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

Uğurcan Eroğlu; Giuseppe Ruta

doi:10.1007/s11012-022-01612-7

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 journal › Article › peer-review

2 Citations (Scopus)

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
Pages (from-to)	3033-3049
Number of pages	17
Journal	Meccanica
Volume	57
Issue number	12
DOIs	https://doi.org/10.1007/s11012-022-01612-7
Publication status	Published - Dec 2022
Externally published	Yes

Bibliographical note

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

Funding

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.

Funders	Funder number
Italian national research	PRIN 20177TTP3S-006
Ministero dell’Istruzione, dell’Università e della Ricerca
Sapienza Università di Roma	RM11916B7ECCFCBF, CUP B82F20001090001, RM12017294D1B7EF

Keywords

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

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10.1007/s11012-022-01612-7

Cite this

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title = "Approximate closed-form solutions for vibration of nano-beams of local/non-local mixture",

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{\textquoteright}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 {\textquoteleft}small{\textquoteright} 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.",

keywords = "Constitutive boundary conditions, Nano-beams, Natural vibration, Non-local elasticity, Perturbation methods",

author = "Uğurcan Eroğlu and Giuseppe Ruta",

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year = "2022",

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doi = "10.1007/s11012-022-01612-7",

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N2 - 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.

AB - 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.

KW - Constitutive boundary conditions

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KW - Natural vibration

KW - Non-local elasticity

KW - Perturbation methods

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ER -

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

Abstract

Bibliographical note

Funding

Keywords

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