Vibration Analysis of Nano-Beam with Consideration of Surface Effects and Damage Effects

Fan, Yin; Chen, Chang Ping; Chen, De Liang

doi:10.1515/nleng-2014-0027

Cited by 2 publications

(1 citation statement)

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“…In the Gurtin-Murdoch surface elasticity theory, the surface elastic layer is assumed to be a zero-thickness membrane perfectly bonded to its wrapped bulk material. Due to the good compromise between model accuracy and simplicity, several structural-mechanics models have been armed with the ability to account for the size dependency using the Gurtin-Murdoch surface elasticity theory [11,36,38,[57][58][59][60][61][62]. As a result, the present work adopts the Gurtin-Murdoch surface elasticity theory to represent the size dependency induced by the surface-energy effect.…”

Section: Introductionmentioning

confidence: 99%

Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems

et al. 2022

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This study presents a newly developed size-dependent beam-substrate medium model for bending, buckling, and free-vibration analyses of nanobeams resting on elastic substrate media. The Euler-Bernoulli beam theory describes the beam-section kinematics and the Winkler-foundation model represents interaction between the beam and its underlying substrate medium. The reformulated strain-gradient elasticity theory possessing three non-classical material constants is employed to address the beam-bulk material small-scale effect. The first and second constants is associated with the strain-gradient and couple-stress effects, respectively while the third constant is related to the velocity-gradient effect. The Gurtin-Murdoch surface elasticity theory is adopted to account for the surface-free energy. To obtain the system governing equation as well as corresponding boundary conditions, Hamilton’s principle is called for. Three numerical simulations are presented to characterize the influences of the material small-scale effect, the surface-energy effect, and the surrounding substrate medium on bending, buckling, and free vibration responses of nanobeam-substrate medium systems. The first simulation focuses on the bending response and shows the ability of the proposed model to eliminate the paradoxical characteristic inherent to nanobeam models proposed in the literature. The second and third simulations perform the sensitivity investigation of the system parameters on the buckling load and the natural frequency, respectively. All analytical results reveal that both material small-scale and surface-energy effects consistently stiffen the system response while the velocity-gradient effect weakens the system response. Furthermore, these sized-scale effects are more pronounced when the underlying substrate medium becomes softer.

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