Large elastic deflections of bars based on nonlocal elasticity

Güçlü, Gökhan; Artan, Reha

doi:10.1002/zamm.201900108

Cited by 8 publications

(2 citation statements)

References 28 publications

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“…Studies expressing a paradox in nonlocal elasticity were presented [22,23]. Various scientific articles related to investigations of various small-scaled elements/structures such as porous FG nanobeam [24], FG nanobeam/microbeam [25][26][27][28][29][30][31][32][33], microplate [34], nanoplate [35], nanobeam/microbeam [36][37][38], porous microplate [39], nanowire [40,41], nanotube [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] and other small-scaled elements/structures [61][62][63][64][65][66][67][68] can be found in open literature. Also, in addition to the above-mentioned studies, scholars presented the papers…”

Section: F I G U R E 1 Demonstration Of Bn Sheetmentioning

confidence: 99%

Finite element formulation for nano‐scaled beam elements

2021

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In the present study, size-dependent buckling and free vibration behaviors of single-walled boron nitride nanotube (SWBNNT) are performed in conjunction with various size-dependent elasticity theories. Modified couple stress theory (MCST) and Eringen's nonlocal elasticity theory are used for size-dependent models of SWBNNT. Also, the buckling loads and frequencies are obtained by using local theory to emphasize the effects and differences of these sizedependent theories. Consequently, three different elasticity theories (two nonclassical and one classical) are utilized to achieve the detailed buckling and vibration analyses of SWBNNT. In this study, the buckling loads and frequencies of SWBNNTs are obtained via presented finite element formulation. In the finite element procedures based on two different size-dependent elasticity theories, matrices containing the small size parameter are derived. With these matrices containing the small size parameters, eigenvalue problems for buckling and free vibration analyses are formed. The buckling loads and frequency values of the SWBNNTs under the size effect are obtained. The influences of the dimensionless nonlocal parameter, dimensionless material length scale parameter, lengthto-diameter ratio and boundary conditions on nanotube's buckling and vibration characteristics are investigated. In addition to these influences, the rotary inertia effect neglected in many other studies is also examined.

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Section: F I G U R E 1 Demonstration Of Bn Sheetmentioning

confidence: 99%

Finite element formulation for nano‐scaled beam elements

2021

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“…Longitudinal vibrations of conical and cylindrical rods have been presented by Fedeto et al [29] and Marais et al [30] based on the Rayleigh-Bishop theory. In addition to the nanorods [31][32][33], nanotubes [34][35][36][37][38][39][40], nanowires [41,42], functionally graded nanobeams/microbeams [43][44][45][46], nanobeams [47][48][49][50][51][52], microcolumns [53] and microbeams [54], which are the other one dimensional ultra-small structures, have been studied extensively with various non-classical elasticity theories which captured the small-scale effect.…”

Section: Introductionmentioning

confidence: 99%

Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions

2020

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In the present work, axial vibrational behavior of nanorods with different boundary conditions is researched. Bishop's rod theory is implemented to simulate the axial deflection. Size‐dependency is captured by using Eringen's nonlocal elasticity theory. Based on nonlocal deformable boundary conditions and Stokes’ transformation, a system of linear equations is derived and then constructed an Eigen value problem. Several numerical examples are presented to investigate the significance of various parameters such as geometric parameters, vibrational modes, various values of nonlocal parameter and axial spring parameters on the axial frequencies of nanorods. The numerical examples indicate that the deformable boundary conditions and small scale parameter have considerable effects on the axial vibration response.

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Nonlinear vibration and parametric excitation of magneto‐thermo elastic embedded nanobeam using homotopy perturbation technique

Selvamani,

Thangamuni,

Yaylacı

et al. 2024

Z Angew Math Mech

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The present study focuses on the modeling and analyzing the nonlinear vibration patterns and parametric excitation of embedded Euler–Bernoulli nanobeams subjected to thermo‐magneto‐mechanical loads. The Euler–Bernoulli nanobeam is developed with external parametric excitation. The governing equation of motion is derived by utilizing nonlocal continuum theory and nonlinear von Karman beam theory. Subsequently, the homotopy perturbation technique is employed to determine the vibration frequencies. Finally, the modulation equation of Euler–Bernoulli nanobeams is derived for simply supported boundary condition. In order to validate our findings, we conduct a comparative analysis against existing literature, thereby underscoring the effectiveness and robustness of our proposed methodology. The influence of stress, magnetic potential, temperature, damping coefficient, Winkler coefficient, and nonlocal parameters are tested numerically on nonlinear frequency‐amplitude and parametric excitation–amplitude responses. The numerical examples indicate the significant impact of physical variables on the nonlinear frequency and parametric excitation. The primary objective of this study is to investigate the effects of external physical variables on the dynamic behavior of nanobeams, particularly in nonlinear regimes. This study provides insights into the design and control of nanostructures under complex load conditions, contributing to developing advanced materials and nanosystems.

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Large elastic deflections of bars based on nonlocal elasticity

Cited by 8 publications

References 28 publications

Finite element formulation for nano‐scaled beam elements

Finite element formulation for nano‐scaled beam elements

Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions

Nonlinear vibration and parametric excitation of magneto‐thermo elastic embedded nanobeam using homotopy perturbation technique

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