On the dynamics of nano-frames

Size-dependent dynamic responses of small-size frames are modelled by stress-driven non-local 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. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

Size-dependent dynamic responses of small-size frames are modeled and evaluated using stress-driven non-local elasticity and a consistent finite-element methodology. The exact dynamic stiffness matrix is evaluated for a two-node stress-driven nonlocal beam element, and a global dynamic stiffness matrix for an arbitrarily-shaped small-size frame is built using standard finite-element assembly procedures. The methodology is suitable for investigating free vibrations of small-size systems in Nano-Engineering.