. and Jafari, A. (2019), "Vibration control of laminated truncated conical shell via magnetostrictive layers", Mech. Adv. Mater. Struct., 1-9. https://doi.org/10.1080/15376494.2018.1525627
  51. Naji, J., Zabihollah, A. and Behzad, M. (2016), "Layerwise theory in modeling of magnetorheological laminated beams and identification of magnetorheological fluid", Mech. Res. Commun., 77, 50-59. https://doi.org/10.1016/J.MECHRESCOM.2016.09.003
  52. Naji, J., Zabihollah, A. and Behzad, M. (2018), "Vibration characteristics of laminated composite beams with magnetorheological layer using layerwise theory", Mech. Adv. Mater. Struct., 25(3), 202-211. https://doi.org/10.1080/15376494.2016.1255819
  53. Ramamoorthy, M., Rajamohan, V. and AK, J. (2016), "Vibration analysis of a partially treated laminated composite magnetorheological fluid sandwich plate", J. Vib. Control, 22(3), 869-895. https://doi.org/10.1177/1077546314532302
  54. Shokravi, M. (2018), "Dynamic buckling of smart sandwich beam subjected to electric field based on hyperbolic piezoelasticity theory", Smart Struct. Syst., Int. J., 22(3), 327-334. https://doi.org/10.12989/sss.2018.22.3.327
  55. Shu, C. (2012), Differential Quadrature and Its Application in Engineering, Springer Science & Business Media.
  56. Sidhoum, I.A., Boutchicha, D., Benyoucef, S. and Tounsi, A. (2018), "A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates", Smart Struct. Syst., Int. J., 22(3), 303-314. https://doi.org/10.12989/sss.2018.22.3.303
  57. Squire, P. (1999), "Magnetostrictive materials for sensors and actuators", Ferroelectrics, 228(1), 305-319. https://doi.org/10.1080/00150199908226144
  58. Suman, S.D., Hirwani, C.K., Chaturvedi, A. and Panda, S.K. (2017), "Effect of magnetostrictive material layer on the stress and deformation behaviour of laminated structure", IOP Conference Series: Materials Science and Engineering, 178(1), 012026. https://doi.org/10.1088/1757-899X/178/1/012026
  59. Tabbakh, M. and Nasihatgozar, M. (2018), "Buckling analysis of nanocomposite plates coated by magnetostrictive layer", Smart Struct. Syst., Int. J., 22(6), 743-751. https://doi.org/10.12989/sss.2018.22.6.743
  60. Thom, D.V., Nguyen, D.K., Duc, N.D., Doan, D.H. and Bui, T.Q. (2017), "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory", Thin-Wall. Struct., 119, 687-699. https://doi.org/10.1016/J.TWS.2017.07.022
  61. Tohidi, H., Hosseini-Hashemi, S.H. and Maghsoudpour, A. (2018), "Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory", Smart Struct. Syst., Int. J., 22(5), 527-546. https://doi.org/10.12989/sss.2018.22.5.527
  62. Tzou, H.S., Lee, H.-J. and Arnold, S.M. (2004), "Smart Materials, Precision Sensors/Actuators, Smart Structures, and Structronic Systems", Mech. Adv. Mater. Struct., 11(4-5), 367-393. https://doi.org/10.1080/15376490490451552
  63. Yeh, J.-Y. (2013), "Vibration analysis of sandwich rectangular plates with magnetorheological elastomer damping treatment", Smart Mater. Struct., 22(3), 035010. https://doi.org/10.1088/0964-1726/22/3/035010
  64. Yeh, J.-Y. (2014), "Vibration characteristics analysis of orthotropic rectangular sandwich plate with magnetorheological elastomer", Procedia Eng., 79, 378-385. https://doi.org/10.1016/J.PROENG.2014.06.358
  65. Yu, T., Yin, S., Bui, T.Q., Xia, S., Tanaka, S. and Hirose, S. (2016), "NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method", Thin-Wall. Struct., 101, 141-156. https://doi.org/10.1016/j.tws.2015.12.008
  66. Yu, T., Yin, S., Bui, T.Q., Liu, C. and Wattanasakulpong, N. (2017), "Buckling isogeometric analysis of functionally graded plates under combined thermal and mechanical loads", Compos. Struct., 162, 54-69. https://doi.org/10.1016/j.compstruct.2016.11.084
  67. Zhang, R., Ni, Y.-Q., Duan, Y. and Ko, J.-M. (2019), "Development of a full-scale magnetorheological damper model for open-loop cable vibration control", Smart Struct. Syst., Int. J., 23(6), 553-564. https://doi.org/10.12989/sss.2019.23.6.553
  68. Zhou, Z.H., Wong, K.W., Xu, X.S. and Leung, A.Y.T. (2011), "Natural vibration of circular and annular thin plates by Hamiltonian approach", J. Sound Vib., 330(5), 1005-1017. https://doi.org/10.1016/J.JSV.2010.09.015
  69. Zucca, M., Raffa, F.A., Fasana, A. and Colella, N. (2015), "A simplified vibration compensation through magnetostrictive actuators", J. Vib. Control, 21(14), 2903-2912. https://doi.org/10.1177/1077546313518956

Cited by

  1. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2020, https://doi.org/10.12989/anr.2021.11.2.115
  2. Vibration analysis of sandwich beam with honeycomb core and piezoelectric facesheets affected by PD controller vol.28, pp.2, 2020, https://doi.org/10.12989/sss.2021.28.2.195