Nonlinear wave propagation analysis in Timoshenko nano-beams considering nonlocal and strain gradient effects

Abstract

This article is aimed to investigate the geometrically nonlinear wave propagation of nano-beams on the basis of the most comprehensive size-dependent elasticity theory. To this end, the integral model of nonlocal elasticity theory in the most general form without any simplification in conjunction with the modified strain gradient theory is implemented in the analysis. Also, the Timoshenko beam model is utilized in the presented nonlocal strain gradient elasticity theory. By Hamilton’s principle, the governing integro-partial differential equations of motion are derived. Employing numerical integration and an efficient method called as periodic grid technique, a semi-analytical approach is presented for the solution procedure. To detect the impacts of nonlocality and small scale effects on the nonlinear wave propagation characteristics of beams at nanoscale, adequate numerical examples and comparison studies are presented.