Nonlocal theoretical approaches and atomistic simulations for longitudinal free vibration of nanorods/nanotubes and verification of different nonlocal models

Li, Cheng; Li, Shuang; Yao, Lin‐Quan; Zhu, Zhongkui

doi:10.1016/j.apm.2015.01.013

Cited by 67 publications

(30 citation statements)

References 39 publications

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“…In the literature, nonlocal elasticity proposed by Eringen [23], Modified Couple stress Theory (MCT) of Yang et al [24] and Modified Strain gradient Theory (MST) of Lam et al [25] are widely used to investigate the behaviour of micro/nano structures. Recent studies on the developments and applications of nonlocal theory to nanobeams and nanopaltes could be found in the works of Li et al [26][27][28][29], Nguyen et al [30], and Phung-Van et al [31]. Based on the MCT, numerous studies have been also carried out to investigate the behaviour of micro beams and plates [32][33][34][35][35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Thai

et al. 2017

Engineering Structures

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The present study uses the isogeometric analysis (IGA) to investigate the post-buckling behavior of functionally graded (FG) microplates subjected to mechanical and thermal loads. The modified a strain gradient theory with three length scale parameters is used to capture the size effect. The Reddy third-order shear deformation plate theory with the von Kámán nonlinearity (i.e., small strains and moderate rotations) is employed to describe the kinematics of the microplates. Material variations in the thickness direction of the plate are described using a rule of mixtures. In addition, material properties are assumed to be either temperature-dependent or temperature-independent. The governing equations are derived using the principle of virtual work, which are then discretized using the IGA approach, whereby a C 2-continuity requirement is fulfilled naturally and efficiently. To trace the post-buckling paths, Newton's iterative technique is utilized. Various parametric studies are conducted to examine the influences of material variations, size effects, thickness ratios, and boundary conditions on the post-buckling behavior of microplates.

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Section: Introductionmentioning

confidence: 99%

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Thai

et al. 2017

Engineering Structures

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“…45into Eqs. (43) and (44), the nondimensional characteristic equations of axially moving functionally graded Timoshenko microbeams can be discretized using the differential quadrature method as…”

Section: Solution Methodologymentioning

confidence: 99%

Free vibration and wave propagation of axially moving functionally graded Timoshenko microbeams

Yao

Shen

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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The transverse free vibration and wave propagation of functionally graded microbeams with an axial motion are investigated based on a nonlocal theory and the Timoshenko beam model. It is assumed the material properties of functionally graded microbeams vary along the thickness direction. The neutral plane of functionally graded materials is introduced, and the inhomogeneity of functionally graded Timoshenko microbeams is considered. The governing equations are derived using Hamilton's principle, and the differential quadrature method is utilized to determine the first three-order natural frequencies of the microbeams with simply supported and clamped boundary conditions, respectively. The effects of gradient index, nonlocal parameter and axial velocity on natural frequencies are investigated. Moreover, the wave propagation characteristics of functionally graded Timoshenko microbeams are analyzed, and the significant influences of wave number and other variables on wave propagation frequencies and wave velocities are studied. The different influence patterns of nonlocal effect are observed in transverse vibration and wave propagation. The nonlocality shows a weakening phenomenon in transverse vibration of axially moving functionally graded Timoshenko microbeams, while it reveals both weakening and strengthening phenomena in wave propagation. Therefore, two kinds of existing nonlocal scale effects are further confirmed and this is an additional contribution of the present paper.

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“…However, the capability of the nonlocal continuum theory for predicting the size-dependent stiffness may exist some limited problems [51,52]. For example, the stiffness enhancement phenomenon noticed from experimental observation and as well as the modified couple stress theories [53] can not be predicted well by considering the nonlocal elastic model [54][55][56][57][58]. Furthermore, It has been reported [51,59,60] that some non-standard boundary conditions are expected to be added in the higher-order elasticity models.…”

Section: Introductionmentioning

confidence: 91%

Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory

Ling

2015

Composite Structures

227

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Nonlocal theoretical approaches and atomistic simulations for longitudinal free vibration of nanorods/nanotubes and verification of different nonlocal models

Cited by 67 publications

References 39 publications

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Free vibration and wave propagation of axially moving functionally graded Timoshenko microbeams

Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory

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