Research PaperNo Access

Nonlinear Thermo-Electro-Mechanical Vibration of Functionally Graded Piezoelectric Nanoshells on Winkler–Pasternak Foundations Via Nonlocal Donnell’s Nonlinear Shell Theory

Department of Mechanics, Northeastern University, Shenyang 110819, P. R. China

Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, P. R. China

E-mail Address: wangyanqing@mail.neu.edu.cn

Corresponding author.

Search for more papers by this author

Yun Fei Liu

Department of Mechanics, Northeastern University, Shenyang 110819, P. R. China

Search for more papers by this author

, and

T. H. Yang

Center for Rock Instability and Seismicity Research, School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0219455419501001Cited by:20 (Source: Crossref)

Abstract

The thermo-electro-mechanical nonlinear vibration of circular cylindrical nanoshells on the Winkler–Pasternak foundation is investigated. The nanoshell is made of functionally graded piezoelectric material (FGPM), which is simulated by the nonlocal elasticity theory and Donnell’s nonlinear shell theory. The Hamilton’s principle is employed to derive the nonlinear governing equations and corresponding boundary conditions. Then, the Galerkin’s method is used to obtain the nonlinear Duffing equation, to which an approximate analytical solution is obtained by the multiple scales method. The results reveal that the system exhibits hardening-spring behavior. External applied voltage and temperature change have significant effect on the nonlinear vibration of the FGPM nanoshells. Moreover, the effect of power-law index on the nonlinear vibration of the FGPM nanoshells depends on parameters such as the external applied voltage, temperature change and properties of the Winkler–Pasternak foundation.

Keywords:

Remember to check out the Most Cited Articles!
Remember to check out the structures

