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A new method for free vibration analysis of nanobeams: Introduction of equivalent lattice stiffness method

Firouz Abadi, R. D ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ssc.2018.10.003
  3. Publisher: Elsevier Ltd , 2019
  4. Abstract:
  5. Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in accordance with lattice dynamics with tunable precision and is more simpler than continuum theories. Since the discrete phenomena in micro/nanostructures can be incorporated into the continuum formulation using this method, it can be competitive with other analytical methods like molecular mechanics approach. Moreover, this study can bridge the gap between the continuum theories and atomic models since it is capable to remedy the ongoing challenge on the accurate values of characteristic length scale parameters. To conform the accuracy of the current study, the dispersion curves of different theories are indicated and compared with lattice dynamics. Then, the longitudinal and transverse vibration of nanobeams subjected to different boundary conditions is investigated using equivalent lattice stiffness method. © 2018
  6. Keywords:
  7. Characteristic length scale parameter ; Dispersion curve ; Lattice dynamics ; Continuum mechanics ; Dispersion (waves) ; Dispersions ; Lattice vibrations ; Nanowires ; Stiffness ; Vibration analysis ; Characteristic length ; Different boundary condition ; Dispersion curves ; Equivalent lattice stiffness method ; Free-vibration analysis ; Longitudinal and transverse vibrations ; Non-classical continuum theories ; Taylor series expansions ; Lattice theory
  8. Source: Solid State Communications ; Volume 287 , 2019 , Pages 35-42 ; 00381098 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S003810981830468X