Approximate closed-form solutions for vibration of nano-beams of local/non-local mixture

Eroğlu U., Ruta G.

Meccanica, cilt.57, sa.12, ss.3033-3049, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 12
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s11012-022-01612-7
  • Dergi Adı: Meccanica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.3033-3049
  • Anahtar Kelimeler: Nano-beams, Non-local elasticity, Perturbation methods, Constitutive boundary conditions, Natural vibration
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

© 2022, Springer Nature B.V.This paper presents an approach to natural vibration of nano-beams by a linear elastic constitutive law based on a mixture of local and non-local contributions, the latter based on Eringen’s model. A perturbation in terms of an evolution parameter lets incremental field equations be derived; another perturbation in terms of the non-local volume fraction yields the variation of the natural angular frequencies and modes with the ‘small’ amount of non-locality. The latter perturbation does not need to comply with the so-called constitutive boundary conditions, the physical interpretation of which is still debated. The possibility to find closed-form solutions is highlighted following a thorough discussion on the compatibility conditions needed to solve the steps of the perturbation hierarchy; some paradigmatic examples are presented and duly commented.