Longitudinal vibrations of bi-directionally functionally graded microbars with deformable boundaries
Journal of the Brazilian Society of Mechanical Sciences and Engineering, cilt.48, sa.9, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 48 Sayı: 9
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s40430-026-06569-2
- Dergi Adı: Journal of the Brazilian Society of Mechanical Sciences and Engineering
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, INSPEC, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Bi-directionally functionally graded microbar, Deformable boundary conditions, Elastic foundation, Longitudinal vibration, Strain gradient theory
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
The present research focuses on the longitudinal vibration analysis of a microbar resting on an elastic foundation, incorporating deformable (spring-based) boundary conditions. The material is modeled as functionally graded in two spatial directions. The governing equation for the axial vibration of the microbar is derived using the Hamilton’s principle and the Aifantis strain gradient theory, which captures small-scale effects. Using the resulting governing and force boundary equations, an eigenvalue problem is constructed, and the roots of this problem yield the axial vibration frequencies. The main novelty of this study lies in the development of a unified and generalized formulation that simultaneously accounts for bi-directional grading, deformable boundary conditions, elastic foundation interaction, and strain gradient elasticity within a single eigenvalue framework. Unlike most existing studies, which often assume idealized boundary conditions, the proposed approach allows general boundary conditions to be modeled simply by adjusting spring parameters. The model is validated through comparisons and convergence studies, and the effects of material gradation, scale parameter, elastic foundation, geometric properties, and spring stiffness are thoroughly examined.