DOI QR코드

DOI QR Code

Variable kinematic beam elements for electro-mechanical analysis

  • Miglioretti, F. (Department of mechanical and aerospace engineering, Politecnico di Torino, Corso Duca degli Abruzzi) ;
  • Carrera, E. (Department of mechanical and aerospace engineering, Politecnico di Torino, Corso Duca degli Abruzzi) ;
  • Petrolo, M. (Department of mechanical and aerospace engineering, Politecnico di Torino, Corso Duca degli Abruzzi)
  • 투고 : 2013.04.15
  • 심사 : 2013.12.13
  • 발행 : 2014.04.25

초록

This paper proposes a refined electro-mechanical beam formulation. Lagrange-type polynomials are used to interpolate the unknowns over the beam cross section. Three- (L3), four- (L4), and nine-point(L9) polynomials are considered which lead to linear, bi-linear, and quadratic displacement field approximations over the beam cross-section. Finite elements are obtained by employing the principle of virtual displacements in conjunction with the Carrera Unified Formulation (CUF). The finite element matrices and vectors are expressed in terms of fundamental nuclei whose forms do not depend on the assumptions made. Additional refined beam models are implemented by introducing further discretizations, over the beam cross-section. Some assessments from bibliography have been solved in order to validate the electro-mechanical formulation. The investigations conducted show that the present formulation is able to detect the electro-mechanical interaction.

