Vibration Analysis of Functionally Graded Piezoelectric Actuators: A Comprehensive Review

Notice

This is an unedited manuscript accepted for publication and provided as an Article in Press for early access at the author’s request. The article will undergo copyediting, typesetting, and galley proof review before final publication. Please be aware that errors may be identified during production that could affect the content. All legal disclaimers of the journal apply.

Year : 2025 | Volume :13 | Special Issue : 01 | Page : S426-S440
By
vector

Srishti Dhakad,

vector

Akshansh Sharma,

vector

Pankaj Sharma,

vector

S. K. Parashar,

  1. PG Scholar, Mechanical Engineering Department, Rajasthan Technical University,Kota, Rajasthan, India
  2. Research Scholar, Mechanical Engineering Department, Rajasthan Technical University, Kota, Rajasthan, India
  3. Faculty, Mechanical Engineering Department, Rajasthan Technical University, Kota, Rajasthan, India
  4. Faculty, Mechanical Engineering Department, Rajasthan Technical University, Kota, Rajasthan, India

Abstract document.addEventListener(‘DOMContentLoaded’,function(){frmFrontForm.scrollToID(‘frm_container_abs_130207’);});Edit Abstract & Keyword

Recent research has been concentrated on a thorough investigation of the vibration evaluation of
functionally graded piezoelectric materials (FGPM), shedding light on the potential for enhancing
structural optimization and controlling deflections and vibrations. Functionally graded piezoelectric
material is a type of advanced composite material possessing diverse characteristics that allow for
customized mechanical and electrical responses. The existing body of academic work extensively
addresses the vibration analysis of functionally graded piezoelectric materials, with a specific focus on
a wide array of facets including material characteristics, geometric parameters, boundary conditions,
and the distinctive features of vibrations. This chapter presents comprehensive literature review of
FGPM fundamental structures, including detailed examinations of the free and forced vibration
responses of functionally graded piezoelectric beams, plates, and shells, thereby providing valuable
insights into the impacts of diverse boundary conditions and material gradation parameters on the
vibration frequencies of these fundamental structures. Recent progress in computational modeling and
experimental validation is emphasized, demonstrating their contribution to improving the precision of
vibration analysis alongside traditional methods. These collective researches serve to deepen our
comprehension of the vibration frequencies and optimization prospects inherent in functionally graded
piezoelectric materials and composites, facilitating the emergence of innovative applications within the
domains of aerospace, automotive engineering, and energy capture systems.

Keywords: Vibration analysis of FGPM, power law, exponential law, FGPM beam, FGPM plate, FGPM shells

[This article belongs to Special Issue under section in Journal of Polymer and Composites (jopc)]

How to cite this article:
Srishti Dhakad, Akshansh Sharma, Pankaj Sharma, S. K. Parashar. Vibration Analysis of Functionally Graded Piezoelectric Actuators: A Comprehensive Review. Journal of Polymer and Composites. 2024; 13(01):S426-S440.
How to cite this URL:
Srishti Dhakad, Akshansh Sharma, Pankaj Sharma, S. K. Parashar. Vibration Analysis of Functionally Graded Piezoelectric Actuators: A Comprehensive Review. Journal of Polymer and Composites. 2024; 13(01):S426-S440. Available from: https://journals.stmjournals.com/jopc/article=2024/view=0

References
document.addEventListener(‘DOMContentLoaded’,function(){frmFrontForm.scrollToID(‘frm_container_ref_130207’);});Edit

