Identification of general added mass distribution in nanorods from two-spectra finite data

Dilena, Michele; Dell’Oste, M. Fedele; Fernández-Sáez, J.; Morassi, Antonino; Zaera, R.

doi:10.1016/j.ymssp.2019.106286

Cited by 6 publications

(2 citation statements)

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“…Remarkable features of CNTs, however, cannot be precisely realized applying the classical approach of the elasticity theory. A great attention is, accordingly, devoted in the recent literature to the generalized elasticity theories, such as nonlocal elasticity approach [6][7][8][9][10][11][12][13][14][15][16], strain gradient theory [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], and unified elasticity frameworks [32][33][34][35][36][37][38][39][40][41][42][43][44], for nanoscopic study of the field quantities.…”

Section: Introductionmentioning

confidence: 99%

Modified couple stress flexure mechanics of nanobeams

Sedighi¹,

Abouelregal²,

Faghidian³

2021

Phys. Scr.

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In view of numerous contributions accessible in the literature associated with the modified couple stress theory, its deficiency in precise description of the material response of continua with nanostructural features is investigated. The flexure mechanics of nano-scale beams in the framework of the modified couple stress theory is reassessed applying a consistent variational scheme. The physically motivated constitutive laws of the stress resultant fields, flexural moment and shear force, associated with the modified couple stress beam are introduced. The well-established differential conditions of equilibrium equipped with the proper mathematical form of the higher-order boundary conditions are reinstated. The exact analytical solutions of the kinematic fields of the nano-sized beam are derived by direct solving of the governing coupled differential equations. The flexure response of the modified couple stress beam is numerically illustrated wherein the effects of the symmetric rotation gradients along with the transverse shear deformation are examined. Closed-form analytical formulae of the elastic modulus of Carbon Nanotubes are detected and thoroughly discussed. Serious suspicions on the applicability of the modified couple stress beam model in accurately capturing the size-effects in nano-materials are emerged as evinced by rigorous examination of the elastic modulus of CNTs.

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Section: Introductionmentioning

confidence: 99%

Modified couple stress flexure mechanics of nanobeams

Sedighi¹,

Abouelregal²,

Faghidian³

2021

Phys. Scr.

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“…Thai et al [4] recently published relevant examples of the application of this theory to the analysis of the mechanical behaviour of nanostructures. Moreover, it is worth to cite the works by Morassi and coworkers [5][6][7][8][9] to address problems related with nanosensors. Other widely used approaches to address the mechanical behaviour of nanomechanical systems fall into the nonlocal continuum mechanics framework.…”

Section: Introductionmentioning

confidence: 99%

Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity

2020

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Zaera et al. (Int J Eng Sci 138:65-81, 2019) recently showed that the nonlocal strain gradient theory (NSGT) is not consistent when it is applied to finite solids, since all boundary conditions associated to the corresponding problems cannot be simultaneously satisfied. Given the large number of works using the NSGT being currently published in the field of generalized continuum mechanics, it is pertinent to evince the shortcomings of the application of this theory. Some authors solved the problem omitting the constitutive boundary conditions. In the current paper we show that, in this case, the equilibrium fields are not compatible with the constitutive equation of the material. Other authors solved it omitting the nonstandard boundary conditions. Here we show that, in this case, the solution does not fulfil conservation of energy. In conclusion, the inconsistency of the NSGT is corroborated, and its application must be prevented in the analysis of the mechanical behaviour of nanostructures.

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