Application of the surface stress-driven nonlocal theory of elasticity for the study of the bending response of FG cracked nanobeams

Lovisi, Giuseppe

doi:10.1016/j.compstruct.2023.117549

Cited by 16 publications

(1 citation statement)

References 43 publications

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“…This model, well-posed mathematically, not only captures long-range interactions but also addresses surface effects. This new model has been recently used to investigate the free vibrations of functionally graded nanobeams [ 44 ], analyze static response in the presence of discontinuous loads [ 45 ], and investigate the effects of cracks in FG nanobeams [ 46 ].…”

Section: Introductionmentioning

confidence: 99%

Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams

Lovisi,

Feo,

Lambiase

et al. 2024

Nanomaterials

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This paper employs a surface stress-driven nonlocal theory to investigate the synergistic impact of long-range interaction and surface energy on higher vibration modes of Bernoulli–Euler nanobeams made of functionally graded material. It takes into account surface effects such as the surface modulus of elasticity, residual surface stresses, surface density, and rotary inertia. The governing equation is derived through the application of Hamilton’s principle. The novelty of this work lies in its pioneering approach to studying higher-order vibrations, carefully considering the combination of long-range interactions and surface energy in nanobeams of functionally graded materials through a well-posed mathematical model of nonlocal elasticity. This study conducts a parametric investigation, examining the effects of the nonlocal parameter and the material gradient index for four static schemes: Cantilever, Simply-Supported, Clamped-Pinned and Clamped-Clamped nanobeams. The outcomes are presented and discussed, highlighting the normalized nonlocal natural frequencies for the second through fifth modes of vibration in each case under study. In particular, this study illustrates the central role of surface effects in the dynamic response of nanobeams, emphasizing the importance of considering them. Furthermore, the parametric analysis reveals that the dynamic response is influenced by the combined effects of the nonlocal parameter, the material gradient index, the shapes of the cross-sections considered, as well as the static scheme analyzed.

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Section: Introductionmentioning

confidence: 99%

Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams

Lovisi,

Feo,

Lambiase

et al. 2024

Nanomaterials

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Size‐dependent buckling loads of non‐uniform Bernoulli–Euler beams with elastic boundary conditions and thermal effects based on two‐phase local/nonlocal elastic model

Xu,

Chen,

Zhang

2024

Z Angew Math Mech

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We present predictive models of the size‐dependent buckling loads of non‐uniform Bernoulli–Euler beams under thermal effects based on the two‐phase local/nonlocal elastic model. The beam ends are assumed to be constrained by elastic springs with translational and rotational stiffness to simulate general boundary conditions. In contrast to most literature in this field, both the bending and thermal deformations of the beams are simultaneously considered to be two‐phase local/nonlocal of two phases, that is, the thermal effect is taken as equivalent to a size‐dependent thermal load. By using the fully equivalent differential form of the local/nonlocal equation with a set of constitutive boundary conditions, the problem is solved numerically with the aid of the generalized differential quadrature method (GDQM). Through conducting validation study, several parametric studies are given for examining the effects of the slope of beams’ thickness variation, nonlocal parameter, and elastically supported conditions on the buckling loads of non‐uniform beams. The results show that constrained stiffness has a drastic influence on the critical bucking loads of the beams. Furthermore, the consideration of the two‐phase thermal load will further reduce the actual buckling load of the beams.

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Size-dependent free vibration analysis of multidirectional functionally graded nanobeams via a nonlocal strain gradient theory

Guerroudj,

Drai,

Daikh

et al. 2024

J Eng Math

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Application of the surface stress-driven nonlocal theory of elasticity for the study of the bending response of FG cracked nanobeams

Cited by 16 publications

References 43 publications

Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams

Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams

Size‐dependent buckling loads of non‐uniform Bernoulli–Euler beams with elastic boundary conditions and thermal effects based on two‐phase local/nonlocal elastic model

Size-dependent free vibration analysis of multidirectional functionally graded nanobeams via a nonlocal strain gradient theory

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