DOI QR코드

DOI QR Code

Effect of pre-magneto-electro-mechanical loads and initial curvature on the free vibration characteristics of size-dependent beam

  • Arefi, M. (Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2018.11.08
  • 심사 : 2019.01.24
  • 발행 : 2019.07.10

초록

This paper studies application of modified couple stress theory and first order shear deformation theory to magneto-electro-mechanical vibration analysis of three-layered size-dependent curved beam. The curved beam is resting on Pasternak's foundation and is subjected to mechanical, magnetic and electrical loads. Size dependency is accounted by employing a small scale parameter based on modified couple stress theory. The magneto-electro-mechanical preloads are accounted in governing equations to obtain natural frequencies in terms of initial magneto-electro-mechanical loads. The analytical approach is applied to investigate the effect of some important parameters such as opening angle, initial electric and magnetic potentials, small scale parameter, and some geometric dimensionless parameters and direct and shear parameters of elastic foundation on the magneto-electro-elastic vibration responses.

키워드

참고문헌

  1. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel. Compos. Struct., 18(3), 659-672. http://doi.org/10.12989/scs.2015.18.3.659.
  2. Arefi, M. and Zenkour, A.M. (2017a), "Effect of thermo-magnetoelectro-mechanical fields on the bending behaviors of a threelayered nanoplate based on sinusoidal shear-deformation plate theory", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636217697497.
  3. Arefi, M. and Zenkour, A.M. (2017b), "Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model", J. Intel. Mater. Syst. Struct., 28(17), 2403-2413. https://doi.org/10.1177/1045389X17689930.
  4. Arefi, M. and Zenkour, A.M. (2017c), "Influence of magnetoelectric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636217723186.
  5. Arefi, M. and Zenkour, A.M. (2017d), "Transient analysis of a three-layer microbeam subjected to electric potential", Int. J. Smart. Nano. Mater., 8(1), 20-40. https://doi.org/10.1080/19475411.2017.1292967.
  6. Arefi, M. and Zenkour, A.M. (2017e), "Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezomagnetic curved nanobeam", Acta. Mech., 228(10), 3657-3674. https://doi.org/10.1007/s00707-017-1892-6.
  7. Arefi, M. and Zenkour, A.M. (2017f), "Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation", Phys. B. Cond. Matt., 521, 188-197. https://doi.org/10.1016/j.physb.2017.06.066.
  8. Arefi, M. (2016), "Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials", Acta Mech., 227, 2529-2542. https://doi.org/10.1007/s00707-016-1584-7.
  9. Arefi, M., Zamani, M.H. and Kiani, M., (2018), "Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak's foundation", J. Intel. Mater. Syst. Struct., 29(5), 774-786. https://doi.org/10.1177/1045389X17721039.
  10. Ghasemi, H. Park, H.S. and Rabczuk, T. (2017), "A level-set based IGA formulation for topology optimization of flexoelectric materials", Comput. Meth. Appl. Mech. Eng., 313, 239-258. https://doi.org/10.1016/j.cma.2016.09.029.
  11. Ghasemi, H. Park, H.S. and Rabczuk, T. (2018), "A multi-material level set-based topology optimization of flexoelectric composites", Comput. Meth. Appl. Mech. Eng., 332, 47-62. https://doi.org/10.1016/j.cma.2017.12.005.
  12. Hamdia, K.M. Silani, M. Zhuang, X. He, P. and Rabczuk, T. (2017), "Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions", Int. J. Fract., 206(2) 215-227. https://doi.org/10.1007/s10704-017-0210-6.
  13. Hamdia, K.M. Ghasemi, H. Zhuang, X. Alajlan, N. and Rabczuk, T. (2018), "Sensitivity and uncertainty analysis for flexoelectric nanostructures", Comput. Meth. Appl. Mech. Eng., 337, 95-109. https://doi.org/10.1016/j.cma.2018.03.016.
