Structural Engineering and Mechanics

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Theoretical investigation on vibration frequency of sandwich plate with PFRC core and piezomagnetic face sheets under variable in-plane load

  • Arani, Ali Ghorbanpour (Department of Solid Mechanics, Faculty of Mechanical Engineering, 6Km Ghotbravandi Blvd, University of Kashan) ;
  • Maraghi, Zahra Khoddami (Department of Solid Mechanics, Faculty of Mechanical Engineering, 6Km Ghotbravandi Blvd, University of Kashan) ;
  • Ferasatmanesh, Maryam (Department of Solid Mechanics, Faculty of Mechanical Engineering, 6Km Ghotbravandi Blvd, University of Kashan)
  • Received : 2016.07.03
  • Accepted : 2017.01.25
  • Published : 2017.07.10
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Abstract

This research investigated the vibration frequency of sandwich plate made of piezoelectric fiber reinforced composite core (PFRC) and face sheets of piezomagnetic materials. The effective electroelastic constants for PFRC materials are obtained by the micromechanical approach. The resting medium of sandwich plate is modeled by Pasternak foundation including normal and shear modulus. Besides, sandwich plate is subjected to linearly varying normal stresses that change by load factor. The coupled equations of motion are derived using first order shear deformation theory (FSDT) and energy method. These equations are solved by differential quadrature method (DQM) for simply supported boundary condition. A detailed numerical study is carried out based on piezoelectricity theory to indicate the significant effect of load factor, volume fraction of fibers, modulus of elastic foundation, core-to-face sheet thickness ratio and composite materials on dimensionless frequency of sandwich plate. These findings can be used to aerospace, building and automotive industries.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. An, C. and Su, J. (2014), "Dynamic analysis of axially moving orthotropic plates: Integral transform solution", Appl. Math. Comput., 228, 489-507.
  2. Araujo, A. and Mota Soares, C. (2010), "A viscoelastic sandwich finite element model for the analysis of passive, active and hybrid structures", Appl. Compos. Mater., 17(5), 529-542. https://doi.org/10.1007/s10443-010-9141-3
  3. Aravinda Kumar, M.S., Panda, S. and Chakraborty, D. (2015), "Design and analysis of a smart graded fiber-reinforced composite laminated plate", Compos. Struct., 124, 176-195. https://doi.org/10.1016/j.compstruct.2014.11.015
  4. Bardell, N.S. (1989), "The application of symbolic computing to the hierarchical finite element method", Int. J. Numer. Meth. Eng., 28(5), 1181-1204. https://doi.org/10.1002/nme.1620280513
  5. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B-Eng., 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  6. Benjeddou, A. and Deu, J.F. (2002), "A two-dimensional closedform solution for the free-vibrations analysis of piezoelectric sandwich plates", Int. J. Solids. Struct., 39(6), 1463-1486. https://doi.org/10.1016/S0020-7683(01)00287-6
  7. Bessaim, A., Houari, M.S., Tounsi, A., Mahmoud, S.R. and Bedia, E.A.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888
  8. Cook, A.C. and Vel, S.S. (2012), "Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators", Compos. Struct., 94(2), 322-336. https://doi.org/10.1016/j.compstruct.2011.06.027
  9. Farajpour, A., Shahidi, A.R., Mohammadi, M. and Mahzoon, M. (2012), "Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics", Compos. Struct., 94(5), 1605-1615. https://doi.org/10.1016/j.compstruct.2011.12.032
  10. 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., 94(15), 361-369.
  11. Ghorbanpour Arani, A., Vossough, H., Kolahchi, R. and Mosallaie Barzoki, A.A. (2012), "Electro-thermo nonlocal nonlinear vibration in an embedded polymeric piezoelectric micro plate reinforced by DWBNNTs using DQM", J. Mech. Sci. Technol., 26(10), 3047-3057. https://doi.org/10.1007/s12206-012-0816-6
  12. Ghorbanpour Arani, A., Haghparast, E., Heidari Rarani, M. and Khoddami Maraghi, Z. (2015), "Strain gradient shell model for nonlinear vibration analysis of visco-elastically coupled Boron Nitride nano-tube reinforced composite micro-tubes conveying viscous fluid", Comp. Mater. Sci. (Part B), 96, 448-458. https://doi.org/10.1016/j.commatsci.2014.06.013
  13. Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004
  14. Jalili, N. (2010), Piezoelectric-Based Vibration Control: From Macro to Micro/Nano Scale Systems, Springer. 536.
