Smart Structures and Systems

  • 제5권6호
  • /
  • Pages.591-612
  • /
  • 2009
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

New insights in piezoelectric free-vibrations using simplified modeling and analyses

  • 투고 : 2009.03.05
  • 심사 : 2009.04.14
  • 발행 : 2009.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

New insights are presented in simplified modeling and analysis of free vibrations of piezoelectric - based smart structures and systems. These consist, first, in extending the wide used piezoelectric-thermal analogy (TA) simplified modeling approach in currently static actuation to piezoelectric free-vibrations under short-circuit (SC) and approximate open-circuit (OC) electric conditions; second, the popular piezoelectric strain induced - potential (IP) simplified modeling concept is revisited. It is shown that the IP resulting frequencies are insensitive to the electric SC/OC conditions; in particular, SC frequencies are found to be the same as those resulting from the newly proposed OC TA. Two-dimensional plane strain (PStrain) and plane stress (PStress) free-vibrations problems are then analyzed for above used SC and approximate OC electric conditions. It is shown theoretically and validated numerically that, for both SC and OC electric conditions, PStress frequencies are lower than PStrain ones, and that 3D frequencies are bounded from below by the former and from above by the latter. The same holds for the modal electro-mechanical coupling coefficient that is retained as a comparator of presented models and analyses.

