Exact Solutions of Functionally Gradient Piezothermoelastic Cantilevers and Parameter Identification

Abstract

Based on the theory of elasticity, some exact solutions of functionally gradient piezothermoelastic cantilevers under different coupled loadings are obtained. As an application, these solutions have been successfully used to identify the gradient piezoelectric parameter and the thermal material coefficients. Besides, some numerical results have been carried out for the cantilever under two different kinds of loadings. It is found that the tip deflection of the cantilever agrees very well with the experimental and theoretical findings provided by other investigations. The present study also shows that the linear change of thermal material parameters does not influence the distribution of the stress and induction of the cantilever. But it influences the components of strain and electric field strength as well as the displacement and electric potential of the cantilever.

Keywords

FGM piezothermoelastic material sensors and actuators inverse problem parameter identification

Get full access to this article

View all access options for this article.

References

Alexander, Paul W. and Brei, Diann 2003. ‘‘Piezoceramic Telescopic Actuator Quasi-static Experimental Characterization,’’ Journal of Intelligent Materials Systems and Structures, 14(10): 643-656 .

Ashida, Fumihiro and Tauchert, Theodore R. 1997. ‘‘Temperature Determination for a Contacting Body based on an Inverse Piezothermoelastic Problem,’’ International Journal of Solids and Structures, 34(20): 2549-2561 .

Bui, H.D. 1993. Introduction Aux Problems Inverses en Mecanique des Materiaux, Direction des Etudes et Recherches d0 Electricite de France/Editions EYROLLES, Paris.

Clark, William W. 2000. ‘‘Vibration Control with State-switched Piezoelectric Materials,’’ Journal of Intelligent Material Systems and Structures, 11(4): 263-271 .

Corr, L.R. and Clark, W.W. 2001. Energy Dissipation Analysis of Piezoceramic Semi-active Vibration Control, Structures, Structural Dynamics, and Materials Conference, Seattle, WA, April 16-19.

Franke, Iwona , Roleder, Krystian , Miga, Seweryn , Maillard, Alain and Kugel, Godefroy 2002. ‘‘Determination of the Elastic Properties of a Li2B4O7 Single Crystal from the Piezoelectric Resonance,’’ Ferroelectrics, 273: 285-290 .

Hauke, T. , Kouvatov, A. , Steinhausen, R. , Seifert, W. , Beige, H. , Langhammer, H.T. and Abicht, H.P. 2000. ‘‘Bending Behavior of Functionally Gradient Materials,’’ Ferroelectrics, 238: 195-202 .

Hou, Max Ti-Kuang and Chen, Rongshun 2003. ‘‘Effect of Width on the Stress-induced Bending of Micromachined Bilayer Cantilevers,’’ J. Micromech. Microeng., 13(1): 141-148 .

Kapuria, S. , Dumir, P.C. and Sengupta, S. 1996. ‘‘Exact Piezothermoelastic Axisymmetric Solution of a Finite Transversely Isotropic Cylindrical Shell,’’ Comput. Struct., 61(6): 1085-1099 .

10.

Kielczynski, P. , Pajewski, W. and Szalewski, M. 1998. ‘‘Piezoelectric Sensors for Investigations of Microstructures,’’ Sensors and Actuators, A65(1): 13-18 .

11.

Kouvatov, A. , Steinhausen, R. , Seifert, W. , Hauke, T. , Langhammer, H.T. , Beige, H. and Abicht, H. 1999. ‘‘Comparison between Bimorphic and Polymorphic Bending Devices,’’ Journal of the European Ceramic Society, 19(6-7): 1153-1156 .

12.

Kruusing, A. 2000. ‘‘Analysis and Optimization of Loaded Cantilever Beam Microactuators,’’ Smart Materials and Structures, 9(2): 186-196 .

13.

Liu, T.T. and Shi, Z.F. 2004. ‘‘Bending Behavior of Functionally Gradient Piezoelectric Cantilever,’’ Ferroelectrics, 308: 43-51 .

14.

Liu, G.R. , Han, X. and Lam, K.Y. 2001. ‘‘Material Characterization of FGM Plates using Elastic Waves and an Inverse Procedure,’’ Journal of Composite Materials, 35(11): 954-971 .

15.

Marcus, M.A. 1984. ‘‘Performance Characteristics of Piezoelectric Polymer Flexure Mode Devices,’’ Ferroelectrics, 57: 203-220 .

16.

