Journal
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
Volume 20, Issue 3, Pages 539-552Publisher
UNIV NIS
DOI: 10.22190/FUME220703035F
Keywords
Stationary variational principle; Nanobeam; Free vibrations; Wave dispersion; Stress gradient elasticity; Strain gradient theory
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The dynamic characteristics of elastic nanobeams are rigorously analyzed using the mixture unified gradient theory of elasticity, with closed-form solutions and numerical evaluations. The study shows that the established elasticity model effectively describes the softening and stiffening responses of nanobeams, providing a practical approach to tackle dynamics of nano-structures.
The mixture unified gradient theory of elasticity is invoked for the rigorous analysis of the dynamic characteristics of elastic nanobeams. A consistent variational framework is established and the boundary-value problem of dynamic equilibrium enriched with proper form of the extra non-standard boundary conditions is detected. As a well-established privilege of the stationary variational theorems, the constitutive laws of the resultant fields cast as differential relations. The wave dispersion response of elastic nano-sized beams is analytically addressed and the closed form solution of the phase velocity is determined. The free vibrations of the mixture unified gradient elastic beam is, furthermore, analytically studied. The dynamic characteristics of elastic nanobeams is numerically evaluated, graphically illustrated, and commented upon. The efficacy of the established augmented elasticity theory in realizing the softening and stiffening responses of nano-sized beams is evinced. New numerical benchmark is detected for dynamic analysis of elastic nanobeams. The established mixture unified gradient elasticity model provides a practical approach to tackle dynamics of nano-structures in pioneering MEMS/NEMS.
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