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.

On the dynamics of nano-frames

Failla G.;Alotta G.;
2021-01-01

Abstract

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.
2021
Carbon nanotubes
Dynamic stiffness matrix
Free vibrations
Nano-engineered material networks
Nonlocal integral elasticity
Stress-driven model
Wittrick–Williams algorithm
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/114224
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