키워드

참고문헌

  1. Bailey, T. and Hubbard, J. (1985), "Distributed piezoelectric polymer active vibration control of a cantilever beam", AIAA J., 8(5), 605-611.
  2. Ballhause, D., D'Ottavio, M., Kroplin, B. and Carrera, E. (2005), "A unified formulation to assess multilayered theories for piezoelectric plates", Comput. Struct., 83(15-16), 1217-1235. https://doi.org/10.1016/j.compstruc.2004.09.015
  3. Bathe, K. (1996), Finite element procedure, Prentice hall.
  4. Beheshti-Aval, S., Lezgy-Nazargah, M., Vidal, P. and Polit, O. (2011), "A refined sinusfinite element model for the analysis of piezoelectric-laminated beams", J. Intel. Mat. Syst. Str., 22(3), 203-210. https://doi.org/10.1177/1045389X10396955
  5. Biscani, F., Nali, P., Belouettar, S. and Carrera, E. (2012), "Coupling of hierarchical piezo-electric plate finite elements via arlequin method", J. Intel. Mat. Syst. Str., 23(7), 749-764. https://doi.org/10.1177/1045389X12437885
  6. Carrera, E. (1997), "An improved Reissner-Mindlin-Type model for the electromechanical analysis of multilayered plates including piezo-layers" J. Intel. Mat. Syst. Str., 8(3)232-248.
  7. Carrera, E. and Boscolo, M. (2006), "Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates", Int. J. Numer. Meth. Eng., 70(10), 1135-1181.
  8. Carrera, E. and Giunta, G. (2010), "Refined beam theories based on a unified formulation", Int. J. Appl. Mech., 2(1), 117-143. https://doi.org/10.1142/S1758825110000500
  9. Carrera, E., Giunta, G., Nali, P. and Petrolo, M. (2010), "Refined beam elements with arbitrary cross-section geometries", Comput. Struct., 88(5-6), 283-293. https://doi.org/10.1016/j.compstruc.2009.11.002
  10. Carrera, E. and Petrolo, M. (2011), "On the effectiveness of higher-order terms in refined beam theories", J. Appl. Mech. - T ASME, 7 (2), 021013, doi:10.1115/1.4002207.
  11. Carrera, E., Biscretto, S. and Nali, P. (2011), Plates and shells for smart structures, JohnWiley and sons.
  12. Carrera, E. and Petrolo, M. (2012), "Refined beam elements with only displacement variables and plate/shell capabilities", Meccanica, 47(3), 537-556. https://doi.org/10.1007/s11012-011-9466-5
  13. Carrera, E., Petrolo, M. and Nali, P. (2011), "Unified formulation applied to free vibrations finite element analysis of beams with arbitrary section", Shock Vib., 18(3), 485-502. https://doi.org/10.1155/2011/706541
  14. Carrera, E., Petrolo, M. and Varello, A. (2012a), "Advanced beam formulations for free vibrations analysis of conventional and joined wings", J. Aerospace Eng., 25(2), 282-293. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000130
  15. Carrera, E., Zappino, E. and Petrolo, M. (2012b), "Advanced elements for the static analysis of beams with compact and bridge-like sections", J. Struct. Eng. - ASCE, 56, 49-61.
  16. Caruso, G., Galeani, S. and Menini, L. (2003), "Active vibration control of an elastic plate using multiple piezoelectric sensors and actuators", Simul. Model. Pract. Th., 11(5-6), 403-419. https://doi.org/10.1016/S1569-190X(03)00056-X
  17. Chee, C., Tong, L. and Steven, G. (1999), "A mixed model for composite beams with piezoelectric actuators and sensors", Smart Mater. Struct., 8(3), 417, doi:10.1088/0964-1726/8/3/313.
  18. Crawley, E. and Luis, J. (1987), "Use of piezoelectric actuators as elements of intelligent structures", AIAA J., 25(10), 1373-1385. https://doi.org/10.2514/3.9792
  19. Dong, X.J., Meng, G. and Peng, J.C. (2006), "Vibration control of piezoelectric actuators smart structures based on system identification technique: numerical simulation and experimental study", J. Sound Vib., 297(3-5), 680-693. https://doi.org/10.1016/j.jsv.2006.04.021
  20. Elshafei, M. and Alraiess, F. (2013), "Modeling and analysis of smart piezoelectric beams using simple higher order shear deformation theory", Smart Mater. Struct., 22(3), doi:10.1088/0964-1726/22/3/035006.
  21. Hwang, W. and Park, H. (1993), "Finite element modelling of piezoelectric sensors and actuators", AIAA J., 31(5), 930-937. https://doi.org/10.2514/3.11707
  22. Kim, T.W. and Kim, J.H. (2005), "Optimal distribution of an active layer for transient vibration control of an flexible plates", Smart Mater. Struct., 14(5), 904-916. https://doi.org/10.1088/0964-1726/14/5/027
  23. Krommer, M. (2003), "Piezoelestic vibrations of composite Reissner-Mindlin-type plates", J. Sound Vib., 263(4), 871-891. https://doi.org/10.1016/S0022-460X(02)01169-0
  24. Kumar, K. and Narayanan, S. (2007), "The optimal location of piezolectric actuators and sensors for vibration controls of plate", Smart Mater. Struct., 16(6), 2680-2691. https://doi.org/10.1088/0964-1726/16/6/073
  25. Kusculuoglu, Z.K. and Royston, T.J. (2005), "Finite element formulation for composite plates with piezoceramic layers for optimal vibration control applications", Smart Mater. Struct., 14(6), 1139-1153. https://doi.org/10.1088/0964-1726/14/6/007
  26. Liu, G., Dai, K. and Lim, K. (2004), "Static and vibration control of composite laminates integrated with piezoelectric sensors and actuators using radial point interpolation method", Smart Mater. Struct., 13(6), 1438-1447. https://doi.org/10.1088/0964-1726/13/6/015
  27. Marinkovic, D., Koppe, H. and Gabber, H. (2007), "Accurate modelling of the electric field within piezoelectric layers for active composite structures", J. Intel. Mat. Syst. Str., 18(5), 503-513. https://doi.org/10.1177/1045389X06067139
  28. Moita, J., Soares, C. and Soares, C. (2005), "Active control of forced vibration in adaptive structures using a higher order model", Compos. Struct., 71(3-4), 349-355. https://doi.org/10.1016/j.compstruct.2005.09.009
  29. Moitha, J., Correira, I., Soares, C. and Soares, C. (2004), "Active control of adaptive laminated structures with bonded piezoelectric sensors and actuators", Comput. Struct., 82(17-19), 1349-1358. https://doi.org/10.1016/j.compstruc.2004.03.030
  30. Onate, E. ( 2009), Structural analysis with the finite element method: linear statics, Springer.
  31. Robbins, D. and Reddy, J. (1991a), "Analysis of piezoelectrically actuated beam using a layer-wise displacements theory", Comput. Struct., 41(2), 265-279. https://doi.org/10.1016/0045-7949(91)90430-T
  32. Robbins, D. and Reddy, J. (1991b), "Analysis of piezoelectrically actuated beams using a layer-wise displacement theory", Comput. Struct., 41(2), 265-279. https://doi.org/10.1016/0045-7949(91)90430-T
  33. Sarvanos, D. and Heyliger, P. (1995), "Coupled layer wise analysis of composite beams with embedded piezoelectric sensors and actuators", J. Intel. Mat. Syst. Str., 6(3), 350-363. https://doi.org/10.1177/1045389X9500600306
  34. Sarvanos, D. and Heyliger, P. (1999), "Mechanics and computational models for laminated piezoelectric beams, plate, and shells", Appl. Mech. Rev., 52(10), 305-320. https://doi.org/10.1115/1.3098918
  35. Sarvanos, D.A. (1997), "Mixed laminate theory and finite element for smart piezoelectric composite shell structures", AIAA J., 35(8), 1327-1333. https://doi.org/10.2514/2.264
  36. Tzou, H. and Ye, R. (1996), "Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements", AIAA J., 34(1), 110-115. https://doi.org/10.2514/3.12907
  37. Tzou, H. and Tseng, C. (1990), "Distributed vibration control and identification of coupled elastic/piezoelectric systems: finite element formulation and applications", Mech. Syst. Signal Pr., 5(3), 215-231.
  38. Umesh, K. and Ganguli, R. (2009), "Shape vibration control of smart plate with matrix cracks", Smart Mater. Struct., 18(2), 1-13.
  39. Valey, D. and Rao, S. (1994), Two-dimensional finite element modeling of composites with embedded piezoelectrics, Collection Tech. Papers Proc. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf. 5, 2629-2633.
  40. Vasques, C. and Rodrigues, J. (2006), "Active vibration of smart piezoelectric beams: comparison of classical and optimal feedback control strategies", Comput. Struct., 84(22-23),1459-1470. https://doi.org/10.1016/j.compstruc.2006.01.014
  41. Vidal, P., D'Ottavio, M., Thaier, M. and Polit, O. (2011), "An efficient finite shell element for the static resposne of piezoelectric laminates", J. Intel. Mat. Syst. Struct., 22(7),671. https://doi.org/10.1177/1045389X11402863
  42. Xu, S. and Koko, T. (2004), "Finite element analysis and design of actively a controlled piezoelectric smart structure", Finite Elem. Anal. Des., 40(3), 241-262. https://doi.org/10.1016/S0168-874X(02)00225-1
  43. Yasin, M.Y., Ahmad, N. and Alam, M.N. (2010), "Finite element analysis of actively controlled smart plate with patched actuators and sensors", Latin Am. J. Solids Struct., 7, 227-247. https://doi.org/10.1590/S1679-78252010000300001
  44. Yocum, M. and Abramovich, H. (2002), "Static behaviour of piezoelectric actuated beams", Comput. Struct., 80(23), 1797-1808. https://doi.org/10.1016/S0045-7949(02)00206-7
  45. Zhou, X., Chattopadhyay, A. and Gu, H. (2000), "Dynamic response of smart composites using a coupled thermo-piezoelectric-mechanical model", AIAA J., 38(10), 1939-1948. https://doi.org/10.2514/2.848

