Analytical solution of free vibration of viscoelastic perforated nanobeam

Eltaher, Mohamed A.; Shanab, Rabab A.; Mohamed, Norhan A.

doi:10.1007/s00419-022-02184-4

Cited by 15 publications

(1 citation statement)

References 76 publications

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“…In some experimental and theoretical research , it is shown that classical elastic theories cause many errors when they have been employed for nanosized structures. To tackle this situation, different higher-order elasticity theories such as doublet mechanics Mohamed 2020, Civalek et al 2021), couple stress (Fan et al 2020), strain gradient elasticity (Akgöz and Civalek 2011, Ansari et al 2016, Yin et al2022, Jiang et al 2022, Bagheri et al 2021, nonlocal strain gradient elasticity (Lim et al 2015, Zhou et al 2023, Xu et al 2022, Boyina et al 2022, Anh et al 2022, Norouzzadeh et al 2019, nonlocal elasticity (NE) (Vosoughi 2016, Vosoughi et al 2018, Eringen and Suhubi 1964, Eringen 1983, Eltaher et al 2023, Mohammed et al 2022, Kumar et al 2021, and modified couple stress theory (Mohtashami and Beni 2019, Asghari et al 2011, Kahrobaiyan et al 2014, Liu and Peng 2022, Zhao and He 2023, Raeisi Estabragh and Baradaran 2021, surface energy (Eltaher et al 2019, Xu andFan 2016), peridynamic model (Yang et al 2022) have been used to overcome small-size effects. Barati (2018) has studied the dynamic analysis of FG porous nanoshells with uneven and even distributions.…”

Section: Introductionmentioning

confidence: 99%

A combined method for the stability characteristics of FG a nanobeam embedded in an elastic matrix

Uzun,

Yaylı

2024

Preprint

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The investigation conducted in this work aims to investigate the stability response of functionally graded restrained nanobeams with four different porosity distributions and embedded in the Winkler foundation. To take into concern the size effects, Eringen's nonlocal elasticity is employed as a higher-order continuum theory. The material properties of the functionally graded porous nano-sized beam with deformable boundaries are changed gradually in spatial coordinates through the power-law model which covers four kinds of porosity distributions. A system of linear equations consists of infinite power series for an embedded functionally graded porous nanobeam under axial point loads obtained from Fourier trigonometric series and Stokes’ transformation is solved by an eigenvalue problem which satisfies rigid or deformable supporting conditions including classical boundary conditions such as simply supported, clamped-clamped and clamped-pinned. Analytical results are obtained for various porosity distributions and boundary conditions to reveal the effects of nonlocality, Winkler foundation and power-law index on the lateral buckling behavior of a functionally graded nanoscale nanobeam.

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Section: Introductionmentioning

confidence: 99%

A combined method for the stability characteristics of FG a nanobeam embedded in an elastic matrix

Uzun,

Yaylı

2024

Preprint

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Mechanics of size-dependent materials

2022

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Elastic medium and torsional spring effects on the nonlocal dynamic of functionally graded porous nanotubes

Uzun,

Yaylı,

Civalek

2024

Arch Appl Mech

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In this study, Eringen’s nonlocal elasticity theory that applies the small size effects in functionally graded porous nanotubes embedded in an elastic matrix is discussed. The material properties of functionally graded porous nanotubes are taken into account to vary over the radius direction with a rule of mixture. The free torsional vibration relation according to nonlocal elasticity theory, via Hamilton’s principle, is obtained and an eigenvalue solution is constructed for the free torsional vibration response of the presented work. The presented analytical model is validated by comparing the calculated mathematical results for homogeneous nanotubes with rigid and non-rigid boundary conditions. Special attention is given to deformable boundary conditions, porosity coefficient, material grading coefficient and also to the influence of elastic medium on the free torsional vibration frequencies. In this paper, it has been proven that the influence of length, elastic medium, elastic torsional spring rigidities, material grading and porosity coefficients on the vary in the torsional vibration frequency of the functionally graded nanotube is not small.

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Analytical solution of free vibration of viscoelastic perforated nanobeam

Cited by 15 publications

References 76 publications

A combined method for the stability characteristics of FG a nanobeam embedded in an elastic matrix

A combined method for the stability characteristics of FG a nanobeam embedded in an elastic matrix

Mechanics of size-dependent materials

Elastic medium and torsional spring effects on the nonlocal dynamic of functionally graded porous nanotubes

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