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

Eroğlu U., Ruta G.

Meccanica, vol.57, no.12, pp.3033-3049, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 12
  • Publication Date: 2022
  • Doi Number: 10.1007/s11012-022-01612-7
  • Journal Name: Meccanica
  • Journal Indexes: 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
  • Page Numbers: pp.3033-3049
  • Keywords: Nano-beams, Non-local elasticity, Perturbation methods, Constitutive boundary conditions, Natural vibration
  • Istanbul Technical University Affiliated: No


© 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.