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

^*Bu çalışma için yazışmadan sorumlu yazar

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

2 Atıf (Scopus)

Özet

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 dil	İngilizce
Sayfa (başlangıç-bitiş)	3033-3049
Sayfa sayısı	17
Dergi	Meccanica
Hacim	57
Basın numarası	12
DOI'lar	https://doi.org/10.1007/s11012-022-01612-7
Yayın durumu	Yayınlandı - Ara 2022
Harici olarak yayınlandı	Evet

Bibliyografik not

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

Finansman

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.

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

Belgeye Erişim

10.1007/s11012-022-01612-7

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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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",

note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature B.V.",

year = "2022",

month = dec,

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

language = "English",

volume = "57",

pages = "3033--3049",

journal = "Meccanica",

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T1 - Approximate closed-form solutions for vibration of nano-beams of local/non-local mixture

AU - Eroğlu, Uğurcan

AU - Ruta, Giuseppe

PY - 2022/12

Y1 - 2022/12

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

KW - Nano-beams

KW - Natural vibration

KW - Non-local elasticity

KW - Perturbation methods

UR - https://www.scopus.com/pages/publications/85142699132

U2 - 10.1007/s11012-022-01612-7

DO - 10.1007/s11012-022-01612-7

M3 - Article

AN - SCOPUS:85142699132

SN - 0025-6455

VL - 57

SP - 3033

EP - 3049

JO - Meccanica

JF - Meccanica

IS - 12

ER -

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

Özet

Bibliyografik not

Finansman

Belgeye Erişim

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