Restricted accessResearch articleFirst published online 2025
Relationship between geometric features and vibration characteristics in functionally graded piezoelectric annular plates: An extended double Legendre polynomial method
The utilization of flexural, longitudinal, and torsional modes in functionally graded piezoelectric (FGP) annular plates depends on their geometric features. The investigation of the relationship between geometric features and vibrational characteristics offers valuable insights for optimal design. In this paper, the double Legendre polynomial method (DLPM) is extended for the first time to study the three-dimensional (3D) flexural vibration of FGP annular plates from two-dimensional (2D) axisymmetric vibration based on 3D elasticity theory. The validity of the proposed method is verified by literature results and finite element method (FEM) results. The influence of the relationship between the radial wall thickness and the height on the flexural, longitudinal and torsional vibrations of FGP annular plates is systematically revealed. The results provide comprehensive guidance for the design and application of FGP annular plates in domains requiring high precision, high stability, and high sensitivity.
AabidAParveezBRahemanMA, et al. (2021) A review of piezoelectric material-based structural control and health monitoring techniques for engineering structures: challenges and opportunities. Actuators10(5): 101.
2.
AlhaifiKKhorshidvandARAl-MasoudyMM, et al. (2023) A shooting method for buckling and post-buckling analyses of FGSP circular plates considering various patterns of pores’ placement. Structural Engineering & Mechanics85(3): 419–432.
3.
AmirSArshidEMaraghiZK (2020) Free vibration analysis of magneto-rheological smart annular three-layered plates subjected to magnetic field in viscoelastic medium. Smart Structures and Systems25(5): 581–592.
4.
ArshidEAmirSLoghmanA (2023a) On the vibrations of FG GNPs-RPN annular plates with piezoelectric/metallic coatings on Kerr elastic substrate considering size dependency and surface stress effects. Acta Mechanica234(9): 4035–4076.
5.
ArshidEAmirSLoghmanA (2023b) Thermoelastic vibration characteristics of asymmetric annular porous reinforced with nano-fillers microplates embedded in an elastic medium: CNTs Vs. GNPs. Archives of Civil and Mechanical Engineering23(2): 100.
6.
ArshidEAmirSLoghmanA (2024a) Aero-hygro-thermoelastic size-dependent analysis of NCMF-reinforced GNPs sector microplates located between piezoelectric patches in supersonic flow considering surface stress effects. Mechanics Based Design of Structures and Machines52(9): 6911–6972.
7.
ArshidEAmirSLoghmanA, et al. (2024b) Aerodynamic stability and free vibration of FGP-reinforced nano-fillers annular sector microplates exposed to supersonic flow. Thin-Walled Structures197: 111610.
8.
ArshidEAzimiMMoradiM, et al. (2024c) Mathematical solution for vibrational response of shear and normal deformable advanced metal foam CMBs treated with nanocomposite actuators. International Journal of Structural Stability and Dynamics2550118. DOI: 10.1142/S0219455425501184.
9.
ArshidEMaraghiZKCivalekÖ (2025) Variable-thickness higher-order sandwich beams with FG cellular core and CNT-RC patches: vibrational analysis in thermal environment. Archive of Applied Mechanics95(1): 2–24.
10.
BabaeiHZavariSKavehA, et al. (2024) Dynamic response of advanced lightweight porous plates integrated with nanocomposite face sheets resting on elastic substrate. International Journal of Structural Stability and Dynamics2550132. DOI: 10.1142/S0219455425501329.
11.
BelardinelliPSouzaSNFDVerlindenE, et al. (2020) Second flexural and torsional modes of vibration in suspended microfluidic resonator for liquid density measurements. Journal of Micromechanics and Microengineering30(5): 055003.
12.
BirmanVByrdLW (2007) Modeling and analysis of functionally graded materials and structures. American Society of Mechanical Engineers60(05): 195–216.
13.
CaoLZhuYXuY, et al. (2021) Elastic bound state in the continuum with perfect mode conversion. Journal of the Mechanics and Physics of Solids154: 104502.
