On the dynamics of nano-frames

TL;DR

This paper develops a finite-element based methodology to analyze the size-dependent dynamic behavior of nano-frames using stress-driven nonlocal elasticity, enabling accurate prediction of vibrations in nano-engineered structures.

Contribution

It introduces a closed-form dynamic stiffness matrix for nonlocal beams and applies it to small-size frames, advancing nano-structure vibration analysis.

Findings

Accurate natural frequencies for nano-frames computed.

Method applicable to carbon nanotube networks.

Efficient finite-element assembly for complex nano-structures.

Abstract

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.