References

1. H. J. Kim and Y. J. Kim, High performance flexible piezoelectric pressure sensor based on CNTs-doped 0–3 ceramic-epoxy nanocomposites, Mater. Des. 151 (2018) 133–140. Web of Science, Google Scholar
2. D. W. Schindel, D. A. Hutchins and W. A. Grandia, Capacitive and piezoelectric air-coupled transducers for resonant ultrasonic inspection, Ultrasonics 34 (1996) 621–627. Web of Science, Google Scholar
3. F. Lu, H. P. Lee and S. P. Lim, Modeling and analysis of micro piezoelectric power generators for micro-electromechanical-systems applications, Smart Mater. Struct. 13 (2003) 57–63. Web of Science, Google Scholar
4. M. Yang and P. Qiao, Modeling and experimental detection of damage in various materials using the pulse-echo method and piezoelectric sensors/actuators, Smart Mater. Struct. 14 (2005) 1083–1100. Web of Science, Google Scholar
5. V. Gupta, M. Sharma and N. Thakur, Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure: A technical review, J. Intell. Mater. Syst. Struct. 21 (2010) 1227–1243. Web of Science, Google Scholar
6. E. Aksel and J. L. Jones, Advances in lead-free piezoelectric materials for sensors and actuators, Sensors 10 (2010) 1935–1954. Web of Science, Google Scholar
7. Y. Q. Wang and J. W. Zu, Nonlinear steady-state responses of longitudinally traveling functionally graded material plates in contact with liquid, Compos. Struct. 164 (2017) 130–144. Web of Science, Google Scholar
8. R. Ansari, T. Pourashraf, R. Gholami and A. Shahabodini, Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers, Compos. Part B Eng. 90 (2016) 267–277. Web of Science, Google Scholar
9. W. Zhang, J. Yang and Y. Hao, Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory, Nonli. Dyn. 59 (2010) 619–660. Web of Science, Google Scholar
10. W. Zhang, Y. X. Hao and J. Yang, Nonlinear dynamics of FGM circular cylindrical shell with clamped–clamped edges, Compos. Struct. 94 (2012) 1075–1086. Web of Science, Google Scholar
11. M. Koizumi, FGM activities in Japan, Compos. Part B Eng. 28 (1997) 1–4. Web of Science, Google Scholar
12. W. Zhang, Y. Hao, X. Guo and L. Chen, Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations, Meccanica 47 (2012) 985–1014. Web of Science, Google Scholar
13. Y. Q. Wang and J. W. Zu, Nonlinear dynamics of a translational FGM plate with strong mode interaction, Int. J. Struct. Stab. Dyn. 18 (2018) 1850031. Link, Web of Science, Google Scholar
14. Y. X. Hao, W. Zhang and J. Yang, Nonlinear oscillation of a cantilever FGM rectangular plate based on third-order plate theory and asymptotic perturbation method, Compos. Part B Eng. 42 (2011) 402–413. Web of Science, Google Scholar
15. Y. X. Hao, L. H. Chen, W. Zhang and J. G. Lei, Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate, J. Sound Vib. 312 (2008) 862–892. Web of Science, Google Scholar
16. C. Wu, M. Kahn and W. Moy, Piezoelectric ceramics with functional gradients: A new application in material design, J. Am. Ceram. Soc. 79 (1996) 809–812. Web of Science, Google Scholar
17. I. I. Shelley, F. William, S. Wan and K. J. Bowman, Functionally graded piezoelectric ceramics, in Mater. Sci. Forum (Trans Tech Publ, 1999), pp. 515–520. Google Scholar
18. J. Qiu, J. Tani, T. Ueno, T. Morita, H. Takahashi and H. Du, Fabrication and high durability of functionally graded piezoelectric bending actuators, Smart Mater. Struct. 12 (2003) 115–121. Web of Science, Google Scholar
19. V. B. Shenoy, Atomistic calculations of elastic properties of metallic fcc crystal surfaces, Phys. Rev. B 71 (2005) 94104. Web of Science, Google Scholar
20. C. Q. Chen, Y. Shi, Y. S. Zhang, J. Zhu and Y. J. Yan, Size dependence of Young’s modulus in ZnO nanowires, Phys. Rev. Lett. 96 (2006) 75505. Web of Science, Google Scholar
21. H. Liang, M. Upmanyu and H. Huang, Size-dependent elasticity of nanowires: Nonlinear effects, Phys. Rev. B. 71 (2005) 241403. Web of Science, Google Scholar
22. T.-J. Park, G. C. Papaefthymiou, A. J. Viescas, A. R. Moodenbaugh and S. S. Wong, Size-dependent magnetic properties of single-crystalline multiferroic BiFeO3 nanoparticles, Nano Lett. 7 (2007) 766–772. Web of Science, Google Scholar
23. A. C. Eringen, Nonlocal Continuum Field Theories (Springer, New York, 2002). Google Scholar
24. A. C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci. 10 (1972) 1–16. Web of Science, Google Scholar
25. L. L. Ke and Y. S. Wang, Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory, Smart Mater. Struct. 21 (2012) 025018. Web of Science, Google Scholar
26. R. Ansari and R. Gholami, Nonlocal free vibration in the pre- and post-buckled states of magneto-electro-thermo elastic rectangular nanoplates with various edge conditions, Smart Mater. Struct. 25 (2016) 095033. Web of Science, Google Scholar
27. R. Ansari and R. Gholami, Size-dependent buckling and postbuckling analyses of first-order shear deformable magneto-electro-thermo elastic nanoplates based on the nonlocal elasticity theory, Int. J. Struct. Stab. Dyn. 17 (2017) 1750014. Link, Web of Science, Google Scholar
28. Y. Q. Wang, Y. F. Liu and J. W. Zu, Analytical treatment of nonlocal vibration of multilayer functionally graded piezoelectric nanoscale shells incorporating thermal and electrical effect, Eur. Phys. J. Plus 134 (2019) 54. Web of Science, Google Scholar
29. 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 (2017) 3039–3053. Web of Science, Google Scholar
30. X.-Q. Fang, C.-S. Zhu, J.-X. Liu and X.-L. Liu, Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures, Phys. B Condens. Matter. 529 (2018) 41–56. Web of Science, Google Scholar
31. A. M. Zenkour and M. Arefi, Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation, J. Therm. Stress. 40 (2017) 167–184. Web of Science, Google Scholar
32. L. L. Ke, Y. S. Wang and Z. D. Wang, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Compos. Struct. 94 (2012) 2038–2047. Web of Science, Google Scholar
33. S. R. Asemi, A. Farajpour and M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Compos. Struct. 116 (2014) 703–712. Web of Science, Google Scholar