14.
DattaSHunsingerBJ (1978) Analysis of surface waves using orthogonal functions. Journal of Applied Physics49(2): 475–479.
15.
FeriMKrommerMAlibeiglooA (2021) Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers. Mechanics Based Design of Structures and Machines51(7): 3843–3867.
16.
GhemariZBelkhiriSSaadS (2023) Improvement of the relative sensitivity for obtaining a high performance piezoelectric sensor. IEEE Instrumentation and Measurement Magazine26(4): 49–56.
17.
GiviSGhorbanpour AraniAKhoddami MaraghiZ, et al. (2024) Free vibration and supersonic flutter analyses of a sandwich cylindrical shell with CNT-reinforced honeycomb core integrated with piezoelectric layers. Mechanics Based Design of Structures and Machines1–29. DOI: 10.1080/15397734.2024.2422413.
18.
GuruNKJainSK (2020) Free axisymmetric vibrations of composite annular sandwich plates by higher-order theory using Chebyshev collocation technique. Thin-Walled Structures155: 106823.
19.
HeshmatiMJalaliSK (2019) Effect of radially graded porosity on the free vibration behavior of circular and annular sandwich plates. European Journal of Mechanics - A: Solids74: 417–430.
20.
HuanQChenMLiF (2019) A practical omni-directional SH wave transducer for structural health monitoring based on two thickness-poled piezoelectric half-rings. Ultrasonics94: 342–349.
21.
HuangC-HMaC-CLinY-C (2005) Theoretical, numerical, and experimental investigation on resonant vibrations of piezoceramic annular disks. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control52(8): 1204–1216.
22.
HuangC-HLiC-CWuY-C, et al. (2021) Theoretical analysis of transverse and planar vibrations for the piezoceramic disk based on mindlin plate theory. Applied Mathematical Modelling97: 568–587.
23.
JianYHuGTangL, et al. (2023) Analytical and experimental study of a metamaterial beam with grading piezoelectric transducers for vibration attenuation band widening. Engineering Structures275: 115091.
24.
KavehABabaeiHZavariS, et al. (2024) Vibrational response of a sandwich microplate considering the impact of flexoelectricity and based on a novel porous-FGM formulation. Mechanics Based Design of Structures and Machines52: 9122–9143.
25.
KhalfiHNaciriIRaghibR, et al. (2023) Axisymmetric free vibration modeling of a functionally graded piezoelectric resonator by a double Legendre polynomial method. Acta Mechanica235(2): 615–631.
26.
Khoddami MaraghiZArshidE (2024) On the vibrational behavior of variable thickness FG porous beams with graphene-reinforced nanocomposite facesheets. Acta Mechanica235: 5161–5185.
27.
Khoddami MaraghiZAmirSArshidE (2024) On the natural frequencies of smart circular plates with magnetorheological fluid core embedded between magnetostrictive patches on Kerr elastic substance. Mechanics Based Design of Structures and Machines52(3): 1651–1668.
28.
LiuC-FChenT-JChenY-J (2008) A modified axisymmetric finite element for the 3-D vibration analysis of piezoelectric laminated circular and annular plates. Journal of Sound and Vibration309(3–5): 794–804.
29.
LiuWSunHZhaoQ (2021) Free vibration and transmission response analysis for torsional vibration of circular annular plate. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering45(3): 631–638.
30.
LiuCYuJZhangB, et al. (2024) Size parameter calibration of nonlocal strain gradient theory based on molecular dynamics simulation of guided wave propagation in aluminum plates. Thin-Walled Structures198: 111659.
31.
MousaviSBAmirSJafariA, et al. (2021) Analytical solution for analyzing initial curvature effect on vibrational behavior of PM beams integrated with FGP layers based on trigonometric theories. Advances in nano research10(3): 235–251.
32.
PalSDasD (2020) Free vibration behavior of rotating bidirectional functionally-graded micro-disk for flexural and torsional modes in thermal environment. International Journal of Mechanical Sciences179: 105635.