  14. Kuang, Y.D., Li, G.Q., Chen, C.Y. and Min, Q. (2007), "The static responses and displacement control of circular curved beams with piezoelectric actuators", Smart. Materi. Struct., 16, 1016-1024. https://doi.org/10.1088/0964-1726/16/4/009
  15. Liu, C., Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2013), "Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory", Compos. Struct., 106, 167-174. https://doi.org/10.1016/j.compstruct.2013.05.031.
  16. Nanthakumar, S.S., Lahmer, T., Zhuang, X., Zi, G. and Rabczuk, T. (2016), "Detection of material interfaces using a regularized level set method in piezoelectric structures", Inv. Prob. Sci. Eng., 24(1), 153-176. https://doi.org/10.1080/17415977.2015.1017485.
  17. Nguyen, B.H., Zhuang, X. and Rabczuk, T. (2018), "Numerical model for the characterization of Maxwell-Wagner relaxation in piezoelectric and flexoelectric composite material", Comput. Struct., 208, 75-91. https://doi.org/10.1016/j.compstruc.2018.05.006.
  18. Petyt, M. and Fleischer, C.C. (1971), "Free vibration of a curved beam", J. Sound. Vib. 18(1), 17-30. https://doi.org/10.1016/0022-460X(71)90627-4.
  19. Piovan, M.T., Olmedo, J.F. and Sampaio, R. (2015), "Dynamics of magneto electro elastic curved beams: Quantification of parametric uncertainties", Compos. Struct., 133, 621-629. https://doi.org/10.1016/j.compstruct.2015.07.084.
  20. Poon, W.Y., Ng, C.F. and Lee, Y.Y. (2002), "Dynamic stability of a curved beam under sinusoidal loading", Proc. Inst. Mech. Eng. Part G: J. Aer. Eng., 216(4), 209-217. https://doi.org/10.1243/09544100260369740.
  21. Raveendranath, P., Singh, G. and Pradhan, B. (2000), "Free vibration of arches using a curved beam element based on a coupled polynomial displacement field", Comput. Struct., 78(4), 583-590. https://doi.org/10.1016/S0045-7949(00)00038-9.
  22. Raveendranath, P., Singh, G. and Pradhan, B. (1999), "A two-noded locking-free shear flexible curved beam element", Int. J. Num. Meth. Eng., 44(2), 265-280. https://doi.org/10.1002/(SICI)1097-0207(19990120)44:2<265::AIDNME505>3.0.CO;2-K
  23. Shi, Z.F. (2005), "Bending behavior of piezoelectric curved actuator", Smart. Materi. Struct. 14, 835-842. https://doi.org/10.1088/0964-1726/14/4/043
  24. Shi, Z.F. and Zhang, T. (2008), "Bending analysis of a piezoelectric curved actuator with a generally graded property for the piezoelectric parameter", Smart. Materi. Struct., 17, 045018. https://doi.org/10.1088/0964-1726/17/4/045018
  25. Surana, K.S. and Sorem, R.M. (1989), "Geometrically non-linear formulation for three dimensional curved beam elements with large rotations", Int. J. Num. Meth. Eng., 28(1), 43-73. https://doi.org/10.1002/nme.1620280106.
  26. Thai, T.Q., Rabczuk, T. and Zhuang, X. (2017), "A large deformation isogeometric approach for flexoelectricity and soft materials", Comput. Meth. Appl. Mech. Eng., 341, 718-739. https://doi.org/10.1016/j.cma.2018.05.019.
  27. Vu-Bac, N., Lahmer, T., Zhuang, X., Nguyen-Thoi, T. and Rabczuk, T. (2016), "A software framework for probabilistic sensitivity analysis for computationally expensive models", Adv. Eng. Softw., 100, 19-31. https://doi.org/10.1016/j.advengsoft.2016.06.005.
  28. Zhou, Y., Nyberg, T.R., Xiong, G., Zhou, H. and Li, S. (2017), "Precise deflection analysis of laminated piezoelectric curved beam", J. Intel. Mater. Syst. Struct, 27(16), 2179-2198. https://doi.org/10.1177/1045389X15624797.
  29. Zhou, Y., Dong, Y. and Li, S. (2010) "Analysis of a Curved Beam MEMS Piezoelectric Vibration Energy Harvester", Adv. Mater. Res., 139-141, 1578-1581. https://doi.org/10.4028/www.scientific.net/AMR.139-141.1578.

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