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

Uğurcan Eroğlu*, Giuseppe Ruta

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)3033-3049
Number of pages17
JournalMeccanica
Volume57
Issue number12
DOIs
Publication statusPublished - Dec 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, Springer Nature B.V.

Keywords

  • Constitutive boundary conditions
  • Nano-beams
  • Natural vibration
  • Non-local elasticity
  • Perturbation methods

Fingerprint

Dive into the research topics of 'Approximate closed-form solutions for vibration of nano-beams of local/non-local mixture'. Together they form a unique fingerprint.

Cite this