33.
PandaSHajraSMistewiczK, et al. (2022) Piezoelectric energy harvesting systems for biomedical applications. Nano Energy100: 107514.
34.
PiaoCYangXKweunJM, et al. (2020) Ultrasonic flow measurement using a high-efficiency longitudinal-to-shear wave mode-converting meta-slab wedge. Sensors and Actuators A: Physical310: 112080.
35.
Rasooli JaziFAmirSArshidE (2024) Vibration analysis of asymmetric sandwich rotating FG porous discs coated with agglomerated nanocomposite facesheets. Archives of Civil and Mechanical Engineering24(4): 201.
36.
RoshanbakhshMZTavakkoliSMNavayi NeyaB (2020) Free vibration of functionally graded thick circular plates: an exact and three-dimensional solution. International Journal of Mechanical Sciences188: 105967.
37.
SezerNKoçM (2021) A comprehensive review on the state-of-the-art of piezoelectric energy harvesting. Nano Energy80: 105567.
38.
SharmaSKAhlawatN (2024) Free axisymmetric vibrations of functionally graded material annular plates via DTM. International Journal of Structural Stability and Dynamics24(3): 2450027.
39.
TuCYangM-HZhangZ-Q, et al. (2022) Highly sensitive temperature sensor based on coupled-beam AlN-on-Si MEMS resonators operating in out-of-plane flexural vibration modes. Research: Ideas for Today’s Investors2022: 9865926.
40.
WangXLiFZhangB, et al. (2021a) Wave propagation in thermoelastic inhomogeneous hollow cylinders by analytical integration orthogonal polynomial approach. Applied Mathematical Modelling99: 57–80.
41.
WangXLiFZhangX, et al. (2021b) Thermoelastic guided wave in fractional order functionally graded plates: an analytical integration legendre polynomial approach. Composite Structures256: 112997.
42.
WangSChenCHuL, et al. (2022) Spherical piezoelectric transducers of functionally graded materials. Journal of the Acoustical Society of America152(1): 193–200.
43.
WangXYeTChengL, et al. (2023) Electro-mechanical vibro-acoustic characteristics of submerged functionally graded piezoelectric plates with general boundary conditions. Composite Structures322: 117411.
44.
YangYLiJ-AChenB, et al. (2023) Symmetric and asymmetric vibrations of rotating GPLRC annular plate. International Journal of Mechanical Sciences250: 108282.
45.
YangYLiuJLiJ-A, et al. (2024) Symmetric and asymmetric free vibrations of rotating eccentric annular plate. Journal of Sound and Vibration576: 118302.
46.
YaoYArshidE (2024) Effects of folding degree and mass fraction on the static and natural frequency characteristics of functionally graded graphene origami-enabled auxetic metamaterials annular plates. International Journal of Structural Stability and Dynamics2650128. DOI: 10.1142/S0219455426501282.
47.
YuJWangXZhangX, et al. (2022) An analytical integration legendre polynomial series approach for lamb waves in fractional order thermoelastic multilayered plates. Mathematical Methods in the Applied Sciences45(12): 7631–7651.
48.
ZafaraniMJafariBHAkinB (2021) Lateral and torsional vibration monitoring of multistack rotor induction motors. IEEE Transactions on Industrial Electronics68(4): 3494–3505.
49.
ZhangXShenSYuJ (2025) Dispersion characteristics of lamb wave in a multilayered magnetoelectroelastic plate with an imperfect interface. Journal of Intelligent Material Systems and Structures36: 1045389X241306779.
50.
ZhongRQinBWangQ, et al. (2021) Prediction of the in-plane vibration behavior of porous annular plate with porosity distributions in the thickness and radial directions. Mechanics of Advanced Materials and Structures29(25): 4206–4223.
51.
ZhouHMHanKLElmaimouniL, et al. (2023) Double Legendre polynomial quadrature-free method for axisymmetric vibration of functionally graded piezoelectric circular plates. Journal of Vibration and Control30(3–4): 598–615.
