A continuum viscoelastic model of Timoshenko NSGT nanobeams

Developed and solved in this article, for the first time, is a coupled continuum viscoelastic model for Timoshenko nonlocal strain gradient theory (NSGT)-based nanobeams; this is performed using a finite difference analysis (FDA). The viscosity of infinitesimal elements of the Timoshenko NSGT nanobeams is incorporated via the Kelvin-Voigt scheme (as a two-parameter rheological scheme) for both the transverse/longitudinal/rotational motions. The NSGT for the normal/shear stress fields is used for ultrasmall size influences on the continuum model. Rotary inertia is automatically present due to the Timoshenko-type rotation. The viscosity in the Timoshenko NSGT nanobeam is responsible for energy dissipation formulated via negative work. Hamilton's balance scheme is utilised and resulted in the coupled continuum viscoelastic dynamic model for Timoshenko NSGT nanobeams, which is solved via a FDA for nonlinear mechanics. A nonlinear bending test is conducted via development of a finite element method model in the absence of the NSGT.

Automated summary

In this article, a coupled continuum viscoelastic model for Timoshenko nonlocal strain gradient theory-based nanobeams is developed and solved using a finite difference analysis. The model incorporates the viscosity of the nanobeams and considers the ultrasmall size influences and rotary inertia. The energy dissipation is formulated via negative work and the coupled continuum viscoelastic dynamic model is solved using a finite difference analysis for nonlinear mechanics.