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

Uğurcan Eroğlu*, Giuseppe Ruta

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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.

Orijinal dilİngilizce
Sayfa (başlangıç-bitiş)3033-3049
Sayfa sayısı17
Basın numarası12
Yayın durumuYayınlandı - Ara 2022
Harici olarak yayınlandıEvet

Bibliyografik not

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


This work was initiated when U. Eroglu was Visiting Professor at the Dipartimento d’ingegneria strutturale e geotecnica of the University of Rome “La Sapienza”, the support of which under the grant ‘Professore visitatore 2020’ CUP B82F20001090001 is gratefully acknowledged. G. Ruta acknowledges the financial support of the institutional grants RM11916B7ECCFCBF and RM12017294D1B7EF of the University “La Sapienza”, Rome, Italy, and of the Italian national research grant PRIN 20177TTP3S-006 from Italian Ministry of University and Research.

FinansörlerFinansör numarası
Italian national researchPRIN 20177TTP3S-006
Ministero dell’Istruzione, dell’Università e della Ricerca
Sapienza Università di RomaRM11916B7ECCFCBF, CUP B82F20001090001, RM12017294D1B7EF

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