Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A 3D finite element static and free vibration analysis of magneto-electro-elastic beam

  • Vinyas., M (Department of Mechanical Engineering, National Institute of Technology Karnataka) ;
  • Kattimani, S.C. (Department of Mechanical Engineering, National Institute of Technology Karnataka)
  • Received : 2017.03.16
  • Accepted : 2017.10.11
  • Published : 2017.12.25
⟨ Previous Next ⟩

Abstract

In this paper, free vibration and static response of magneto-electro-elastic (MEE) beams has been investigated. To this end, a 3D finite element formulation has been derived by minimization the total potential energy and linear constitutive equation. The coupling between elastic, electric and magnetic fields can have a significant influence on the stiffness and in turn on the static behaviour of MEE beam. Further, different Barium Titanate ($BaTiO_3$) and Cobalt Ferric oxide ($CoFe_2O_4$) volume fractions results in indifferent coupled response. Therefore, through the numerical examples the influence of volume fractions and boundary conditions on the natural frequencies of MEE beam is illustrated. The study is extended to evaluate the static response of MEE beam under various forms of mechanical loading. It is seen from the numerical evaluation that the volume fractions, loading and boundary conditions have a significant effect on the structural behaviour of MEE structures. The observations made here may serve as benchmark solutions in the optimum design of MEE structures.

