Research PaperNo Access

Active Control of Plates Made of Functionally Graded Piezoelectric Material Subjected to Thermo-Electro-Mechanical Loads

Yu Xue

College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, P. R. China

College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China

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Jinqiang Li

College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, P. R. China

College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China

E-mail Address: lijinqiang@hrbeu.edu.cn

E-mail Address: lijinqiang@yahoo.com

Corresponding author.

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Fengming Li

College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, P. R. China

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, and

Zhiguang Song

College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, P. R. China

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https://doi.org/10.1142/S0219455419501074Cited by:18 (Source: Crossref)

Abstract

The present paper concentrates on the active control of the static bending and dynamic response of a functionally graded piezoelectric material (FGPM) plate subjected to thermo-electro-mechanical loads. Using the first-order shear deformation theory and Hamilton’s principle, the equation of motion for the FGPM plate is deduced. Based on the smart properties of piezoelectric ceramic, the active control of the static bending and vibration of the FGPM plate is studied by the mechanical load feedback, velocity feedback and LQR control methods in thermal environment. The effects of load parameter, temperature, volume fraction index and feedback control gain on the static bending and dynamic response of the FGPM plate are examined in detail. The simulation results show that the present control method can largely improve both the static and dynamic stability of the FGPM plate.

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References

1. K. Tanaka, Y. Tanaka, H. Watanabe, V. F. Poterasu and Y. Sugano, An improved solution to thermoelastic material design in functionally gradient materials: Scheme to reduce thermal stresses, Comput. Meth. Appl. Mech. Eng. 109(3–4) (1993) 377–389. Web of Science, Google Scholar
2. G. N. Praveen and J. N. Reddy, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, Int. J. Solids Struct. 35(33) (1998) 4457–4476. Web of Science, Google Scholar
3. J. N. Reddy and C. D. Chin, Thermomechanical analysis of functionally graded cylinders and plates, J. Therm. Stresses 21(6) (1998) 593–626. Web of Science, Google Scholar
4. J. R. Cho and J. T. Oden, Functionally graded material: A parametric study on thermal-stress characteristics using the Crank–Nicolson–Galerkin scheme, Comput. Meth. Appl. Mech. Eng. 188(1–3) (2000) 17–38. Web of Science, Google Scholar
5. J. N. Reddy, Analysis of functionally graded plates, Int. J. Numer. Methods Eng. 47(1–3) (2010) 663–684. Web of Science, Google Scholar
6. J. Yang and H. S. Shen, Dynamic response of initially stressed functionally graded rectangular thin plates, Compos. Struct. 54(4) (2001) 497–508. Web of Science, Google Scholar
7. X. L. Huang and H. S. Shen, Nonlinear vibration and dynamic response of functionally graded plates in thermal environments, Int. J. Solids Struct. 41(9) (2005) 2403–2427. Web of Science, Google Scholar
8. Y. Y. Lee, X. Zhao and K. M. Liew, Thermoelastic analysis of functionally graded plates using the element-free kp-Ritz method, Smart Mater. Struct. 18(3) (2009) 035007. Web of Science, Google Scholar
9. A. Shahrjerdi, F. Mustapha, M. Bayat and D. L. A. Majid, Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory, J. Mech. Sci. Technol. 25(9) (2011) 2195–2209. Web of Science, Google Scholar
10. P. Malekzadeh and S. M. Monajjemzadeh, Dynamic response of functionally graded plates in thermal environment under moving load, Compos. Pt. B-Eng. 45(1) (2013) 1521–1533. Web of Science, Google Scholar
11. N. Valizadeh, S. Natarajan, O. A. Gonzalez-Estrada, T. Rabczuk, T. Q. Bui and S. P. A. Bordas, NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter, Compos. Struct. 99 (2013) 309–326. Web of Science, Google Scholar
12. M. Mahinzare, M. M. Barooti and M. Ghadiri, Vibrational investigation of the spinning bi-dimensional functionally graded (2-FGM) micro plate subjected to thermal load in thermal environment, Microsyst. Technol. 24(3) (2018) 1695–1711. Web of Science, Google Scholar
13. S. Parida and S. C. Mohanty, Free vibration and buckling analysis of functionally graded plates resting on elastic foundation using higher order theory, Int. J. Struct. Stab. Dyn. 18(4) (2018) 1850049. Link, Web of Science, Google Scholar
14. M. Amir and M. Talha, Thermoelastic vibration of shear deformable functionally graded curved beams with microstructural defects, Int. J. Struct. Stab. Dyn. 18 (2018) 1850135. Link, Web of Science, Google Scholar
15. J. N. Reddy, Mechanics of Laminated Composite Plates-Theory and Analysis (CRC Press, New York, 1997). Google Scholar
16. J. H. Han and I. Lee, Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms, Smart Mater. Struct. 8 (1999) 257–267. Web of Science, Google Scholar
17. K. Y. Lam and T. Y. Ng, Active control of composite plates with integrated piezoelectric sensors and actuators under various dynamic loading conditions, Smart Mater. Struct. 8(2) (1999) 223–237. Web of Science, Google Scholar
18. S. Y. Wang, S. T. Quek and K. K. Ang, Vibration control of smart piezoelectric composite plates, Smart Mater. Struct. 10 (2001) 637–644. Web of Science, Google Scholar
19. I. Bruant, F. Pablo and O. Polit, Active control of laminated plates using a piezoelectric finite element, Mech. Adv. Mater. Struct. 15 (3–4) (2008) 276–290. Web of Science, Google Scholar
