On the dynamics of porous nanotubes with variable material properties and variable thickness

In the current work, free vibration of porous nanotubes is studied using Timoshenko beam model. The stiffness enhancement and stiffness reduction mechanisms of nanostructure systems are described by the nonlocal strain gradient theory. The thickness and material terms are varying along the length where an even distribution of porosity is considered using a modified power-law rule. The governing equations and boundary conditions are achieved via a virtual work of Hamilton's principle. The equations of motion are solved using the generalized differential quadrature method (G-DQM) and also the accuracy and convergency of the present methodology are studied. It shows that the dynamic characteristics of porous nanotubes are influenced by size effects, geometry, material composition, porosity, and various boundary conditions. Furthermore, for all boundary conditions except for the first mode in the case of nano-cantilever porous tubes, the rising of the nonlocal and strain gradient parameters lead to decreasing and increasing the natural frequencies, respectively. (C) 2019 Elsevier Ltd. All rights reserved.