Bending Analysis of A Cantilever Nanobeam With End Forces By Laplace Transform

Yaylı, Mustafa Özgür; Kandemir, Süheyla Yerel

doi:10.24107/ijeas.314635

Cited by 4 publications

(5 citation statements)

References 26 publications

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“…An eigenvalue problem is defined in the equation given in (33). Eigenvalues can easily be found if the equation is set to "0" by adjusting the determinant of the coefficient matrix in Eq.…”

Section: Defined Boundariesmentioning

confidence: 99%

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An EIGENVALUE SOLUTION OF FUNCTIONALLY GRADED NANOBEAM with an ATTACHED SPRING MASS SYSTEM

KÜPELİ

ÇAVUŞ

Uzun³

et al. 2021

Uludağ University Journal of the Faculty of Engineering

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Nanobeams are now widely used in numerous vibration frequency research. In this study, an eigenvalue problem has used to determine the vibration frequency analysis of the buckyball and spring attached to the end of the nanobeam. The vibration frequencies of the system may be discovered using a single (2x2) matrix in this eigenvalue problem. A mathematical method for analyzing sensors has attached to nanobeams is presented in this paper. The results, which is obtained in this study, has showed a result that has compatible with the flicker frequency studies conducted in the literature, and the results have presented in tables and graphics.

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“…An eigenvalue problem is defined in the equation given in (33). Eigenvalues can easily be found if the equation is set to "0" by adjusting the determinant of the coefficient matrix in Eq.…”

Section: Defined Boundariesmentioning

confidence: 99%

“…Eigenvalues can easily be found if the equation is set to "0" by adjusting the determinant of the coefficient matrix in Eq. (33).…”

Section: Defined Boundariesmentioning

confidence: 99%

An EIGENVALUE SOLUTION OF FUNCTIONALLY GRADED NANOBEAM with an ATTACHED SPRING MASS SYSTEM

KÜPELİ

ÇAVUŞ

Uzun³

et al. 2021

Uludağ University Journal of the Faculty of Engineering

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“…The geometric fitness condition, equilibrium equations and constitutive relations of the FG nano beam in the two-dimensional plane are as follows [40,41] 𝑑𝑤 𝑑𝑥 = 𝜑…”

Section: Theory and Formulationsmentioning

confidence: 99%

Bending Analysis of Functionally Graded Nanobeam Using Chebyshev Pseudospectral Method

ŞENYER

CAN

Keles

2021

International Journal of Engineering and Applied Sciences

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Static performance of functionally graded cantilever nanobeams exposed to lateral and axial loads from the end was examined by applying the Pseudospectral Chebyshev Method. A solution is given for bending analysis using Euler-Bernoulli beam theory. The nonlocal elasticity theory was first introduced by Eringen and is used to represent effect on a small scale. Using the aforementioned theory, the governing differential equations the phenomenon for functionally graded nanobeams are reproduced. It is supposed that the modulus of elasticity of the beam changes exponentially in the x-axis direction, except for the values taken as constant. The exponential change of material properties may not allow analytical problems to be solved with known methods. Therefore, numerical approach is inevitable for the solution of the problem.

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“…burada H, Heaviside fonksiyonunu belirtmektedir. Bölgesel veya noktasal yayılı yük, kuvvet veya moment gibi etkilerin tanımlanmasında Heaviside ve Dirac Delta fonksiyonları (Civalek vd., 2009) ve Laplace dönüşümleri (Yaylı, 2017) kullanılmaktadır. Statik analizlerde uygulamaları bulunmakla birlikte dinamik modellemelerde kullanımları yaygın değildir (Eftekhari ve Young, 2014;Eftekhari, 2016).…”

Section: Nano-kirişinunclassified

Kismi̇ Yayili Yük Etki̇si̇ndeki̇ Nano Ki̇ri̇şleri̇n Di̇nami̇k Anali̇zi̇

Arda

2020

Mühendislik Bilimleri Ve Tasarım Dergisi

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Kısmi yayılı yük etkisindeki karbon nanotüp kirişlerin dinamik analizi gerçekleştirilmiştir. Nano kiriş için hareketin yönetici denklemi ve sınır şartları Eringen'in Yerel Olmayan Elastisite Teorisi kullanılarak elde edilmiştir. Kısmi yayılı yük etkisi Heaviside fonksiyonu ile modellenmiştir. Oluşturulan model, nano kirişin parçalara bölünmesiyle elde edilen model sonuçlarıyla karşılaştırılarak doğrulanmıştır. Nano kiriş titreşim frekansının yerel olmayan parametre, boyutsuz yayılı yük, yükün başlangıç noktası gibi parametrelerle değişimi incelenmiştir. Farklı titreşim frekanslarında çeşitli parametrelerin nano kirişin genlik değerlerine olan etkisi gösterilmiştir. Nano kirişin parçalara ayrılmasıyla artan süreklilik şartı sayısının oluşturduğu yüksek boyutlu matrislerin çözümüne alternatif olarak oluşturulan modelde dört sınır şartıyla çözüme ulaşılmıştır. Bu çalışmanın sonuçları bakteri veya virüs gibi nano kütle sensörlerinin modellenmesinde kullanılabilir.

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Bending Analysis of A Cantilever Nanobeam With End Forces By Laplace Transform

Abstract: In this study, the static behavior of nanobeams subjected to end concentrated loads is theoretically investigated in the

Cited by 4 publications

References 26 publications

An EIGENVALUE SOLUTION OF FUNCTIONALLY GRADED NANOBEAM with an ATTACHED SPRING MASS SYSTEM

An EIGENVALUE SOLUTION OF FUNCTIONALLY GRADED NANOBEAM with an ATTACHED SPRING MASS SYSTEM

Bending Analysis of Functionally Graded Nanobeam Using Chebyshev Pseudospectral Method

Kismi̇ Yayili Yük Etki̇si̇ndeki̇ Nano Ki̇ri̇şleri̇n Di̇nami̇k Anali̇zi̇

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