On the dynamics of nano-frames

Size-dependent dynamic responses of small-size frames are modelled by stress-driven nonlocal elasticity and assessed by a consistent finite-element methodology. Starting from uncoupled axial and bending differential equations, the exact dynamic stiffness matrix of a two-node stress-driven nonlocal b...

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Bibliographic Details
Published in:International journal of engineering science 2021-03, Vol.160, p.103433, Article 103433
Main Authors: Russillo, Andrea Francesco, Failla, Giuseppe, Alotta, Gioacchino, Marotti de Sciarra, Francesco, Barretta, Raffaele
Format: Article
Language:English
Subjects:
Algorithms
Carbon
Carbon nanotubes
Differential equations
Dynamic stiffness matrix
Finite element analysis
Finite element method
Free vibration
Free vibrations
Mathematical analysis
Matrix
Nano-engineered material networks
Nanoengineering
Nanotubes
Nonlocal elasticity
Nonlocal integral elasticity
Resonant frequencies
Stiffness matrix
Stress-driven model
Trusses
Wittrick–Williams algorithm
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Summary:Size-dependent dynamic responses of small-size frames are modelled by stress-driven nonlocal elasticity and assessed by a consistent finite-element methodology. Starting from uncoupled axial and bending differential equations, the exact dynamic stiffness matrix of a two-node stress-driven nonlocal beam element is evaluated in a closed form. The relevant global dynamic stiffness matrix of an arbitrarily-shaped small-size frame, where every member is made of a single element, is built by a standard finite-element assembly procedure. The Wittrick–Williams algorithm is applied to calculate natural frequencies and modes. The developed methodology, exploiting the one conceived for straight beams in [International Journal of Engineering Science 115, 14–27 (2017)], is suitable for investigating free vibrations of small-size systems of current applicative interest in Nano-Engineering, such as carbon nanotube networks and polymer-metal micro-trusses.
ISSN:0020-7225
1879-2197
DOI:10.1016/j.ijengsci.2020.103433