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 language | English |
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Pages (from-to) | 3033-3049 |
Number of pages | 17 |
Journal | Meccanica |
Volume | 57 |
Issue number | 12 |
DOIs | |
Publication status | Published - Dec 2022 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, Springer Nature B.V.
Keywords
- Constitutive boundary conditions
- Nano-beams
- Natural vibration
- Non-local elasticity
- Perturbation methods