An analytical–numerical framework for vibration and pull-in analysis of auxetic sandwich microplates with FG PZT/Ag facesheets

Abstract

This paper presents a design-oriented analytical–numerical framework for vibration and electrostatic pull-in of a three-layer microplate with a re-entrant auxetic core and functionally graded (FG) PZT/Ag facesheets (PZT: lead zirconate titanate; Ag: silver). Piezoelectric coupling is not considered; the facesheets are modeled only through graded elastic properties. The aim is to provide a compact and validated workflow for predicting both resonance and pull-in of auxetic-core FG sandwich microplates under simply supported boundaries. A harmonic (series-compliance) shear-transfer correction is incorporated at the laminate level, and the transverse dynamics are solved using a Mindlin–Navier series solution. The framework is verified against an in-house Mindlin plate FEM and cross-validated using ABAQUS composite-shell simulations. Pull-in is assessed using a Mindlin-consistent single-mode ROM based on static condensation and numerical projection of the electrostatic pressure, yielding $V_{P I} \approx 118.16 V$ for a $d = 0.52 μ m$ gap. Size effects are examined via MCST through the normalized parameter $l_{0} / h$ , reported as a sensitivity to the assumed (or calibrated) length scale.

Keywords

auxetic core functionally graded facesheets sandwich microplate pull-in instability modified couple-stress theory MEMS

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References

Attia

Mohamed

(2017) Nonlinear modeling and analysis of electrically actuated viscoelastic microbeams based on the modified couple stress theory. Applied Mathematical Modelling 41: 195–222. https://doi.org/10.1016/j.apm.2016.08.036

Barati

Shahverdi

(2019) Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams. Journal of the Brazilian Society of Mechanical Sciences and Engineering 42: 33. https://doi.org/10.1007/s40430-019-2118-8

Batra

Porfiri

Spinello

(2007) Review of modeling electrostatically actuated microelectromechanical systems. Smart Materials and Structures 16(6): R23–R31. https://doi.org/10.1088/0964-1726/16/6/r01

Benaoum

Khelil

Baltach

, et al. (2025) The behavior of beams reinforced with patches under three-point bending: an experimental investigation. Polymers 17: 2993. https://doi.org/10.3390/polym17222993

Carrera

Brischetto

(2008) A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Applied Mechanics Reviews 62(1): 010803. https://doi.org/10.1115/1.3013824

Cook

(2001) Concepts and Applications of Finite Element Analysis. Wiley.

Farokhi

Ghayesh

(2018) Nonlinear mechanics of electrically actuated microplates. International Journal of Engineering Science 123: 197–213. https://doi.org/10.1016/j.ijengsci.2017.08.017

Gibson

Ashby

(1997) Cellular Solids: Structure and Properties. Cambridge University Press.

Gurkan

Burak

(2025) Assessment of seismic fragility of reinforced concrete buildings retrofitted with steel bracing elements: a numerical study. Structural Engineering & Mechanics: International Journal 96(2): 117–129.

10.

Habib

Ghezail

Zagane

MES

, et al. (2025) Numerical analysis of three-point bending of sandwich panels with different core cross-sections: finite element study. Advances in nano research: 481–488.

11.

Ilbak

Ghorbanpour Arani

Khoddami Maraghi

, et al. (2025) Aeroelastic analysis of composite sandwich rectangular plates with auxetic honeycomb core: free vibration and instability investigation. Arabian Journal for Science and Engineering 50(17): 14255–14276. https://doi.org/10.1007/s13369-024-09742-8

12.

Lezgy-Nazargah

Yaylacı

Shad

(2025) Double superposition shear deformation theory for buckling analysis of layered composite circular closed cylindrical shells in underwater environments. Ocean Engineering 340: 122230. https://doi.org/10.1016/j.oceaneng.2025.122230

13.

Mahboubi Nasrekani

(2025) A closed-form solution for dynamic analysis of auxetic sandwich cylindrical structures with FG face sheets under moving pressure. Mechanics Based Design of Structures and Machines 53(10): 6789–6807. https://doi.org/10.1080/15397734.2025.2490808

14.

