Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

Ansari, R.; Gholami, R.; Norouzzadeh, A.; Darabi, Mohammad Ali

doi:10.1007/s10409-015-0435-4

Cited by 51 publications

(19 citation statements)

References 51 publications

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“…By substituting Eqs. (8)(9)(10)(11) into Eq. (1), the strain energy owing to both the variations of the classical and higher order stresses with respect to the initial configuration can be obtained as…”

Section: Derivation Of Governing Equations and Boundary Conditionsmentioning

confidence: 99%

“…Some experiments have demonstrably approved the size-dependent mechanical behaviors in microbeams [4][5][6][7] and have shown that size-dependency is an inherent property that gets important when the thickness of A C C E P T E D M A N U S C R I P T 3 beam is comparable to the internal material length scale parameter. Therefore, a variety of examinations have been performed on the estimation of mechanical characteristics of small-scale structures based upon the non-classical continuum mechanics theories [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Ansari

Gholami

Shojaei

et al. 2016

Applied Mathematical Modelling

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1 Highlights  Development of a nonlinear first-order shear deformable small-scale beam model  Presenting formulation based on the most general Mindlin's strain gradient theory  Prediction of coupled free vibration of post-buckled micro-and nano-beams with various BCS  Study of the effects of ⁄ , ⁄ , and BCs on the postbuckling path and frequency  Comparing the results predicted by CT, MCST and MSGT Abstract Presented herein is a comprehensive study on the size-dependent coupled longitudinal-transverserotational free vibration behavior of post-buckled functionally graded (FG) micro-and nano-beams based on the most general Mindlin's strain gradient theory. The current model enables us to incorporate size effects via introducing material length scale parameters and is developed in the framework of the firstorder shear deformable beam model and the von Karman geometric nonlinearity. The FG micro-and nano-beams, whose volume fraction is expressed by using a power law function, are assumed to be made of a mixture of metals and ceramics. By using Hamilton's principle, the nonlinear governing equations and associated boundary conditions are derived for FG micro-and nano-beams in the postbuckling domain. Afterwards, the governing equations and boundary conditions are discretized using the generalized differential quadrature (GDQ) method in conjunction with a direct approach without linearization, before solving numerically by Newton's method. The effects of length scale parameter, length-to-thickness ratio, material gradient index and boundary conditions on the postbuckling path and frequency of FG micro-and nano-beams are carefully investigated. Finally, numerical results obtained from both the modified strain gradient theory (MSGT) and modified couple stress theory (MCST) are compared.Mindlin's strain gradient elasticity; Size-dependent first-order shear deformable beam model.

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Section: Derivation Of Governing Equations and Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Ansari

Gholami

Shojaei

et al. 2016

Applied Mathematical Modelling

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“…Reza and Shahrokh [40] investigated the impacts of surface density on the nonlinear vibration of Timoshenko and Euler-Bernoulli nanobeams. Ansari et al [41] carried out an investigation of the surface effect on the vibration characteristics and instability of fluid-conveying nanoscale pipes. They summarised that surface modulus and surface residual stress have great impacts on the frequencies.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in fluid‐conveying nanotubes under multi‐physical fields based on non‐local higher‐order strain gradient model

Pang

Wang

Zhang

2019

Micro & Nano Letters

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This work studies the wave propagation in embedded single-walled carbon nanotubes (CNTs) conveying fluid and placed in multi-physical fields based on the non-local higher-order strain gradient model with surface effect considered. The nanotubes are modelled as Timoshenko beams. Utilising Hamilton's principle, the governing equations of wave motion in CNTs are derived. The solution for the phase velocity of wave motion is obtained, which can not only consider the stiffness softening effect but also reflect the stiffness enhancement effect of scale parameter observed by experiments. The numerical simulations are conducted to compare the results on the basis of different order non-local strain gradient models. It is shown that the behaviours of wave propagation based on the non-local higher-order strain gradient models are quite different from those based on the classical continuum model. In addition, the scale and surface effects and influences of various external factors including inner flow, surrounding medium, temperature field, and magnetic field on the wave dispersion are investigated.

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“…Employing the micropolar theory, Ansari et al 6 reported the free vibration behavior of microscale beams and plates considering a three dimensional formulation. Based on Timoshenko beam theory (TBT) and Gurtin-Murdoch continuum elasticity, Ansari et al 7 presented the vibration and instability characteristics of fluid-conveying nanoscale pipes. Based on HSDT and non-linear finite element method (FEM), non-linear free vibration behavior of laminated composite shells were investigated under uniform thermal loading 8,9 and also considering hygrothermal environment.…”

Section: Introductionmentioning

confidence: 99%

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Paul¹,

Das

2018

The Journal of Strain Analysis for Engineering Design

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Geometrically non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam under harmonic excitation and supported on three-parameter non-linear elastic foundation is presented. The beam is immovably clamped and is considered to be under static thermal loading due to uniform temperature rise. Reddy's third-order shear-deformable beam theory in conjunction with von Kármán geometric non-linearity is considered to derive the governing equations employing Hamilton's principle, and Ritz method is followed for approximating the displacement and rotation fields. A numerical algorithm based on iterative substitution method and Broyden's method is proposed to predict the stable regions of frequency-response behavior. The frequency-response curves are presented in normalized plane for variations of load-amplitude, elastic foundation parameters, temperature rise, gradation index and functionally graded material composition, and their effects are discussed in detail. It is found that the load-amplitude, elastic foundation parameters, thermal loading and some of the functionally graded material compositions significantly affect the frequency response; whereas, the effect of gradation index is found to be relatively small. A comparative frequency-response curve between Voigt model and Mori-Tanaka scheme of functionally graded material modeling is presented, and it shows negligible difference between these two models. The present problem under thermal environment is studied for the first time through this work, and the proposed model and the numerical algorithm provide a simplified approach to study the non-linear frequency-response behavior.

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Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

Cited by 51 publications

References 51 publications

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Wave propagation in fluid‐conveying nanotubes under multi‐physical fields based on non‐local higher‐order strain gradient model

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

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