  1. Sharma P. Vibration analysis of functionally graded piezoelectric actuators. New York (NY): Springer; 2019. p. 52-60.
  2. Zhu XH, Meng ZY. Operational principle, fabrication and displacement characteristic of a functionally gradient piezoelectric ceramic actuator. Sens Actuators. 1995;48:169-176.
  3. Mahamood RM, Akinlabi ET, Shukla M, Pityana S. Functionally graded material: an overview. In: Proceedings of the World Congress on Engineering, WCE; 2012.
  4. Craig B. Limitations of alloying to improve the threshold for hydrogen stress cracking of steels. Hydrog Eff Mater Behav. 1989;955-963.
  5. Rajput RK. Manufacturing technology. India: Laxmi Publication; 2008.
  6. Wang SS. Fracture mechanics for delamination problems in composite materials. J Compos Mater. 1983;17(3):210-223.
  7. Knoppers GE, Gunnink JW, Van den Hout J, Van Wliet WP. The reality of functionally graded material products. In: Intelligent production machines and systems: first I* PROMS virtual conference. Amsterdam: Elsevier; 2005. p. 467-474.
  8. Mohammad J. Vibration Modeling of a Bi-morph Functional Graded Piezoelectric Energy Harvester Based on The Timoshenko Beam Theory. 2023;1-7. Available from: doi: 10.1109/IRASET57153.2023.10153021.
  9. Pradhan N, Sarangi S, Basa B. Analysis of Smart Functionally Graded Beams combined with piezoelectric material using Finite Element Method. 2022;1(1):1603-1606. Available from: doi: 10.38208/acp.v1.695.
  10. Pham M, Phuc Vu, Nguyen T. On the Vibration Analysis of Rotating Piezoelectric Functionally Graded Beams Resting on Elastic Foundation with a Higher-Order Theory. Int J Aerosp Eng. 2022;1-16. Available from: doi: 10.1155/2022/9998691.
  11. Manish K, Sarangi SK. Bending and vibration study of carbon nanotubes reinforced functionally graded smart composite beams. Eng Res Express. 2022;4(2):025043. Available from: doi: 10.1088/2631-8695/ac76a0.
  12. Li JF, Takagi K, Ono M, Pan W, Watanabe R, Almajid A, Taya M. Fabrication and evaluation of porous piezoelectric ceramics and porosity-graded piezoelectric actuators. J Am Ceram Soc. 2003;86:1094-8.
  13. Djabrouhou I, Mahieddine A, Bentridi S, Kouadria KM, Hemis M. Dynamic behavior of unimorph FGPM tapered beam actuator subjected to electrical harmonic load. J Vib Eng Technol. 2024;12(2):2425-35.
  14. Bi HH, Wang B, Deng ZC, Wang SD. Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam. Appl Math Mech (Engl Ed). 2020;41(2):313-326.
  15. Qiu J, Tani J, Ueno T, Morita T, Takahashi H, Du HJ. Fabrication and high durability of functionally graded piezoelectric bending actuators. Smart Mater Struct. 2003;12:115-21.
  16. Chu L, Dui G, Ju C. Flexoelectric effect on the bending and vibration responses of functionally graded piezoelectric nanobeams based on general modified strain gradient theory. Compos Struct. 2018;186:39-49.
  17. Chen M, Chen H, Ma X, Jin G, Ye T, Zhang Y, Liu Z. The isogeometric free vibration and transient response of functionally graded piezoelectric curved beam with elastic restraints. Results Phys. 2018;11:712-725.
  18. Pandey VB, Parashar SK. Static bending and dynamic analysis of functionally graded piezoelectric beam subjected to electromechanical loads. Proc Inst Mech Eng Part C J Mech Eng Sci. 2016;230(19):3457-69.
  19. Su Z, Jin G, Ye T. Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions. Smart Mater Struct. 2016;25(6):065003.
  20. Parashar SK, Sharma P. Modal analysis of shear-induced flexural vibration of FGPM beam using Generalized Differential Quadrature method. Compos Struct. 2016;139:222-32.