  15. Khalili, S.M.R., Kheirikhah, M.M. and Malekzadeh Fard, K. (2014), "Biaxial wrinkling analysis of composite-faced sandwich plates with soft core using improved high-order theory", Eur. J. Mech. A. Solid., 43, 67-77.
  16. Kutlu, A. and Hakk Omurtag, M. (2012), "Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method", Int. J. Mech. Sci., 65(1), 64-74. https://doi.org/10.1016/j.ijmecsci.2012.09.004
  17. Lal, R. and Rani, R. (2014), "On the use of differential quadrature method in the study of free axisymmetric vibrations of circular sandwich plates of linearly varying thickness", J. Vib. Control, 22(7), 1729-1748. https://doi.org/10.1177/1077546314544695
  18. Lee, K.H., Wang, C.M. and Reddy, J.N. (2000), Shear Deformable Beams and Plates, Elsevier Science Ltd: Oxford. 279-291.
  19. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound. Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
  20. Loja, M.A.R., Mota Soares, C.M. and Barbosa, J.I. (2013), "Analysis of functionally graded sandwich plate structures with piezoelectric skins, using B-spline finite strip method", Compos. Struct., 96, 606-615. https://doi.org/10.1016/j.compstruct.2012.08.010
  21. Mallick, P.K. (2007), Fiber reinforced composites Materials, Manufacturing, and Design, Taylor & Francis Group, 616.
  22. Natarajan, S., Haboussi, M. and Manickam, G. (2014), "Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets", Compos. Struct., 113, 197-207. https://doi.org/10.1016/j.compstruct.2014.03.007
  23. Nayak, A.K., Moy, S.S.J. and Shenoi, R.A. (2002), "Free vibration analysis of composite sandwich plates based on Reddy's higherorder theory", Compos. Part B-Eng., 33(7), 505-519. https://doi.org/10.1016/S1359-8368(02)00035-5
  24. Plagianakos, T.S. and Papadopoulos, E.G. (2015), "Higher-order 2-D/3-D layerwise mechanics and finite elements for composite and sandwich composite plates with piezoelectric layers", Aerosp. Sci. Technol., 40, 150-163. https://doi.org/10.1016/j.ast.2014.10.015
  25. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Discrete layer solution to free vibrations of functionally graded magnetoelectro-elastic plates", Mech. Adv. Mater. Struct., 13(3), 249-266. https://doi.org/10.1080/15376490600582750
  26. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, 2nd Edition, in Energy Principles and Variational Methods in Applied Mechanics, 2nd Edition. WILEY. 592.
  27. Shu, C. (2000), Differential Quadrature and its Application in Engineering, Springer publishers Singapore.
  28. Steele, C.R. and Balch, C.D. (2009), "Introduction to the theory of plates", Stanford University.
  29. Tan, P. and Tong, L. (2001), "Micromechanics models for nonlinear behavior of piezo-electric fiber reinforced composite materials", Int. J. Solids. Struct., 38(50-51), 8999-9032. https://doi.org/10.1016/S0020-7683(01)00181-0
  30. Tan, P. and Tong, L. (2002), "Investigation of loading assumptions on the effective electroelastic constants for PFRC materials", Compos. Struct., 57(1-4), 101-108. https://doi.org/10.1016/S0263-8223(02)00073-9
  31. Tan, P. and Tong, L. (2002), "Modeling for the electro-magnetothermo-elastic properties of piezoelectric-magnetic fiber reinforced composites", Compos. Part A-Appl. S., 33(5), 631-645. https://doi.org/10.1016/S1359-835X(02)00015-5
  32. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  33. Tu, T.M., Thach, L.N. and Quoc, T.H. (2010), "Finite element modeling for bending and vibration analysis of laminated and sandwich composite plates based on higher-order theory", Comput. Mater. Sci., 49(4), 390-394. https://doi.org/10.1016/j.commatsci.2010.03.045
  34. Wang, T., Sokolinsky, V., Rajaram, S. and Nutt, S.R. (2008), "Consistent higher-order free vibration analysis of composite sandwich plates", Compos. Struct., 82(4), 609-621. https://doi.org/10.1016/j.compstruct.2007.02.009
  35. Wang, Y., Wang, X. and Zhou, Y. (2004), "Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method", Int. J. Numer. Meth. Eng., 59(9), 1207-1226. https://doi.org/10.1002/nme.913
  36. Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets", Compos. Part B-Eng., 43(2), 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040
  37. Yang, J. (2005), An Introduction to the Theory of Piezoelectricity, Springer US. 309.
  38. Zhang, X.D. and Sun, C.T. (1999), "Analysis of a sandwich plate containing a piezoelectric core", Smart. Mater. Struct., 8(1), 31. https://doi.org/10.1088/0964-1726/8/1/003

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