피인용 문헌

  1. Numerical analyses of piezoceramic actuators for high temperature applications vol.151, 2016, https://doi.org/10.1016/j.compstruct.2016.01.084
  2. Analysis of beams with piezo-patches by node-dependent kinematic finite element method models 2017, https://doi.org/10.1177/1045389X17733332
  3. Improved one-dimensional model of piezoelectric laminates for energy harvesters including three dimensional effects vol.127, 2015, https://doi.org/10.1016/j.compstruct.2015.02.065
  4. Recent developments on refined theories for beams with applications vol.2, pp.2, 2015, https://doi.org/10.1299/mer.14-00298
  5. Structural Control of Piezoelectric Laminated Beams under Thermal Load vol.38, pp.1, 2015, https://doi.org/10.1080/01495739.2014.976138
  6. Application of refined beam elements to the coupled-field analysis of magnetostrictive microbeams vol.115, 2017, https://doi.org/10.1016/j.compositesb.2016.10.055
  7. Thermo-piezo-elastic analysis of amplified piezoceramic actuators using a refined one-dimensional model 2018, https://doi.org/10.1177/1045389X17721026
  8. Node-dependent kinematic elements for the dynamic analysis of beams with piezo-patches vol.29, pp.16, 2018, https://doi.org/10.1177/1045389X18798942