Perturbations for vibration of nano-beams of local/nonlocal mixture

Ugurcan Eroglu, Giuseppe Ruta

Araştırma sonucu: ???type-name???Konferans katkısıbilirkişi

Özet

Here we extend the perturbation approach, previously presented in the literature for Eringen’s two-phase local/nonlocal mixture model, to free vibration of purely flexible beams. In particular, we expand the eigenvalues and the eigenvectors into power series of the fraction coefficient of the non-local material response up to 2nd order. We show that the family of 0th order bending couples satisfy the natural and essential boundary conditions of the 1st order; hence, the 1st order solution can conveniently be constructed using the eigenspace of the 0th order with no necessity of additional conditions. We obtain the condition of solvability that provides the incremental eigenvalue in closed form. We further demonstrate that the 1st order increment of the eigenvalue is always negative, providing the well-known softening effect of long-range interactions among the material points of a continuum modelled with Eringen’s theory. We examine a simply supported beam as a benchmark problem and present the incremental eigenvalues in closed form.

Orijinal dilİngilizce
Ana bilgisayar yayını başlığıTheoretical and Applied Mechanics - Proceedings of the 25th AIMETA conference hosted by the Italian Association of Theoretical and Applied Mechanics in Palermo, AIMETA 2022
EditörlerMario Di Paola, Livan Fratini, Fabrizio Micari, Antonina Pirrotta
YayınlayanAssociation of American Publishers
Sayfalar619-624
Sayfa sayısı6
ISBN (Basılı)9781644902424
DOI'lar
Yayın durumuYayınlandı - 2023
Harici olarak yayınlandıEvet
Etkinlik25th Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2022 - Palermo, Italy
Süre: 4 Eyl 20228 Eyl 2022

Yayın serisi

AdıMaterials Research Proceedings
Hacim26
ISSN (Basılı)2474-3941
ISSN (Elektronik)2474-395X

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???event.eventtypes.event.conference???25th Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2022
Ülke/BölgeItaly
ŞehirPalermo
Periyot4/09/228/09/22

Bibliyografik not

Publisher Copyright:
© 2023, Association of American Publishers. All rights reserved.

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