Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure

  • Arefi, M. (Department of Mechanical Engineering, Tarbiat Modares University) ;
  • Rahimi, G.H. (Department of Mechanical Engineering, Tarbiat Modares University)
  • Received : 2010.12.24
  • Accepted : 2011.07.29
  • Published : 2011.11.25
⟨ Previous Next ⟩

Abstract

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

Keywords

References

  1. Alinia, M.M. and Ghannadpour, S.A.M. (2009), "Nonlinear analysis of pressure loaded FGM plates", Compos. Struct., 88(3), 354-359. https://doi.org/10.1016/j.compstruct.2008.04.013
  2. Allahverdizadeh, A., Naei, M.H. and Nikkhah Bahrami, M. (2008), "Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates", Int. J. Mech. Sci., 50(3), 445-454. https://doi.org/10.1016/j.ijmecsci.2007.09.018
  3. Allahverdizadeh, A., Naei, M.H. and Nikkhah Bahrami, M. (2008), "Nonlinear free and forced vibration analysis of thin circular functionally graded plates", J. Sound. Vib., 310(4-5), 966-984. https://doi.org/10.1016/j.jsv.2007.08.011
  4. Banerjee, A., Bhattacharya, B. and Mallik, A.K. (2008), "Large deflection of cantilever beams with geometric nonlinearity: Analytical and numerical approaches", Int. J. Nonlinear Mech., 43(5), 366-376. https://doi.org/10.1016/j.ijnonlinmec.2007.12.020
  5. Boresi, A. (1993), Advanced mechanics of materials, John wiley & sons.
  6. Ebrahimi, F. and Rastgo, A. (2008), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin. Wall. Struct., 46(12), 1402-1408. https://doi.org/10.1016/j.tws.2008.03.008
  7. GhannadPour, S.A.M. and Alinia, M.M. (2006), "Large deflection behavior of functionally graded plates under pressure loads", Compos. Struct., 75(1-4), 67-71. https://doi.org/10.1016/j.compstruct.2006.04.004
  8. Hui-Shen, S. (2007), "Nonlinear thermal bending response of FGM plates due to heat conduction", Compos. Part. B-Eng., 38(2), 201-215. https://doi.org/10.1016/j.compositesb.2006.06.004
  9. Khoshgoftar, M.J., Ghorbanpour Arani, A. and Arefi, M. (2009) "Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material", Smart. Mater. Struct., 18(11), 115007. https://doi.org/10.1088/0964-1726/18/11/115007
  10. Lai, M. Rubin, D. and Krempl, E. (1999), Introduction to continuum mechanics, Buttenvorth-Heinemann.
  11. Malekzadeh, P. and Vosoughi, A.R. (2009), "DQM large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edges", Commun. Nonlin. Sci. Num. Sim., 14(3), 906-915. https://doi.org/10.1016/j.cnsns.2007.10.014
  12. Olfatnia, M., Xu, T., Miao, J.M., Ong, L.S., Jing, X.M. and Norford, L. (2010), "Piezoelectric circular microdiaphragm based pressure sensors", Sensor. Actuat. A - Phys., 163(1), 32-36 https://doi.org/10.1016/j.sna.2010.06.016
  13. Rahimi, G.H., Arefi, M. and Khoshgoftar, M.J. (2011), "Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads", Appl Math Mech - Engl Ed., 32(8), 1-12. https://doi.org/10.1007/s10483-011-1388-x
  14. Sarfaraz Khabbaz, R., Dehghan Manshadi, B. and Abedian, A. (2009), "Non-linear analysis of FGM plates under pressure loads using the higher-order shear deformation theories", Compos. Struct., 89(3), 333-344. https://doi.org/10.1016/j.compstruct.2008.06.009
  15. Soufyane, A. (2009), "Exponential stability of the linearized non uniform Timoshenko beam", Nonlinear. Anal - Real., 10, 1016-1020. https://doi.org/10.1016/j.nonrwa.2007.11.019
  16. Ugural, A.C. (1981), Stress in plate and shells, McGraw-Hill.
  17. Woo, J. and Meguid, S.A. (2001), "Nonlinear analysis of functionally graded plates and shallow shells", Int. J. Solids. Struct., 38(42-43), 7409-7421. https://doi.org/10.1016/S0020-7683(01)00048-8
  18. Zy kaa, P. and Janus, P. (2010), "Applicability of MEMS cantilever micro-dilatometer for direct transverse strain monitoring in electroactive polymers", Sensor. Actuat. A - Phys., 163(1), 111-117. https://doi.org/10.1016/j.sna.2010.08.001

