In this paper, 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 size-dependent free vibrations of small-size systems of current applicative interest in Nano-Engineering, such as carbon nanotube networks and polymer-metal micro-trusses.
@article{arxiv.2107.12728,
title = {On the dynamics of nano-frames},
author = {Andrea Francesco Russillo and Giuseppe Failla and Gioacchino Alotta and Francesco Marotti de Sciarra and Raffaele Barretta},
journal= {arXiv preprint arXiv:2107.12728},
year = {2021}
}