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Large amplitude free vibration analysis of laminated composite spherical shells embedded with piezoelectric layers

  • Singh, Vijay K. (Department of Mechanical Engineering, National Institute of Technology) ;
  • Panda, Subrata K. (Department of Mechanical Engineering, National Institute of Technology)
  • Received : 2015.02.06
  • Accepted : 2015.05.02
  • Published : 2015.11.25
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Abstract

Numerical analysis of large amplitude free vibration behaviour of laminated composite spherical shell panel embedded with the piezoelectric layer is presented in this article. For the investigation purpose, a general nonlinear mathematical model has been developed using higher order shear deformation mid-plane kinematics and Green-Lagrange nonlinearity. In addition, all the nonlinear higher order terms are included in the present mathematical model to achieve any general case. The nonlinear governing equation of freely vibrated shell panel is obtained using Hamilton's principle and discretised using isoparametric finite element steps. The desired nonlinear solutions are computed numerically through a direct iterative method. The validity of present nonlinear model has been checked by comparing the responses to those available published literature. In order to examine the efficacy and applicability of the present developed model, few numerical examples are solved for different geometrical parameters (fibre orientation, thickness ratio, aspect ratio, curvature ratio, support conditions and amplitude ratio) with and/or without piezo embedded layers and discussed in details.

Keywords

Acknowledgement

Supported by : Department of Science and Technology (DST)