34. R. Ansari and R. Gholami, Size-dependent nonlinear vibrations of first-order shear deformable magneto-electro-thermo elastic nanoplates based on the nonlocal elasticity theory, Int. J. Appl. Mech. 8 (2016) 1650053. Link, Web of Science, Google Scholar
35. R. Ansari, R. Gholami and H. Rouhi, Geometrically nonlinear free vibration analysis of shear deformable magneto-electro-elastic plates considering thermal effects based on a novel variational approach, Thin-Walled Struct. 135 (2019) 12–20. Web of Science, Google Scholar
36. R. Gholami, R. Ansari and Y. Gholami, Nonlocal large-amplitude vibration of embedded higher-order shear deformable multiferroic composite rectangular nanoplates with different edge conditions, J. Intell. Mater. Syst. Struct. 29 (2018) 944–968. Web of Science, Google Scholar
37. R. Gholami and R. Ansari, A unified nonlocal nonlinear higher-order shear deformable plate model for postbuckling analysis of piezoelectric-piezomagnetic rectangular nanoplates with various edge supports, Compos. Struct. 166 (2017) 202–218. Web of Science, Google Scholar
38. C. Liu, L.-L. Ke, Y.-S. Wang and J. Yang, Nonlinear vibration of nonlocal piezoelectric nanoplates, Int. J. Struct. Stab. Dyn. 15 (2015) 1540013. Link, Web of Science, Google Scholar
39. A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys. 54 (1983) 4703–4710. Web of Science, Google Scholar
40. L. L. Ke, Y. S. Wang, J. Yang and S. Kitipornchai, The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells, Smart Mater. Struct. 23 (2014) 125036. Web of Science, Google Scholar
41. M. Komijani, J. N. Reddy and M. R. Eslami, Nonlinear analysis of microstructure-dependent functionally graded piezoelectric material actuators, J. Mech. Phys. Solids 63 (2014) 214–227. Web of Science, Google Scholar
42. Y. Q. Wang, Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state, Acta Astronaut. 143 (2018) 263–271. Web of Science, Google Scholar
43. Y. Q. Wang and J. W. Zu, Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment, Aerosp. Sci. Technol. 69 (2017) 550–562. Web of Science, Google Scholar
44. F. Ebrahimi and E. Salari, Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams, Smart Mater. Struct. 24 (2015) 125007. Web of Science, Google Scholar
45. W. Soedel, Vibrations of Shells and Plates (CRC Press, 2004). Google Scholar
46. M. Amabili, Nonlinear Vibrations and Stability of Shells and Plates (Cambridge University Press, 2008). Google Scholar
47. Q. Wang, On buckling of column structures with a pair of piezoelectric layers, Eng. Struct. 24 (2002) 199–205. Web of Science, Google Scholar
48. M. Zhao, C. Qian, S. W. R. Lee, P. Tong, H. Suemasu and T. Y. Zhang, Electro-elastic analysis of piezoelectric laminated plates, Adv. Compos. Mater. Off. J. Japan Soc. Compos. Mater. 16 (2007) 63–81. Web of Science, Google Scholar
49. D. P. Zhang, Y. J. Lei and Z. B. Shen, Thermo-electro-mechanical vibration analysis of piezoelectric nanoplates resting on viscoelastic foundation with various boundary conditions, Int. J. Mech. Sci. 131–132 (2017) 1001–1015. Web of Science, Google Scholar
50. F. Bakhtiari-Nejad and S. M. Mousavi Bideleh, Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation, Thin-Walled Struct. 53 (2012) 26–39. Web of Science, Google Scholar
51. W. Zhang, Global and chaotic dynamics for a parametrically excited thin plate, J. Sound Vib. 239 (2001) 1013–1036. Web of Science, Google Scholar
52. Y. Q. Wang, X. B. Huang and J. Li, Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process, Int. J. Mech. Sci. 110 (2016) 201–216. Web of Science, Google Scholar
53. Y. Q. Wang, C. Ye and J. W. Zu, Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets, Aerosp. Sci. Technol. 85 (2019) 359–370. Web of Science, Google Scholar
54. A. H. Nayfeh, Perturbation Methods (John Wiley & Sons, 2008). Google Scholar
55. Y. Q. Wang, Y. H. Wan and J. W. Zu, Nonlinear dynamic characteristics of functionally graded sandwich thin nanoshells conveying fluid incorporating surface stress influence, Thin-Walled Struct. 135 (2019) 537–547. Web of Science, Google Scholar
56. W. Zhang, Z. Yao and M. Yao, Periodic and chaotic dynamics of composite laminated piezoelectric rectangular plate with one-to-two internal resonance, Sci. China Ser. E Technol. Sci. 52 (2009) 731–742. Web of Science, Google Scholar
57. P. B. Gonçalves and N. R. S. S. Ramos, Numerical method for vibration analysis of cylindrical shells, J. Eng. Mech. 123 (1997) 544–550. Web of Science, Google Scholar
58. C. L. Dym, Some new results for the vibrations of circular cylinders, J. Sound Vib. 29 (1973) 189–205. Web of Science, Google Scholar
59. H.-S. Shen and Y. Xiang, Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments, Comput. Methods Appl. Mech. Eng. 213 (2012) 196–205. Web of Science, Google Scholar
60. L. L. Ke, Y. S. Wang and J. N. Reddy, Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions, Compos. Struct. 116 (2014) 626–636. Web of Science, Google Scholar
61. J. Yang, Special Topics in the Theory of Piezoelectricity (Springer Science & Business Media, 2010). Google Scholar
62. K. K. Raju and G. V. Rao, Large amplitude asymmetric vibrations of some thin shells of revolution, J. Sound Vib. 44 (1976) 327–333. Web of Science, Google Scholar
63. M. Rafiee, M. Mohammadi, B. Sobhani Aragh and H. Yaghoobi, Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Part II: Numerical results, Compos. Struct. 103 (2013) 188–196. Web of Science, Google Scholar
64. Q. Wang, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, J. Appl. Phys. 98 (2005) 124301. Web of Science, Google Scholar
65. L. Wang and H. Hu, Flexural wave propagation in single-walled carbon nanotubes, Phys. Rev. B. 71 (2005) 195412. Web of Science, Google Scholar
66. S. Narendar, D. R. Mahapatra and S. Gopalakrishnan, Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation, Int. J. Eng. Sci. 49 (2011) 509–522. Web of Science, Google Scholar