Keywords

References

  1. Aktas, A. (2001), "Determination of the deflection function of a composite cantilever beam using theory of anisotropic elasticity", Math. Comput. Appl., 6(1), 67-74.
  2. Annigeri, A.R., Ganesan, N. and Swarnamani, S. (2007), "Free vibration behaviour of multiphase and layered magneto-electro-elastic beam", J. Sound Vibr., 299(1-2), 44-63. https://doi.org/10.1016/j.jsv.2006.06.044
  3. Arefi, M. and Zenkour, A.M. (2017), "Electro-magneto-elastic analysis of a three layer curved beam", Smart Struct. Syst., 19(6), 695-703. https://doi.org/10.12989/SSS.2017.19.6.695
  4. Balu, S., Kannan, G.R. and Rajalingam, K. (2014), "Static studies on piezoelectric/piezomagnetic composite structure under mechanical and thermal loading", IJERST, 3(2), 678-685.
  5. Benedetti, I. and Milazzo, A. (2017), "Advanced models for smart multilayered plates based on reissner mixed variational theorem", Compos. Part B: Eng., 119, 215-229. https://doi.org/10.1016/j.compositesb.2017.03.007
  6. Bhangale, R.K. and Ganesan, N. (2006), "Free vibration of simply supported functionally graded and layered magneto-electro-elastic plates by finite element method", J. Sound Vibr., 294(4), 1016-1038. https://doi.org/10.1016/j.jsv.2005.12.030
  7. Biju, B.N., Ganesan, N. and Shankar, K. (2011), "Dynamic response of multiphase magnetoelectroelastic sensors using 3D magnetic vector potential approach", IEEE Sens. J., 11(9), 2169-2176. https://doi.org/10.1109/JSEN.2011.2112346
  8. Carrera, E., Brischetto, S., Fagiano, C. and Nali, P. (2009), "Mixed multilayered plate elements for coupled magneto-electro-elastic analysis", Multidiscipl. Model. Mater. Struct., 5, 251-256. https://doi.org/10.1163/157361109789017050
  9. Chen, J., Chen, H., Pan, E. and Heyliger, P.R. (2007), "Modal analysis of magneto-electro-elastic plates using the state-vector approach", J. Sound Vibr., 304, 722-734. https://doi.org/10.1016/j.jsv.2007.03.021
  10. Ebrahimi, F. and Barati, M.R. (2016a), "A nonlocal higher-order magneto electro visco-elastic beam model for dynamic analysis of smart nanostructures", J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  11. Ebrahimi, F. and Barati, M.R. (2016b), "Dynamic modeling of a thermos-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 451. https://doi.org/10.1007/s00339-016-0001-3
  12. Ebrahimi, F. and Barati, M.R. (2016c), "Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates", J. Brazil. Soc. Mech. Sci. Eng., 39(6), 2203-2223.
  13. Ebrahimi, F., Jafari, A. and Barati, M.R. (2017), "Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations", Thin-Wall. Struct., 119, 33-46. https://doi.org/10.1016/j.tws.2017.04.002
  14. Fan, X. and Wu, Z. (2016), "$C_0$-type Reddy's theory for composite beams using FEM under thermal loads", Struct. Eng. Mech., 57(3), 457-471. https://doi.org/10.12989/sem.2016.57.3.457
  15. Huang, D.J., Ding, H.J. and Chen, W.Q. (2007), "Analytical solution for functionally graded magneto-electro-elastic plane beams", J. Eng. Sci., 45, 467-485. https://doi.org/10.1016/j.ijengsci.2007.03.005
  16. Jandaghian, A.A. and Rahmani, O. (2016), "Free vibration analysis of magneto-electro-thermo-elastic nanobeams resting on a Pasternak foundation", Smart Mater. Struct., 25(3), 035023. https://doi.org/10.1088/0964-1726/25/3/035023
  17. Kattimani, S.C. (2017), "Geometrically nonlinear vibration analysis of multiferroic composite plates and shells", Compos. Struct., 163, 185-194. https://doi.org/10.1016/j.compstruct.2016.12.021
  18. Kattimani, S.C. and Ray, M.C (2014a), "Smart damping of geometrically nonlinear vibrations of magneto-electro-elastic plates", Compos. Struct., 114(1), 51-63. https://doi.org/10.1016/j.compstruct.2014.03.050
  19. Kattimani, S.C. and Ray, M.C. (2014b), "Active control of large amplitude vibrations of smart magneto-electro-elastic doubly curved shells", J. Mech. Mater. Des., 10(4), 351-378. https://doi.org/10.1007/s10999-014-9252-3
  20. Kattimani, S.C. and Ray, M.C. (2015), "Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates", J. Mech. Sci., 99, 154-167. https://doi.org/10.1016/j.ijmecsci.2015.05.012
  21. Kondaiah, P., Shankar, K. and Ganesan, N. (2015), "Pyroeffects on magneto-electro-elastic sensor bonded on mild steel cylindrical shell", Smart Struct. Syst., 16(3), 537-554. https://doi.org/10.12989/sss.2015.16.3.537
  22. Kondaiah, P., Shankar, K. and Ganesan, N. (2017), "Pyroeffects on magneto-electro-elastic sensor patch subjected to thermal load", Smart Struct. Syst., 19(3), 299-307. https://doi.org/10.12989/sss.2017.19.3.299
  23. Kondaiah. P., Shankar, K. and Ganesan, N. (2012), "Studies on magneto-electro-elastic cantilever beam under thermal environment", Coupled Syst. Mech., 1(2), 205-217. https://doi.org/10.12989/csm.2012.1.2.205
  24. Lage, R.G. and Soares, C.M.M. (2004), "Layerwise partial mixed finite element analysis of magneto-electro-elastic plates", Comput. Struct., 82, 1293-1301. https://doi.org/10.1016/j.compstruc.2004.03.026
  25. Milazzo, A. (2013), "A one-dimensional model for dynamic analysis of generally layered magneto-electro-elastic beams", J. Sound Vibr., 332(2), 465-483. https://doi.org/10.1016/j.jsv.2012.09.004
  26. Milazzo, A., Orlando, C. and Alaimo, A. (2009), "An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem", Smart Mater. Struct., 18(8), 85012. https://doi.org/10.1088/0964-1726/18/8/085012
  27. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", J. Eng. Sci., 43(3-4), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006
  28. Simoes Moita, J.M., Mota Soares, C.M. and Mota Soares, C.A. (2009), "Analyses of magneto-electro-elastic plates using a higher order finite element model", Compos. Struct., 91(4), 421-426. https://doi.org/10.1016/j.compstruct.2009.04.007
  29. Simsek, M. and Reddy, J.N. (2013), "Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory", J. Eng. Sci., 64, 37-53. https://doi.org/10.1016/j.ijengsci.2012.12.002
  30. Sladek, J., Sladek, V., Krahulec, S. and Pan, E. (2013), "The MLPG analyses of large deflections of magnetoelectroelastic plates", Eng. Analy. Bound. Elem., 37(4), 673-682. https://doi.org/10.1016/j.enganabound.2013.02.001
  31. Sladek, J., Sladek, V., Repka, M., Kasala, J. and Bishay, P. (2017), "Evaluation of effective material properties in magneto-electro-elastic composite materials", Compos. Struct., 174, 176-186. https://doi.org/10.1016/j.compstruct.2017.03.104
  32. Vaezi, M., Shirbani, M.M. and Hajnayeb, A. (2016), "Free vibration analysis of magneto-electro-elastic microbeams subjected to magneto-electric loads", Phys. E: Low-Dimens. Syst. Nanostruct., 75, 280-286. https://doi.org/10.1016/j.physe.2015.09.019
  33. Vinyas, M. and Kattimani, S.C. (2017c), "Static behavior of thermally loaded multilayered magneto-electro-elastic beam", Struct. Eng. Mech., 63(4), 481-495. https://doi.org/10.12989/SEM.2017.63.4.481
  34. Vinyas, M. and Kattimani, S.C. (2017e), "Multiphysics response of magneto-electro-elastic beams in thermo-mechanical environment", Coupled Syst. Mech., 3(4), 351-367.
  35. Vinyas, M. and Kattimani, S.C. (2017f), "Hygrothermal analysis of magneto-electro-elastic plate using 3D finite element analysis", Compos. Struct., 180, 617-637. https://doi.org/10.1016/j.compstruct.2017.08.015
  36. Vinyas, M. and Kattimani, S.C. (2017a), "Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads", Compos. Struct., 163, 216-237. https://doi.org/10.1016/j.compstruct.2016.12.040
  37. Vinyas, M. and Kattimani, S.C. (2017b), "Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: A finite element study", Compos. Struct., 178, 63-86. https://doi.org/10.1016/j.compstruct.2017.06.068
  38. Vinyas, M. and Kattimani, S.C. (2017d), "A Finite element based assessment of static behavior of multiphase magneto-electro-elastic beams under different thermal loading", Struct. Eng. Mech., 62(5), 519-535. https://doi.org/10.12989/sem.2017.62.5.519

Cited by

  1. Thermal response analysis of multi-layered magneto-electro-thermo-elastic plates using higher order shear deformation theory vol.73, pp.6, 2017, https://doi.org/10.12989/sem.2020.73.6.667