  21. Sharma P, Parashar SK. Exact analytical solution of shear induced flexural vibration of functionally graded piezoelectric beam. In: AIP Conference Proceedings (Vol. 1728, No. 1, p. 020167). AIP Publishing; 2016.
  22. Majdi A, Yasin Y, Farag M, Altalbawy A, Abdul-Malek S, Tamimi AL, et al. Size-dependent vibrations of bi-directional functionally graded porous beams under moving loads incorporating thickness effect. Mech Based Des Struct Mach. 2023;1-32. Available from: doi: 10.1080/15397734.2023.2165098.
  23. Liu B, Chen H, Cao W. A novel method for tailoring elasticity distributions of functionally graded porous materials. Int J Mech Sci. 2019;157:457-70.
  24. Gupta B, Sharma P, Rathore SK. A new numerical modeling of an axially functionally graded piezoelectric beam. J Vib Eng Technol. 2022;10:3191-3206.
  25. Gupta B, Sharma P, Rathore SK. Free vibration analysis of AFGPM non-uniform beam: A mathematical modeling. J Vib Eng Technol. 2023;11(7):2945-54.
  26. Sharma P, Gupta B, Rathore SK. Parametric study on natural frequency of axially tapered functionally graded piezoelectric beam. Mater Today Proc. 2022;62:3647-50.
  27. Sharma P, Gupta B, Rathore SK, Khinchi A, Gautam M. Computational characteristics of an exponentially functionally graded piezoelectric beam. Int J Interact Des Manuf (IJIDeM). 2022;1-7.
  28. Zhou H, Han K, Elmaimouni L, Wang X, Yu J. Double Legendre polynomial quadrature-free method for axi-symmetric vibration of functionally graded piezoelectric circular plates. J Vib Control. 2024;30(3-4):598-615. Available from: doi:10.1177/10775463221149087.
  29. Singh SJ, Shikha S, Kumar V, Harsha SP. Effect of thickness stretching and electro-mechanical loading on sandwich FGM plate with piezoelectric face sheet with different boundary conditions: A semi-analytical approach. Mech Based Des Struct Mach. 2024;52(2):1074-1108. Available from: https://doi.org/10.1080/15397734.2022.2136687.
  30. Kumar P, Harsha A. Vibration response analysis of the bi-directional porous functionally graded piezoelectric (BD-FGP) plate. Mech Based Des Struct Mach. 2024;52(1):126-151. Available from: doi: 10.1080/15397734.2022.2099418.
  31. Wang X, Ye T, Cheng L, Jin G, Chen Y, Liu Z. Electro-mechanical vibro-acoustic characteristics of submerged functionally graded piezoelectric plates with general boundary conditions. Compos Struct. 2023;322:117411.
  32. Sharma JK, Kumar S, Kumar N, Hasnain SM, Pandey S, Deifalla AF, Ragab AE. Computational modeling of sigmoid functionally graded material (SFGM) plate. Mater Res Express. 2023;10(7):075701.
  33. Zhang P, Qi C, Sun X, Fang H, Huang Y. Bending behaviors of the in-plane bidirectional functionally graded piezoelectric material plates. Mech Adv Mater Struct. 2022;29(13):1925-45.
  34. Sawarkar SS, Pendhari SS. Functionally Graded Piezoelectric Plates in Cylindrical Bending by Semi-analytical Approach. Mech Adv Compos Struct. 2022;9(2):409-24.
  35. Kumar P, Harsha SP. Static and vibration response analysis of sigmoid function-based functionally graded piezoelectric non-uniform porous plate. J Intell Mater Syst Struct. 2022;33(17):2197-227.
  36. Kumar P, Harsha SP. Vibration response analysis of exponential functionally graded piezoelectric (EFGP) plate subjected to thermo-electro-mechanical load. Compos Struct. 2021;267:113901.
  37. Praksh D, Kumar J, Panda S. Nonlinear free vibration analysis of piezoelectric laminated plate with random actuation electric potential difference and thermal loading. Appl Math Model. 2021.
