Free vibration problem of fluid-conveying double-walled boron nitride nanotubes via nonlocal strain gradient theory in thermal environment

This article is a comprehensive investigation into the equations of the size-dependent free vibration of a special type of fluid-conveying nanotubes, i.e., double-walled boron nitride nanotubes, in a thermal environment. The motion equations are obtained through the use of nonlocal strain gradient theory for piezoelectric materials combined with the first-order shear deformation theory and Hamilton's principle. Lennard-Jones potential function imposes the coupling between the pair of nanotubes that are bound together via van der Waals forces. This study also considers softening and hardening effects to better understand important aspects of modeling. After setting proper boundary conditions, the differential quadrature method is exploited to solve the obtained equations. This numerical study allows us to evaluate the effects of many parameters that include delta-temperature, aspect ratio, size scale and boundary conditions on the nondimensional eigenfrequency of considered system and critical flow velocity.