Analysis of Nano-Scale Effects on the Vibration of Functionally Graded Plates Using a Higher-Order Shear Deformation Theory
| Authors | B. Rebai1 , L. Touam1, E. Benaddi1, T. Messas1 , B. Mamen1 , B. Litouche2 |
| Affiliations |
1University Abbes Laghrour, Civil Engineering Department, 40000 Khenchela, Algeria 2University Center Abdelhafid Boussouf, Mechanic and ElectroMechanic Department, 43000 Mila, Algeria |
| Е-mail | billel.rebai@univ-khenchela.dz |
| Issue | Volume 18, Year 2026, Number 5 |
| Dates | Received 15 April 2026; revised manuscript received 22 October 2026; published online 28 October 2026 |
| Citation | B. Rebai, L. Touam, et al., J. Nano- Electron. Phys. 18 No 5, 05008 (2026) |
| DOI | https://doi.org/10.21272/jnep.18(5).05008 |
| PACS Number(s) | 77.84. – s, 77.84.Lf, 78.66.Sq |
| Keywords | Functionally graded materials (FGM), Nano-scale elasticity theory, Higher-order shear deformation theory (HSDT), Free vibration, Scale effect, Power-law index, Layering scheme. |
| Annotation |
This paper presents a comprehensive investigation into the free vibration behavior of functionally graded sandwich (FGSW) nanoplates, accounting for small-scale effects via Eringen's nonlocal elasticity theory. A novel inverse hyperbolic shear deformation theory (IHSDT) is developed to accurately model shear deformation and rotary inertia without requiring shear correction factors. The material properties of the plate's face sheets are graded through the thickness according to a power-law distribution, while the core can be homogeneous or graded, defined by various layering schemes. The governing equations are derived using Hamilton's principle and solved analytically for simply supported boundary conditions using the Navier solution technique. A detailed parametric study quantifies the influence of the power-law index (p), the nonlocal parameter (μ), and the material layering scheme on the non-dimensional fundamental frequencies. Results demonstrate that increasing the nonlocal parameter consistently reduces the fundamental frequency due to a stiffness-softening effect. Crucially, the optimal layering scheme for maximizing frequency depends on the scale; symmetric sandwich configurations outperform pure functionally graded material (FGM) plates at the nanoscale. This study provides critical insights and benchmark data for the design and optimization of FGSW structures in micro- and nano-electromechanical systems (MEMS/NEMS). |
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