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Mathematical Model of Cantilever Plate Using Finite Element Technique Based on Hamilton’s Principle

  • Behrouz Kheiri Sarabi
  • Manu Sharma
  • Damanjeet Kaur
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 490)

Abstract

In this work, the finite element model of a cantilevered plate is derived using Hamilton’s principle. A cantilevered plate structure instrumented with one piezoelectric sensor patch and one piezoelectric actuator patch is taken as a case study. Quadrilateral plate finite element having three degrees of freedom at each node is employed to divide the plate into finite elements. Thereafter, Hamilton’s principle is used to derive equations of motion of the smart plate. The finite element model is reduced to the first three modes using orthonormal modal truncation, and subsequently, the reduced finite element model is converted into a state-space model.

Keywords

Mathematical model Cantilevered plate Finite element Hamilton’s principal State-space 

References

  1. 1.
    Kheiri Sarabi B, Sharma M, Kaur D (2014) Techniques for creating mathematical model of structures for active vibration control. IEEE, Recent Adv Eng Comput Sci (RAECS)Google Scholar
  2. 2.
    Benjeddou A (2000) Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Comput Struct 76:347–363CrossRefGoogle Scholar
  3. 3.
    Allemang RJ (1983) Experimental modal analysis for vibrating structuresGoogle Scholar
  4. 4.
    Moita JMS, Soares CMM, Soares CAM (2002) Geometrically non-linear analysis of composite structures with integrated piezoelectric sensors and actuators. Compos Struct 57:253–261CrossRefGoogle Scholar
  5. 5.
    Reddy JN (2007) Theory and analysis of elastic plates and shells, 2nd edn. CRC Press, Boca RatonGoogle Scholar
  6. 6.
    Park SK, Gao XL (2006) Bernoulli-Euler beam model based on a modified couple stress theory. J Micromech Microeng 16:2355CrossRefGoogle Scholar
  7. 7.
    Umesh K, Ganguli R (2009) Shape and vibration control of a smart composite plate with matrix cracks. Smart Mater Struct 18:1–13CrossRefGoogle Scholar
  8. 8.
    Heidary F, Eslami MR (2004) Dynamic analysis of distributed piezothermoelastic composite plate using first-order shear deformation theory. J Therm Stresses 27:587–605CrossRefGoogle Scholar
  9. 9.
    Peng XQ, Lam KY, Liu GR (1998) Active vibration control of composite beams with piezoelectrics: a finite element model with third order theory. J Sound Vib 209:635–650CrossRefGoogle Scholar
  10. 10.
    Kulkarni SA, Bajoria KM (2003) Finite element modeling of smart plates/shells using higher order shear deformation theory. Compos Struct 62:41–50CrossRefGoogle Scholar
  11. 11.
    Robbins DH, Reddy JN (1991) Analysis of piezoelecrically actuated beams using a layer-wise displacement theory. Comput Struct 41:265–279CrossRefMATHGoogle Scholar
  12. 12.
    Reddy JN (1999) On laminated composite plate with integrated sensors and actuators. Eng Struct 21:568–593CrossRefGoogle Scholar
  13. 13.
    Kheiri Sarabi B, Sharma M, Kaur D (2016) Simulation of a new technique for vibration tests, based upon active vibration control. IETE J Res 63:1–9Google Scholar
  14. 14.
    Kheiri Sarabi B, Sharma M, Kaur D, Kumar N (2016) A novel technique for generating desired vibrations in structure. Integr Ferroelectr 176:236–250CrossRefGoogle Scholar
  15. 15.
    Kheiri Sarabi B, Sharma M, Kaur D, Kumar N (2017) An optimal control based technique for generating desired vibrations in a structure. Iran J Sci Technol Trans Electr Eng 41:219–228Google Scholar
  16. 16.
    Petyt M (1990) Introduction to finite element vibration analysis, 2nd edn. Cambridge University Press, New YorkGoogle Scholar
  17. 17.
    Acharjee S, Zabaras N (2007) A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes. Comput Struct 85:244–254CrossRefGoogle Scholar
  18. 18.
    Pradhan KK, Chakraverty S (2013) Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method. Compos B Eng 51:175–184CrossRefGoogle Scholar
  19. 19.
    Dovstam K (1995) Augmented Hooke’s law in frequency domain. A three dimensional, material damping formulation. Int J Solids Struct 32:2835–2852CrossRefMATHGoogle Scholar
  20. 20.
    Tzou HS, Howard RV (1994) A piezothermoelastic thin shell theory applied to active structures. J Vibr Acoust 116:295–302Google Scholar
  21. 21.
    Sharma S, Vig R, Kumar N (2015) Active vibration control: considering effect of electric field on coefficients of PZT patches. Smart Struct Syst 16:1091–1105CrossRefGoogle Scholar
  22. 22.
    Smittakorn W, Heyliger PR (2000) A discrete-layer model of laminated hygrothermopiezoelectric plates. Mech Compos Mater Struct 7:79–104CrossRefGoogle Scholar
  23. 23.
    Dyke SJ, Spencer BF, Sain MK, Carlson JD (1996) Modeling and control of magnetorheological dampers for seismic response reduction. Smart Mater Struct 5:565CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Behrouz Kheiri Sarabi
    • 1
  • Manu Sharma
    • 1
  • Damanjeet Kaur
    • 1
  1. 1.UIET, Panjab UniversityChandigarhIndia

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