Cited by

  1. Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation vol.16, pp.1, 2015, https://doi.org/10.12989/sss.2015.16.1.195
  2. The effect of nonhomogeneity and end supports on the thermo elastic behavior of a clamped–clamped FG cylinder under mechanical and thermal loads vol.96-97, 2012, https://doi.org/10.1016/j.ijpvp.2012.05.009
  3. Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT vol.20, pp.3, 2016, https://doi.org/10.12989/scs.2016.20.3.513
  4. A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment vol.18, pp.5, 2016, https://doi.org/10.1177/1099636216652581
  5. Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder vol.224, pp.11, 2013, https://doi.org/10.1007/s00707-013-0888-0
  6. The effect of different functionalities of FGM and FGPM layers on free vibration analysis of the FG circular plates integrated with piezoelectric layers vol.15, pp.5, 2015, https://doi.org/10.12989/sss.2015.15.5.1345
  7. Comprehensive piezo-thermo-elastic analysis of a thick hollow spherical shell vol.14, pp.2, 2014, https://doi.org/10.12989/sss.2014.14.2.225
  8. Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers vol.12, pp.9, 2015, https://doi.org/10.1590/1679-78251449
  9. Large amplitude free vibration analysis of laminated composite spherical shells embedded with piezoelectric layers vol.16, pp.5, 2015, https://doi.org/10.12989/sss.2015.16.5.853
  10. Buckling analysis of the functionally graded sandwich rectangular plates integrated with piezoelectric layers under bi-axial loads vol.19, pp.6, 2017, https://doi.org/10.1177/1099636216642393
  11. Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation vol.16, pp.1, 2015, https://doi.org/10.12989/sss.2015.16.1.081
  12. Nonlinear thermal analysis of a hollow functionally graded cylinder with temperature-variable material properties vol.56, pp.2, 2015, https://doi.org/10.1134/S0021894415020121
  13. Nonlinear electro thermo elastic analysis of a thick spherical functionally graded piezoelectric shell vol.118, 2014, https://doi.org/10.1016/j.compstruct.2014.08.002
  14. Application of shear deformation theory for two dimensional electro-elastic analysis of a FGP cylinder vol.13, pp.1, 2014, https://doi.org/10.12989/sss.2014.13.1.001
  15. An efficient shear deformation theory for wave propagation of functionally graded material plates vol.57, pp.5, 2016, https://doi.org/10.12989/sem.2016.57.5.837
  16. Magneto-electro-mechanical bending analysis of three-layered exponentially graded microplate with piezomagnetic face-sheets resting on Pasternak's foundation via MCST pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1473538
  17. Free vibration analysis of a sandwich nano-plate including FG core and piezoelectric face-sheets by considering neutral surface pp.1537-6532, 2019, https://doi.org/10.1080/15376494.2018.1455939
  18. Studying the nonlinear behavior of the functionally graded annular plates with piezoelectric layers as a sensor and actuator under normal pressure vol.9, pp.2, 2011, https://doi.org/10.12989/sss.2012.9.2.127
  19. Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field vol.9, pp.5, 2011, https://doi.org/10.12989/sss.2012.9.5.427
  20. Nonlinear and linear thermo-elastic analyses of a functionally graded spherical shell using the Lagrange strain tensor vol.19, pp.1, 2011, https://doi.org/10.12989/sss.2017.19.1.033
  21. Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell vol.27, pp.4, 2018, https://doi.org/10.12989/scs.2018.27.4.479
  22. Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels vol.27, pp.4, 2011, https://doi.org/10.12989/scs.2018.27.4.525
  23. Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory vol.22, pp.1, 2011, https://doi.org/10.12989/sss.2018.22.1.027
  24. Creep analysis of the FG cylinders: Time-dependent non-axisymmetric behavior vol.28, pp.3, 2011, https://doi.org/10.12989/scs.2018.28.3.331
  25. Analysis of functionally graded plates resting on elastic foundation and subjected to non-linear hygro-thermo-mechanical loading vol.1, pp.4, 2011, https://doi.org/10.1007/s42791-019-00024-1
  26. Thermoelastic behaviour of FGM rotating cylinder resting on friction bed subjected to a thermal gradient and an external torque vol.19, pp.1, 2011, https://doi.org/10.1080/14484846.2018.1552736
  27. The Third-Order Shear Deformation Theory for Modeling the Static Bending and Dynamic Responses of Piezoelectric Bidirectional Functionally Graded Plates vol.2021, pp.None, 2011, https://doi.org/10.1155/2021/5520240
  28. Free Vibration Analysis of Cylindrical Micro/Nano-Shell Reinforced with CNTRC Patches vol.13, pp.4, 2011, https://doi.org/10.1142/s175882512150040x
  29. Radial vibration analysis for functionally graded ring piezoelectric transducers based on electromechanical equivalent circuit method vol.120, pp.None, 2022, https://doi.org/10.1016/j.ultras.2021.106640