Comprehensive dynamic analysis of Pasternak-supported FGM beams in the Laplace domain via the complementary functions method
Mechanics Based Design of Structures and Machines, cilt.54, sa.1, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 54 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1080/15397734.2026.2741920
- Dergi Adı: Mechanics Based Design of Structures and Machines
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, DIALNET, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO)
- Anahtar Kelimeler: Complementary functions method, FGM beams, forced vibration, free vibration, Laplace transformation, Pasternak Foundation
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
This research paper examines the dynamic response of FGM beams resting on Pasternak’s foundation. The minimum total energy principle based on the Timoshenko’s theory is used. The set of differential canonical equations for the problem at hand is obtained for the first time. The undamped and damped transient responses are examined. In the visco-elastic case, the Kelvin Damping model is employed. Stepped, impulsive, and periodic loads are applied to the beams for several damping ratios. The application of the complementary functions method (CFM), together with the Laplace transformation in the solution, is the second novelty of this research. The results demonstrate specific dynamic behaviors: increasing the length-to-height ratio increases natural frequencies, while higher material gradient indices (n) inversely reduce frequencies and increase vibration amplitudes. Additionally, the Winkler foundation parameter has a significantly greater influence on frequencies than the shear layer stiffness. Finally, applied periodic loads with periods close to the structure’s natural period successfully capture the beat phenomenon.