Mahboubi Nasrekani

Eipakchi

(2025a) FG layers' effect on nonlinear free vibrations of sandwich auxetic cylinders. European Journal of Mechanics - A: Solids 114: 105784. https://doi.org/10.1016/j.euromechsol.2025.105784

15.

Mahboubi Nasrekani

Eipakchi

(2025b) Geometrically nonlinear free vibration analysis of axially loaded super-light auxetic beams reinforced by functionally graded face sheets. Journal of Vibration Engineering & Technologies 13(1): 102. https://doi.org/10.1007/s42417-024-01680-x

16.

Najar

Choura

El-Borgi

, et al. (2005) Modeling and design of variable-geometry electrostatic microactuators. Journal of Micromechanics and Microengineering 15(3): 419–429. https://doi.org/10.1088/0960-1317/15/3/001

17.

Nasrekani

(2025) An analytical model for nonlinear static and buckling analysis of sandwich auxetic cylinders with functionally graded face sheets under combined axial and radial loading. Acta Mechanica Solida Sinica 39: 666–680. https://doi.org/10.1007/s10338-025-00646-0

18.

Nasrekani

Eipakchi

(2026) Moderately large amplitude forced vibration of sandwich functionally graded auxetic beams: an analytical approach. Applied Mathematics and Mechanics 47(1): 99–114. https://doi.org/10.1007/s10483-026-3340-7

19.

Novak

Vesenjak

Ren

(2016) Auxetic cellular materials - a review. Strojniški vestnik – Journal of Mechanical Engineering 62: 485–493. https://doi.org/10.5545/sv-jme.2016.3656

20.

Öner

Oktay

Uzun

, et al. (2025) Tri-method analysis of contact mechanics in orthotropic-isotropic materials. Archive of Applied Mechanics 95(5): 116. https://doi.org/10.1007/s00419-025-02832-5

21.

Reddy

(2000) Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering 47(1-3): 663–684. https://doi.org/10.1002/(sici)1097-0207(20000110/30)47:1/3<663::aid-nme787>3.0.co;2-8

22.

Reddy

(2004) Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. Boca Raton London New York Washington, D.C: CRC Press.

23.

Sekban

Aktarer

Ozdemir

, et al. (2025) Investigation of the effect of changes in material values of FSPed Al5754 on contact mechanics. Adv. Nano Res 19(2): 117–127.

24.

Selvamani

Prabhakaran

Yaylacı

, et al. (2025) Doublet structural modeling of nonhomogeneous euler mass sensor nanobeams using boundary characteristics bernstein polynomials. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 105(3): e202401264. https://doi.org/10.1002/zamm.202401264

25.

Semih Mahmut

Tevfik

Dursun

, et al. (2025) Analysis of the changes in microstructure, mechanical, and contact properties of multi-pass friction stir processed DP800 steel. Advances in nano research: 253–264.

26.

Terzi

Öner

Uzun Yaylacı

, et al. (2026) A multi-perspective exploration of contact behavior in orthotropic layer resting on isotropic half-plane. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 50(1): 253–269. https://doi.org/10.1007/s40997-025-00933-8

27.

Thai

H-T

Nguyen

T-K

, et al. (2017) A review of continuum mechanics models for size-dependent analysis of beams and plates. Composite Structures 177: 196–219. https://doi.org/10.1016/j.compstruct.2017.06.040

28.

Yaylacı

Yazıcıoğlu

Yaylacı

, et al. (2025) Evaluation of the contact problem of two layers one of functionally graded, loaded by circular rigid block and resting on a pasternak foundation by analytical and numerical (FEM and MLP) methods. Archive of Applied Mechanics 95(4): 78. https://doi.org/10.1007/s00419-025-02787-7

29.

Yazıcıoğlu

Yaylacı

Sekban

, et al. (2025) Analysis of the contact problem functionally graded layer placed on a pasternak foundation. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 105(8): e70152. https://doi.org/10.1002/zamm.70152

30.

Zenkour

(2018) A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities. Composite Structures 201: 38–48. https://doi.org/10.1016/j.compstruct.2018.05.147

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