References

  1. Arefi, M. and Khoshgoftar, M.J. (2014), "Comprehensive piezo-thermo-elastic analysis of a thick hollow spherical shell", Smart Struct. Syst., 14(2), 225-246. https://doi.org/10.12989/sss.2014.14.2.225
  2. Arefi, M. and Rahimi, G.H. (2011), "Nonlinear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure", Smart Struct. Syst., 8(5), 433-447. https://doi.org/10.12989/sss.2011.8.5.433
  3. Benjeddou, A. (2000), "Advances in piezoelectric finite element modeling of adaptive structural elements: a survey", Comput. Struct., 76, 347-363. https://doi.org/10.1016/S0045-7949(99)00151-0
  4. Balamurugan, V. and Narayanan, S. (2001), "Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control", Finite Elem. Anal. Des., 37, 713-738. https://doi.org/10.1016/S0168-874X(00)00070-6
  5. Balamurugan, V. and Narayanan, S. (2009), "Multilayer higher order piezlaminated smart composite shell finite element and its application to active vibration control", J. Intell. Mat. Syst. Str., 20, DOI: 10.1177/1045389x08095269.
  6. Benjeddou, A. Deu, J.F. and Letombe, S. (2002), "Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation", Thin Wall. Struct., 40, 573-593. https://doi.org/10.1016/S0263-8231(02)00013-7
  7. Carrera, E., Brischetto, S. and Nali P (2011), Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis, (1st Ed.), John Wiley & Sons Ltd, United Kingdom.
  8. Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2009), Concepts and applications of finite element analysis, (4th Ed.), John Wiley & Sons, Singapore.
  9. Chakravorty, D. Bandyopadhyay, J.N. and Sinha P.K. (1996), "Finite element free vibration analysis of doubly curved laminated composite shells", J. Sound Vib., 191(4) 491-504. https://doi.org/10.1006/jsvi.1996.0136
  10. Dash, P. and Singh, B.N. (2009), "Nonlinear free vibration of piezoelectric laminated composite plate", Finite Elem. Anal. Des., 45, 686-694. https://doi.org/10.1016/j.finel.2009.05.004
  11. Heyliger, P. and Brooks, S. (1995), "Free vibration of piezoelectric laminates in cylindrical bending", Int. J. Solids Struct., 32(20), 2945-2960. https://doi.org/10.1016/0020-7683(94)00270-7
  12. Huang, X.L. and Shen, H.S. (2005), "Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators", Int. J. Mech. Sci., 47, 187-208. https://doi.org/10.1016/j.ijmecsci.2005.01.003
  13. Huang, D. and Sun, B.H. (2001), "Approximate solution on smart composite beams by using MATLAB", Compos. Struct., 54, 197-205. https://doi.org/10.1016/S0263-8223(01)00088-5
  14. Kattimani, S.C. and Ray, M.C. (2014), "Active control of large amplitude vibrations of smart magneto-electro-elastic doubly curved shells", Int. J. Mech. Mater. Des., DOI: 10.1007/s10999-014-9252-3.
  15. Kerur, S.B. and Ghosh A. (2011), "Active control of geometrically non-linear transient response of smart laminated composite plate integrated with AFC actuator and PVDF sensor", J. Intell. Mat. Syst. Str., 22, 1149-1160. https://doi.org/10.1177/1045389X11414222
  16. Kulkarni S.A. and Bajoria K.M. (2007), "Large deformation analysis of piezolaminated smart structures using higher-order shear deformation theory", Smart Mater. Struct., 16, 1506-1516. https://doi.org/10.1088/0964-1726/16/5/002
  17. Lee, S.J. and Reddy, J.N. (2004), "Vibration suppression of laminated shell structures investigated using higher order shear deformation theory", Smart Mater. Struct., 13, 1176-1119. https://doi.org/10.1088/0964-1726/13/5/022
  18. Lee, S.J., Reddy, J.N. and Rostam-Abadi, F. (2006), "Nonlinear finite element analysis of laminated composite shells with actuating layers", Finite Elem. Anal. Des., 43, 1-21. https://doi.org/10.1016/j.finel.2006.04.008
  19. Nanda, N. (2010), "Non-linear free and forced vibrations of piezoelectric laminated shells in thermal environments", The IES Journal Part A: Civil & Structural Engineering, 3(3), 147-160. https://doi.org/10.1080/19373260.2010.490329
  20. Rafiee, M., Mohammadi, M., Aragh, B.S. and Yaghoobi, H. (2013), "Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells Part II: Numerical results", Compos. Struct., 103, 188-196. https://doi.org/10.1016/j.compstruct.2012.12.050
  21. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Free vibration response of two-dimensional magneto-electro-elastic laminated plates", J. Sound Vib., 292, 626-644. https://doi.org/10.1016/j.jsv.2005.08.004
  22. Reddy, J.N. (1999), "On laminated composite plates with integrated sensors and actuators", Eng. Struct., 21, 568-593. https://doi.org/10.1016/S0141-0296(97)00212-5
  23. Reddy, J.N. (2004), "Mechanics of laminated composite plates and shells: Theory and Analysis", (2nd Edition), CRC Press, Boca Raton, Florida, FL, USA.
  24. Saravanos, D.A., Heyliger. P.R., and Hopkins, D.A. (1997), "Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates", Int. J. Solids Struct., 34(3), 359-378. https://doi.org/10.1016/S0020-7683(96)00012-1
  25. Sarangi, S.K. and Ray, M.C. (2011), "Active damping of geometrically nonlinear vibrations of doubly curved laminated composite shells", Compos. Struct., 93, 3216-3228. https://doi.org/10.1016/j.compstruct.2011.06.005
  26. Sarangi, S.K. and Ray, M.C. (2010), "Smart damping of geometrically nonlinear vibrations of laminated composite beams using vertically reinforced 1-3 piezoelectric composites", Smart Mater. Struct., 19(075020), 1-14.
  27. Singh, V.K. and Panda S.K. (2014), "Nonlinear free vibration analysis of single/doubly curved composite shallow shell panels", Thin Wall. Struct., 85, 341-349. https://doi.org/10.1016/j.tws.2014.09.003
  28. Xu, K., Noor, A.K. and Tang, Y.Y. (1997), "Three-dimensional solutions for free vibrations of initially-stressed thermoelectroelastic multilayered plates", Comput. Method. Appl. M., 141, 125-139. https://doi.org/10.1016/S0045-7825(96)01065-1

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