  38. Khorshidi K, Karimi M, Siahpush A. Size-dependent electro-mechanical vibration analysis of FGPM composite plates using modified shear deformation theories. Mech Adv Compos Struct. 2021;8(1):157-69.
  39. Sharma TK. Free vibration analysis of functionally graded circular piezoelectric plate using COMSOL Multi-physics. In: AIP Conference Proceedings (Vol. 2220, No. 1). AIP Publishing; 2020.
  40. Wang Q, Zhong R, Qin B, Yu H. Dynamic analysis of stepped functionally graded piezoelectric plate with general boundary conditions. Smart Mater Struct. 2022;29(3):035022.
  41. Abbaspour F, Arvin H. Vibration and thermal buckling analyses of three-layered centro-symmetric piezoelectric microplates based on the modified consistent couple stress theory. J Vib Control. 2020;26(15-16):1253-65.
  42. Sharma P. Vibration analysis of FGPM annular plate. In: Vibration Analysis of Functionally Graded Piezoelectric Actuators. Singapore: Springer Singapore; 2019. p. 45-70.
  43. Li J, Xue Y, Li F, Narita Y. Active vibration control of functionally graded piezoelectric material plate. Compos Struct. 2019;207:509-18.
  44. Wang YQ. Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state. Acta Astronaut. 2018;143:263-71.
  45. Mahinzare M, Ranjbarpur H, Ghadiri M. Free vibration analysis of a rotary smart two directional functionally graded piezoelectric material in axial symmetry circular nanoplate. Mech Syst Signal Process. 2018;100:188-207.
  46. Wang YQ, Zu JW. Porosity-dependent nonlinear forced vibration analysis of functionally graded piezoelectric smart material plates. Smart Mater Struct. 2017;26(10):105014.
  47. Ashoori AR, Sadough Vanini SA. Vibration of circular functionally graded piezoelectric plates in pre-/post-buckled configurations of bifurcation/limit load buckling. Acta Mech. 2017;228:2945-64.
  48. Sharma P, Parashar SK. Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using generalized differential quadrature method. Compos Struct. 2016;155:213-22.
  49. Yas MH, Moloudi N. Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space-based differential quadrature method. Appl Math Mech. 2015;36(4):439-64
  50. Dai HL, Dai T, Yang L. Free vibration of a FGPM circular plate placed in a uniform magnetic field. Meccanica. 2013;48(10):2339-47.
  51. Jodaei A, Jalal M, Yas MH. Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates via SSDQM and comparative modeling by ANN. Math Comput Model. 2013;57:1408-25.
  52. Yas MH, Jodaei A, Irandoust S, Aghdam MN. Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates on elastic foundations. Meccanica. 2012;47:1401-23.
  53. Alibeigloo A, Simintan V. Elasticity solution of functionally graded circular and annular plates integrated with sensor and actuator layers using differential quadrature. Compos Struct. 2011;93(10)
  54. Ebrahimi F, Rastgoo A. Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates. Arch Appl Mech. 2011;81(3):361-83.
  55. Li XY, Wu J, Ding HJ, Chen WQ. 3D analytical solution for a functionally graded transversely isotropic piezoelectric circular plate under tension and bending. Int J Eng Sci. 2011;49(7):664-76.
  56. Jam JE, Nia NG. Semi-analytical solution for 3-D vibration of FGPM annular plates. Int J Emerg Trends Eng Dev. 2011;3:149-66.
  57. Shakeri M, Mirzaeifar R. Static and dynamic analysis of thick functionally graded plates with piezoelectric layers using layerwise finite element model. Mech Adv Mater Struct. 2009;16(8):561-75.
  58. Zhong Z, Yu T. Vibration of a simply supported functionally graded piezoelectric rectangular plate. Smart Mater Struct. 2006;15:1404-12.