20. V. P. Phung, T. T. Nguyen, D. T. Le and X. H. Nguyen, static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3), Smart Mater. Struct. 22(9) (2013) 095026. Web of Science, Google Scholar
21. V. P. Phung, L. B. Nguyen, L. V. Tran, T. D. Dinh, C. H. Thai, S. P. A. Bordas, W. M. Abdel and X. H. Nguyen, An efficient computational approach for control of nonlinear transient responses of smart piezoelectric composite plates, Int. J. Non-Linear Mech. 76 (2015) 190–202. Web of Science, Google Scholar
22. V. P. Phung, L. De Lorenzis, C. H. Thai, W. M. Abdel and X. H. Nguyen, Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements, Comput. Mater. Sci. 96 (2015) 495–505. Web of Science, Google Scholar
23. J. N. Reddy and Z. Q. Cheng, Three dimensional solutions of smart functionally graded plates, J. Appl. Mech.-Trans. ASME 68(2) (2001) 234–241. Web of Science, Google Scholar
24. K. M. Liew, X. O. He and S. Kitipomehai, Finite element method for the feedback control of FGM shells in frequency domain via piezoelectric sensors and actuators, Comput. Meth. Appl. Mech. Eng. 193(3–5) (2004) 257–273. Web of Science, Google Scholar
25. V. Rizov, Delamination of multilayered functionally graded beams with material nonlinearity, Int. J. Struct. Stab. Dyn. 18(4) (2018) 1850051. Link, Web of Science, Google Scholar
26. X. L. Huang and H. S. Shen, Vibration and dynamic response of functionally graded plates with piezoelectric actuators in thermal environments. J. Sound Vib. 289(1–2) (2006) 25–53. Web of Science, Google Scholar
27. N. L. Shegokar and A. Lal, Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties, Meccanica 49(5) (2014) 1039–1068. Web of Science, Google Scholar
28. A. Lal, N. L. Shegokar and B. N. Singh, Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties, Appl. Math. Model. 44 (2017) 274–295. Web of Science, Google Scholar
29. V. P. Phung, L. V. Tran, A. J. M. Ferreira, X. H. Nguyen and W. M. Abdel, Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads, Nonli. Dyn. 87(2) (2017) 879–894. Web of Science, Google Scholar
30. J. Yang and H. J. Xiang, Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators, Smart Mater. Struct. 16(3) (2007) 784–797. Web of Science, Google Scholar
31. H. J. Xiang and Z. F. Shi, Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load, Eur. J. Mech. A-Solids 28(2) (2009) 338–346. Web of Science, Google Scholar
32. Z. Zhong and E. T. Shang, There-dimensional exact analysis of a simply supported functionally graded piezoelectric plate, Int. J. Solids Struct. 40(20) (2003) 5335–5352. Web of Science, Google Scholar
33. G. G. Sheng and X. Wang, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Appl. Math. Model. 34(9) (2010) 2630–2643. Web of Science, Google Scholar
34. A. A. Jandaghian and O. Rahmani, Size-dependent free vibration analysis of functionally graded piezoelectric plate subjected to thermo-electro-mechanical loading, J. Intell. Mater. Syst. Struct. 28(20) (2017) 3039–3053. Web of Science, Google Scholar
35. X. H. Nguyen, L. V. Tran, C. H. Thai and T. T. Nguyen, Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing, Thin-Walled Struct. 54 (2012) 1–18. Web of Science, Google Scholar
36. N. Sundararajan, T. Prakash and M. Ganapathi, Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments, Finite Elem. Anal. Des. 42(2) (2005) 152–168. Web of Science, Google Scholar
37. M. Taya, A. A. Almajid, M. Dunn and H. Takahashi, Design of bimorph piezo-composite actuators with functionally graded microstructure, Sens. Actuator A-Phys. 107(3) (2003) 248–260. Web of Science, Google Scholar
38. S. Xiang and G. W. Kang, Static analysis of functionally graded plates by the various shear deformation theory, Compos. Struct. 99(5) (2013) 224–230. Web of Science, Google Scholar
39. J. Li and Y. Narita, Vibration suppression for laminated cylindrical panels with arbitrary edge conditions, J. Vib. Control 19(4) (2013) 626–640. Web of Science, Google Scholar
40. D. F. Gilhooley, R. C. Batra, J. R. Xiao, M. A. McCarthy and J. W. Gillespie, Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions, Compos. Struct. 80(4) (2007) 539–552. Web of Science, Google Scholar
41. G. Castellazzi, C. Gentilini, P. Krysl and I. Elishakoff, Static analysis of functionally graded plates using a nodal integrated finite element approach, Compos. Struct. 103 (2013) 197–200. Web of Science, Google Scholar
42. B. Behjat, M. Salehi, A. Armin, M. Sadighi and M. Abbasi, Static and dynamic analysis of functionally graded piezoelectric plates under mechanical and electrical loading, Sci. Iran. 18(4) (2011) 986–994. Web of Science, Google Scholar
43. A. M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Appl. Math. Model. 30(1) (2006) 67–84. Web of Science, Google Scholar
44. G. R. Liu, K. Y. Dai and K. M. Lim, Static and vibration control of composite laminates integrated with piezoelectric sensors and actuators using the radial point interpolation method, Smart Mater. Struct. 13(6) (2004) 1438–1447. Web of Science, Google Scholar
45. X. H. Nguyen, L. V. Tran, T. T. Nguyen and D. H. Vu, Analysis of functionally graded plates using an edge-based smoothed finite element method, Compos. Struct. 93(11) (2011) 3019–3039. Web of Science, Google Scholar
46. Y. Q. Mao and Y. M. Fu, Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate, J. Sound Vibr. 329(11) (2010) 2015–2028. Web of Science, Google Scholar
47. I. K. Oh and D. W. Lee, Resonant frequency and instability of multi-layered micro-resonators with initial imperfection subject to piezoelectric loads, Microelectron. Eng. 84(5–8) (2007) 1388–1392. Web of Science, Google Scholar