Nonlocal Transverse Vibration Analysis of Rotationally Restrained B-FG Nanobeams Under Axial Compression
Journal of Peridynamics and Nonlocal Modeling, cilt.8, sa.1, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 8 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s42102-026-00147-9
- Dergi Adı: Journal of Peridynamics and Nonlocal Modeling
- Derginin Tarandığı İndeksler: Scopus
- Anahtar Kelimeler: Axial compression, Bi-directional FGM, Nonlocal elasticity theory, Rotational springs, Transverse vibration
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
This study develops an analytical framework for examining the transverse vibration behavior of bi-directional functionally graded (B-FG) nanobeams, whose material characteristics vary through both the width and height of the cross-section. The nanobeam is modelled within the context of the nonlocal Euler–Bernoulli beam theory and is supported by simple supports at both ends, while also being constrained by rotational springs. Under the presence of an axial compressive force, the governing relations for the beam with spatially varying material properties and the corresponding nonlocal vibration equations are first formulated. Subsequently, an analytical solution strategy combining the Fourier sine series with Stokes’ transform is employed. Enforcing the force and moment boundary conditions leads to an eigenvalue system explicitly incorporating the rotational spring stiffnesses. Setting the determinant of the resulting characteristic equation equal to zero provides the natural frequencies, which are evaluated for varying material gradation parameters, spring stiffnesses, nonlocal effects, and axial load compression levels. The principal novelty of this work lies in presenting an analytical solution for B-FG nanobeams with deformable rotational end restraints under axial compression.