  59. Duan WH, Quek ST, Wang Q. Free vibration analysis of piezoelectric coupled thin and thick annular plate. J Sound Vib. 2005;281(1-2):119-39.
  60. Zhang XR, Zhong Z. Three-dimensional exact solution for free vibration of functionally gradient piezoelectric circular plate. Chin Q Mech. 2005;26:81-6.
  61. Chen WQ, Ding HJ. On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mech. 2002;153:207-16.
  62. Aref M, Sajjad R, Ansari S, Sadrabadi, Xiongqi P, Sichen Y, Jandro L. Three-dimensional thermoelastic analysis of a functionally graded truncated conical shell with piezoelectric layers. Int J Comput Mater Sci Eng. 2022;12(03).
  63. Ebrahimi Z. Free vibration and stability analysis of a functionally graded cylindrical shell embedded in piezoelectric layers conveying fluid flow. J Vib Control. 2022;29:2515-27.
  64. Wang X, Liu J, Hu B, Li Z, Zhang B. Wave propagation in porous functionally graded piezoelectric nanoshells resting on a viscoelastic foundation. Phys E Low Dimens Syst Nanostruct. 2023;151:115615.
  65. Xue Y, Jin G, Zhang C, Han X, Chen J. Free vibration analysis of functionally graded porous cylindrical panels and shells with porosity distributions along the thickness and length directions. Thin-Walled Struct. 2023;184:110448.
  66. Lyu Z, Liu W, Liu C, Zhang Y, Fang M. Thermo-electro-mechanical vibration and buckling analysis of a functionally graded piezoelectric porous cylindrical microshell. J Mech Sci Technol. 2021;35:4655-72.
  67. Zhang SQ, Huang ZT, Zhao YF, Ying SS, Ma SY. Static and dynamic analyses of FGPM cylindrical shells with quadratic thermal gradient distribution. Compos Struct. 2021;277:114658.
  68. Susheel C. Shape and vibration control of spherical shell using functionally graded piezoelectric materials. In: Advances in Engineering Design: Select Proceedings of ICOIED 2020. Singapore: Springer Singapore; 2021. p. 61-73.
  69. Pengpeng S, Jun X, Shuai H. Static response of functionally graded piezoelectric-piezomagnetic hollow cylinder/spherical shells with axial/spherical symmetry. J Mech Sci Technol. 2021;35:1583-96.
  70. Parhizkar YM, Ghannad M. Electro-elastic analysis of functionally graded piezoelectric variable thickness cylindrical shells using a first-order electric potential theory and perturbation technique. J Intell Mater Syst Struct. 2020;31(17):2044-68..
  71. Sadeghzadeh S, Mahinzare M. Free vibration analysis of a spinning smart piezoelectrically actuated heterogeneous nanoscale shell with nonlocal strain gradient theory. J Nano Res. 2020;64:1-9.
  72. Wang YQ, Liu YF, Zu JW. Analytical treatment of nonlocal vibration of multilayer functionally graded piezoelectric nanoscale shells incorporating thermal and electrical effect. Eur Phys J Plus. 2019;134:1-5.
  73. Zhang X, Li Z, Yu J, Zhang B. Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells. Adv Mech Eng. 2019;4:1687814019836878.
  74. Liu YF, Wang YQ. Thermo electro-mechanical vibrations of porous functionally graded piezoelectric nano shells. Nanomaterials. 2019;9(2):301.
  75. Wang YQ, Liu YF, Yang TH. Nonlinear thermo-electro-mechanical vibration of functionally graded piezoelectric nano shells on Winkler–Pasternak foundations via nonlocal Donnell’s nonlinear shell theory. Int J Struct Stab Dyn. 2019;19(09):1950100.
  76. Mehralian F, Beni YT. Vibration analysis of size-dependent bimorph functionally graded piezoelectric cylindrical shell based on nonlocal strain gradient theory. J Braz Soc Mech Sci Eng. 2018;40:1-5.
  77. Fang XQ, Zhu CS, Liu JX, Liu XL. Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures. Phys B Condens Matter. 2018;529:41-56.
