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Unified solutions for piezoelectric bilayer cantilevers and solution modifications
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  • Journal title : Smart Structures and Systems
  • Volume 16, Issue 5,  2015, pp.759-780
  • Publisher : Techno-Press
  • DOI : 10.12989/sss.2015.16.5.759
 Title & Authors
Unified solutions for piezoelectric bilayer cantilevers and solution modifications
Wang, Xianfeng; Shi, Zhifei;
 Abstract
Based on the theory of piezoelasticity, the static performance of a piezoelectric bilayer cantilever fully covered with electrodes on the upper and lower surfaces is studied. Three models are considered, i.e., the sensor model, the driving displacement model and the blocking force model. By establishing suitable boundary conditions and proposing an appropriate Airy stress function, the exact solutions for piezoelectric bilayer cantilevers are obtained, and the effect of ambient thermal excitation is taken into account. Since the layer thicknesses and material parameters are distinguished in different layers, this paper gives unified solutions for composite piezoelectric bilayer cantilevers including piezoelectric bimorph and piezoelectric heterogeneous bimorph, etc. For some special cases, the simplifications of the present results are compared with other solutions given by other researches based on one-dimensional constitutive equations, and some amendments have been found. The present investigation shows: (1) for a PZT-4 piezoelectric bimorph, the amendments of tip deflections induced by an end shear force, an end moment or an external voltage are about 19.59%, 23.72% and 7.21%, respectively; (2) for a PZT-4-Al piezoelectric heterogeneous bimorph with constant layer thicknesses, the amendments of tip deflections induced by an end shear force, an end moment or an external voltage are 9.85%, 11.78% and 4.07%, respectively, and the amendments of the electrode charges induced by an end shear force or an end moment are both 1.04%; (3) for a PZT-4-Al piezoelectric heterogeneous bimorph with different layer thicknesses, the maximum amendment of tip deflection approaches 23.72%, and the maximum amendment of electrode charge approaches 31.09%. The present solutions can be used to optimize bilayer devices, and the Airy stress function can be used to study other piezoelectric cantilevers including multi-layered piezoelectric cantilevers under corresponding loads.
 Keywords
piezoelectric;bimorph;unimorph;sensor;actuator;thermal effect;
 Language
English
 Cited by
 References
1.
Ashida, F. and Tauchert, T.R. (1997), "Temperature determination for a contacting body based on an inverse piezothermoelastic problem", Int. J. Solids Struct., 34(20), 2549-2561. crossref(new window)

2.
Ashida, F. and Tauchert, T.R. (1998), "Transient response of a piezothermoelastic circular disk under axisymmetric heating", Acta Mech., 128(1-2), 1-14. crossref(new window)

3.
Chen, Y. and Shi, Z.F. (2005a), "Double-layered piezothermoelastic hollow cylinder under thermal loading", Key Eng Mater., 302, 684-692.

4.
Chen, Y. and Shi, Z.F. (2005b), "Exact solutions of functionally gradient piezothermoelastic cantilevers and parameter identification", J. Intel. Mat. Syst. Str., 16(6), 531-539. crossref(new window)

5.
Erturk, A. (2011), "Piezoelectric energy harvesting for civil infrastructure system applications: Moving loads and surface strain fluctuations", J. Intel. Mat. Syst. Str., 22(17), 1959-1973. crossref(new window)

6.
Erturk, A. and Inman, D.J. (2009), "An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations", Smart Mater Struct., 18(2), 25009. crossref(new window)

7.
Gehring, G.A., Cooke, M.D., Gregory, I.S., Karl, W.J. and Watts, R. (2000), "Cantilever unified theory and optimization for sensors and actuators", Smart Mater Struct., 9(6), 918-931. crossref(new window)

8.
Hauke, T., Kouvatov, A., Steinhausen, R., Seifert, W., Beige, H. and Theo, H. et al. (2000), "Bending behavior of functionally gradient materials", Ferroelectrics, 238(1), 195-202. crossref(new window)

9.
Kapuria, S. and Achary, G. (2005), "A coupled consistent third-order theory for hybrid piezoelectric plates", Compos Struct., 70(1), 120-133. crossref(new window)

10.
Kapuria, S., Bhattacharyya, M. and Kumar, A.N. (2006), "Assessment of coupled 1D models for hybrid piezoelectric layered functionally graded beams", Compos Struct., 72(4), 455-468. crossref(new window)

11.
Malgaca, L. and Karaguelle, H. (2009), "Simulation and experimental analysis of active vibration control of smart beams under harmonic excitation", Smart Struct. Syst., 5(1), 55-68. crossref(new window)

12.
Peng, W.Y., Xiao, Z.X. and Farmer, K.R. (2003), "Optimization of thermally actuated bimorph cantilevers for maximum deflection", Nanotechnology Conference and Trade Show (Nanotech 2003), San Francisco, USA, February.

13.
Ray, M.C. and Reddy, J.N. (2005), "Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites", Compos Sci. Technol., 65(7-8), 1226-1236. crossref(new window)

14.
Schoeftner, J. and Irschik, H. (2011), "Passive shape control of force-induced harmonic lateral vibrations for laminated piezoelastic Bernoulli-Euler beams-theory and practical relevance", Smart Struct. Syst., 7(5), 417-432. crossref(new window)

15.
Shi, Z.F. (2002), "General solution of a density functionally gradient piezoelectric cantilever and its applications", Smart Mater Struct., 11(1), 122-129. crossref(new window)

16.
Shi, Z.F. (2005), "Bending behavior of piezoelectric curved actuator", Smart Mater Struct., 14(4), 835-842. crossref(new window)

17.
Smits, J.G. and Choi, W. (1991), "The constituent equations of piezoelectric heterogeneous bimorphs", IEEE T. Ultrason Ferr., 38(3), 256-270. crossref(new window)

18.
Smits, J.G. and Choi, W. (1993), "Equations of state including the thermal domain of piezoelectric and pyroelectric heterogeneous bimorphs", Ferroelectrics, 141(1), 271-276. crossref(new window)

19.
Smits, J.G., Dalke, S.I. and Cooney, T.K. (1991), "The constituent equations of piezoelectric bimorphs", Sensor Actuat. A-Phys., 28(1), 41-61. crossref(new window)

20.
Tzou, H.S. and Bao, Y. (1995), "A theory on anisotropic piezothermoelastic shell laminates with sensor/actuator applications", J. Sound Vib., 184(3), 453-473. crossref(new window)

21.
Tzou, H.S. and Howard, R.V. (1994), "A piezothermoelastic thin shell theory applied to active structures", J. Vib. Acoust., 116(3), 295-302. crossref(new window)

22.
Xiang, H.J. and Shi, Z.F. (2008), "Static analysis for multi-layered piezoelectric cantilevers", Int. J. Solids Struct., 45(1), 113-128. crossref(new window)

23.
Xiang, H.J. and Shi, Z.F. (2009), "Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load", Eur. J.Mech. A-Solid., 28(2), 338-346. crossref(new window)

24.
Zhang, T.T. and Shi, Z.F. (2006), "Two-dimensional exact analysis for piezoelectric curved actuators", J Micromech. Microeng., 16(3), 640-647. crossref(new window)