키워드

참고문헌

  1. Al-Ajmi, M.A. and Benjeddou, A. (2008), "Damage indication in smart structures using modal effective electromechanical coupling coefficients", Smart Mater. Struct., 17(6), 035023 (15p).
  2. Benjeddou, A. (2000), "Advances in piezoelectric finite element modeling of adaptive structural elements: a survey", Comput. Struct., 76(1-3), 347-363. https://doi.org/10.1016/S0045-7949(99)00151-0
  3. Benjeddou, A. (2002), "Modelling of piezoelectric adaptive beam, plate and shell structures: some developments and results", Proc. of the Sixth Int. Conf. on Computational Structures Technology, B.H.V Topping and Z. Bittnar (Eds.), Civil-Comp Press, Stirling, Scotland, Paper 81. Invited Lecture.
  4. Benjeddou, A. (2004), Modelling and simulation of adaptive structures and composites: current trends and future directions, in Progress in Computational Structures Technology, B.H.V Topping and C.A. Mota Soares (Eds.), Saxe-Coburg Publications, Stirling, Scotland, Chapter 10, 251-280. Special Lecture.
  5. Benjeddou, A. (2008), Piezoelectricity experimentation, modeling and simulation: common practices and realistic considerations, in Advances in Science and Technology, Trans Tech Publications, Switzerland, 56, 22-31. Invited Lecture.
  6. Benjeddou, A. and Ranger, J.A. (2006), "Use of shear-mode piezoceramics for structural vibration passive damping", Comput. Struct., 84(22-23), 1415-1425. https://doi.org/10.1016/j.compstruc.2005.10.010
  7. Benjeddou, A., Trindade, M.A. and Ohayon, R. (1997), "A unified beam finite element model for extension and shear piezoelectric actuation mechanisms", J. Intel. Mat. Syst. Str., 8(12), 1012-1025. https://doi.org/10.1177/1045389X9700801202
  8. Brockmann, T.H., Lammering, R. and Yang, F. (2006), "Modelling and computational analysis of structures with integrated piezoelectric material", Mech. Adv. Mater. Struc., 13(5), 371-378. https://doi.org/10.1080/15376490600777632
  9. Chevallier, G., Ghorbel, S. and Benjeddou, A. (2008), "A benchmark for free-vibration and effective coupling of thick smart structures", Smart Mater. Struct., 17(6), 065007 (11p).
  10. Collet, M. and Cunefare, K.A. (2008), "Modal synthesis and dynamical condensation methods for accurate piezoelectric systems impedance computation", J. Intel. Mat. Syst. Str., 19(11), 1251-1269. https://doi.org/10.1177/1045389X07084956
  11. Cote, F., Masson, P., Mrad, N. and Cotoni, V. (2004), "Dynamic and static modelling of piezoelectric composite structures using a thermal analogy with MSC/NASTRAN", Compos. Struct., 65, 471-484. https://doi.org/10.1016/j.compstruct.2003.12.008
  12. Deu, J.F. and Benjeddou, A. (2005), "Free-vibration analysis of laminated plates with embedded shear-mode piezoceramic layers", Int. J. Solids Struct., 42(7), 2059-2088. https://doi.org/10.1016/j.ijsolstr.2004.09.003
  13. Fernandes, A. and Pouget, J. (2003), "Analytical and numerical approaches to piezoelectric bimorph", Int. J. Solids Struct., 40, 4331-4352. https://doi.org/10.1016/S0020-7683(03)00222-1
  14. Hagood, N.W., Chung, W.H. and von Flotow, A. (1990), "Modelling of piezoelectric actuator dynamics for active structural control", J. Intel. Mat. Syst. Str., 1(7), 327-354. https://doi.org/10.1177/1045389X9000100305
  15. Hagood, N.W. and von Flotow, A. (1991), "Damping of structural vibrations with piezoelectric materials and passive electrical networks", J. Sound Vib., 146, 243-268. https://doi.org/10.1016/0022-460X(91)90762-9
  16. Heyliger, P. and Brooks, S. (1995), "Free vibration of piezoelectric laminates in cylindrical bending", Int. J. Solids Struct., 32, 2945-2960. https://doi.org/10.1016/0020-7683(94)00270-7
  17. IEEE Inc. (1988), Standard on Piezoelectricity, ANS/IEEE Std 176-1987, USA.
  18. Jiang, J.D. and Li, D.X. (2008), "Finite element formulation for thermopiezoelectric elastic laminated composite plates", Smart Mater. Struct., 17, 015027 (13pp).
  19. Kim, D.K., Kim, H.I., Han, J.H. and Kwon, K.J. (2008), "Experimental investigation on the aerodynamic characteristics of a bio-mimetic flapping wing with macro-fiber composites", J. Intel. Mat. Syst. Str., 19(3), 423-431. https://doi.org/10.1177/1045389X07083618
  20. Krommer, M. (2000), "An electromechanically coupled plate theory taking into account the influence of shear rotary inertia and electric field", Mech. Res. Comm., 27, 197-202. https://doi.org/10.1016/S0093-6413(00)00082-3
  21. Krommer, M. (2003a), "The significance of non-local constitutive relations for composite thin plates including piezoelastic layers with prescribed electric charge", Smart Mater. Struct., 12, 318-330. https://doi.org/10.1088/0964-1726/12/3/302
  22. Krommer, M. (2003b), "Piezoelectric vibrations of composite Reissner-Mindlin type plate", J. Sound Vib., 263, 871-891. https://doi.org/10.1016/S0022-460X(02)01169-0
  23. Lin, M.W., Abatan, A.O. and Rogers, C.A. (1994), "Application of commercial finite element codes for the analysis of induced strain actuated structures", J. Intel. Mat. Syst. Str., 5, 869-875. https://doi.org/10.1177/1045389X9400500621
  24. Marinkovic, D., Koppe, H. and Gabbert, U. (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
  25. Poizat, C. and Benjeddou, A. (2006), "On analytical and finite element modeling of piezoelectric extension and shear bimorphs", Comput. Struct., 84(22-23), 1426-1437. https://doi.org/10.1016/j.compstruc.2005.01.005
  26. Rahmoune, M., Benjeddou, A., Ohayon, R. and Osmont, D. (1998), "New thin piezoelectric plate models", J. Intel. Mat. Syst. Str., 9(12), 1017-1029. https://doi.org/10.1177/1045389X9800901207
  27. Shu, X. (2005), "Free vibration of laminated piezoelectric composite plates based on accurate theory", Compos. Struct., 67, 375-382. https://doi.org/10.1016/j.compstruct.2004.01.022
  28. Thornburgh, R.P. and Chattopadhyay, A. (2001), "Electrical-mechanical coupling effects on the dynamic response of smart composite structures", Proc. of the Smart Structures and Materials: Smart Structures and Integrated Systems, L.P. Davis (Ed.), SPIE, 4327, 413-424.
  29. Vel, S.S., Mewer, R.C. and Batra, R.C. (2004), "Analytical solution for the cylindrical bending vibration of piezoelectric composite plates", Int. J. Solids Struct., 41, 1625-1643. https://doi.org/10.1016/j.ijsolstr.2003.10.012
  30. Wang, S.Y. (2004), "A finite element model for the static and dynamic analysis of a piezoelectric bimorph", Int. J. Solids Struct., 41, 4075-4096. https://doi.org/10.1016/j.ijsolstr.2004.02.058
  31. Zhang, Z., Feng, C. and Liew, K.M. (2006), "Three-dimensional vibration analysis of multilayered piezoelectric composite plates", Int. J. Eng. Sci., 44, 397-408. https://doi.org/10.1016/j.ijengsci.2006.02.002