Philippe, Bouchilloux and Kenji, Uchino 2003. ‘‘Combined Finite Element Analysis - Genetic Algorithm Method for the Design of Ultrasonic Motors,’’ Journal of Intelligent Materials Systems and Structures, 14(10): 657-667 .

17.

Pritchard, Jane and Bowen, Chris Rhys 2002. ‘‘Characterization of Mulyi-layer Actuators,’’ Ferroelectrics, 273: 255-260 .

18.

Qiu, Jinhao , Tani, Junji , Ueno, Toshiyuki , Morita, Teppei , Takahashi, Hirofumi and Du, Hejun 2003. ‘‘Fabrication and High Durability of Functionally Gradient Piezoelectric Bending Actuators,’’ Smart Materials and Structures, 12(1): 115-121 .

19.

Raja, S. , Rohwer, K. and Rose, M. 1999. ‘‘Piezothermoelastic Modeling and Active Vibration Control of Laminated Composite Beams,’’ Journal of Intelligent Material Systems and Structures, 10(11): 890-899 .

20.

Schult, Mark J. , Sundaresan, Mannur, J. , Mcmichael, Jason , Clayton, David , Sadler, Robert and Nagel, Bill . 2003. ‘‘Piezoelectric Materials at Elevated Temperature,’’ Journal of Intelligent Materials Systems and Structures, 14(11): 693-705 .

21.

Shi, Z.F. 2002. ‘‘General Solution of a Density Functionally Gradient Piezoelectric Cantilever and its Applications,’’ Smart Materials and Structures, 11(1): 122-129 .

22.

Shi, Z.F. and Chen, Y. 2004. ‘‘Functionally Graded Piezoelectric Cantilever Beam Under Load.’’ Archive of Applied Mechanics, 74(3-4): 237-247 .

23.

Sirohi, Jayant and Chopra, Inderjit 2000a. ‘‘Fundamental Behavior of Piezoceramic Sheet Actuators,’’ Journal of Intelligent Material Systems and Structures, 11(1): 47-61 .

24.

Sirohi, Jayant and Chopra, Inderjit 2000b. ‘‘Fundamental Understanding of Piezoelectric Strain Sensors,’’ Journal of Intelligent Material Systems and Structures, 11(4): 246-257 .

25.

Sirohi, Jayant and Chopra, Inderjit 2003. ‘‘Design and Development of a High Pumping Frequency Piezoelectric-hydraulic Hybrid Actuator,’’ Journal of Intelligent Materials Systems and Structures, 14(3): 135-147 .

26.

Tian, X.G. and Shen, Y.P. 2003. ‘‘Finite Element Analysis of Thermo-mechanical Behaviour of Piezoelectric Structures under Finite Deformation,’’ Acta mechanica solida sinica, 24(2): 169-178 .

27.

Uchino, Kenji 1997. Piezoelectric Actuators and Ultrasonic Motors, Kluwer Academic Publ., Boston/Dordrecht/London .

28.

Vazquez, Carazo Alfredo and Kenji, Uchino 2001. ‘‘Novel Piezoelectric-based Power Supply for Driving Piezoelectric Actuators Designed for Active Vibration Damping Applications,’’ Journal of Electroceramics, 7(3): 197-210 .

29.

Vendlinski, James and Brei, Diann 2003. ‘‘Dynamic Behavior of Telescopic Actuators,’’ Journal of Intelligent Materials Systems and Structures, 14(9): 577-586 .

30.

Victor, Birman 1996. ‘‘Thermal Effects on Measurements of Dynamic Processes in Composite Structures using Piezoelectric Sensors,’’ Smart Materials and Structures, 5(4): 379-385 .

31.

Weileun, Fang 1999. ‘‘Determination of the Elastic Modulus of Thin Film Materials Using Self-deformed Micromachined Cantilevers,’’ J. Micromech. Microeng., 9(3): 230-235 .

32.

Zhong, Z. and Shang, E.T. 2003. ‘‘Three Dimensional Exact Analysis of Functionally Gradient Piezothermoelectric Material Rectangular Plate,’’ Acta mechanical sinica, 35(5): 542-552 .

33.

Zhu, X.H. , Wang, Q. and Meng, Z.Y. 1995. ‘‘A Functionally Gradient Piezoelectric Actuator Prepared by Powder Metallurgical Process in PNN-PZ-PT System,’’ Journal of Materials Science Letters, 14(7): 516-518 .