  78. Parashar SK, Gahlaut A. On free vibration analysis of FGPM cylindrical shell excited under d15 effect. In: Advances in Materials: Proceedings of the International Conference on “Physics and Mechanics of New Materials and Their Applications”, PHENMA 2017. Springer International Publishing; 2018. p. 331-52.
  79. Dai HL, Luo WF, Dai T, Luo WF. Exact solution of thermoelectroelastic behavior of a fluid-filled FGPM cylindrical thin-shell. Compos Struct. 2017;162:411-23.
  80. Razavi H, Babadi AF, Tadi Beni Y. Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory. Compos Struct. 2017;160(9):1299–1309.
  81. Hong LD, Wei LF, Ting D. Exact solution of thermoelectro-elastic behavior of a fluid-filled FGPM cylindrical thin shell. Compos Struct. 2017;162(16):411-423.
  82. Razavi H, Faramarzi BA, Tadi BY. Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory. Compos Struct. 2016; [Epub ahead of print].
  83. Dai HL, Qi YN, Luo WF. Investigation on electrothermoelastic behavior of FGPM cylindrical shells. Int J Nonlinear Sci Numer Simul. 2016;17(1):55-64.
  84. Dai HL, Luo WF, Dai T. Multi-field coupling static bending of a finite length inhomogeneous double-layered structure with inner hollow cylinder and outer shell. Appl Math Modell. 2016;40(11-12):6006-25.
  85. Ghorbanpour A, Abdollahian M, Khoddami ZM. Thermoelastic analysis of a non-axisymmetrically heated FGPM hollow cylinder under multi-physical fields. Int J Mech Mater Des. 2014; [Epub ahead of print].
  86. Jafari AA, Khalili SMR, Tavakolian M. Nonlinear vibration of functionally graded cylindrical shells embedded with a piezoelectric layer. Thin Wall Struct. 2014;79:8–15.
  87. Dai HL, Jiang HJ. Forced vibration analysis for a FGPM cylindrical shell. Shock Vib. 2013;20(3):531-50.
  88. Ke LL, Wang YS, Reddy JN. Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions. Compos Struct. 2014;116:626–636.
  89. Hong-Liang D, Hao-Jie J. Forced vibration analysis for a FGPM cylindrical shell. Shock Vib. 2013;20(3):531–550.
  90. Javanbakht M, Daneshmehr AR, Shakeri M, Nateghi A. The dynamic analysis of the functionally graded piezoelectric (FGP) shell panel based on three-dimensional elasticity theory. Appl Math Modell. 2012;36(11):5320-33.
  91. Xie H, Dai HL, Guo ZY. Dynamic response of a FGPM hollow cylinder under the coupling of multi-fields. Appl Math Comput. 2012;218(21):10492–10499.
  92. Alibeigloo A, Nouri V. Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method. Compos Struct. 2010;92:1775–1785.
  93. Sheng GG, Wang X. Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells. Appl Math Modell. 2010;34(9):2630-43.
  94. Li XF, Peng XL, Lee KY. Radially polarized functionally graded piezoelectric hollow cylinders as sensors and actuators. Eur J Mech A-Solids. 2011;29:704-713.
  95. Li XF, Peng XL, Lee KY. The static response of functionally graded radially polarized piezoelectric spherical shells as sensors and actuators. Smart Mater Struct. 2010;19(3):035010.
  96. Wu P, Tsai YH. Cylindrical bending vibration of functionally graded piezoelectric shells using the method of perturbation. J Eng Math. 2009;63(1):95–119.
  97. Wu C, Liu K. A state space approach for the analysis of doubly curved functionally graded elastic and piezoelectric shells. CMC-TECH SCI PRESS. 2007;6(3):177.
  98. Wang HM, Ding HJ. Spherically symmetric transient responses of functionally graded magneto-electro-elastic hollow sphere. Struct Eng Mech. 2006;25(6):525-542.
Special Issue Subscription Original Research
Volume 13
Special Issue 01
Received 02/08/2024
Accepted 09/09/2024
Published 16/10/2024
64