피인용 문헌

  1. A contribution on the optimal design of a vibrating cantilever in a power harvesting application – Optimization of piezoelectric layer distributions in combination with advanced harvesting circuits vol.53, 2013, https://doi.org/10.1016/j.engstruct.2013.03.022
  2. Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates vol.332, pp.22, 2013, https://doi.org/10.1016/j.jsv.2013.05.010
  3. Robust inverse identification of piezoelectric and dielectric effective behaviors of a bonded patch to a composite plate vol.12, pp.5, 2013, https://doi.org/10.12989/sss.2013.12.5.523
  4. A probabilistic multi-class classifier for structural health monitoring vol.60-61, 2015, https://doi.org/10.1016/j.ymssp.2015.01.017
  5. Modal effective electromechanical coupling approximate evaluations and simplified analyses: numerical and experimental assessments vol.225, pp.10, 2014, https://doi.org/10.1007/s00707-014-1206-1
  6. Approximate evaluations and simplified analyses of shear- mode piezoelectric modal effective electromechanical coupling vol.2, pp.3, 2015, https://doi.org/10.12989/aas.2015.2.3.275
  7. Active shape control of a cantilever by resistively interconnected piezoelectric patches vol.12, pp.5, 2013, https://doi.org/10.12989/sss.2013.12.5.501
  8. Quantity vs. Quality in the Model Order Reduction (MOR) of a Linear System vol.13, pp.1, 2014, https://doi.org/10.12989/sss.2014.13.1.099
  9. Static and dynamic shape control of slender beams by piezoelectric actuation and resistive electrodes vol.111, 2014, https://doi.org/10.1016/j.compstruct.2013.12.015
  10. Assessment of a smart concept for d15 shear piezoceramic direct torsion actuation vol.20, pp.1-4, 2011, https://doi.org/10.3166/ejcm.20.103-124
  11. Passive shape control of force-induced harmonic lateral vibrations for laminated piezoelastic Bernoulli-Euler beams-theory and practical relevance vol.7, pp.5, 2009, https://doi.org/10.12989/sss.2011.7.5.417
  12. Mathematical modeling of actively controlled piezo smart structures: a review vol.8, pp.3, 2009, https://doi.org/10.12989/sss.2011.8.3.275
  13. Nonlocal thermo-electro-mechanical vibration analysis of smart curved FG piezoelectric Timoshenko nanobeam vol.20, pp.3, 2009, https://doi.org/10.12989/sss.2017.20.3.351
  14. Modeling and simulation of an open channel PEHF system for efficient PVDF energy harvesting vol.28, pp.8, 2021, https://doi.org/10.1080/15376494.2019.1601307