OICC Press Journal of Solid Mechanics 2008-7683 13 2 2021 06 30 Size-Dependent Vibration Problem of Two Vertically-Aligned Single-Walled Boron Nitride Nanotubes Conveying Fluid in Thermal Environment Via Nonlocal Strain Gradient Shell Model 164 185 EN P Roodgar Saffari Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran M Fakhraie Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran M. A Roudbari School of Engineering, RMIT University, PO Box 71, Bundoora, VIC, 3083, Australia Journal Article 2021 06 30 The free vibration behavior of two fluid-conveying vertically-aligned single-walled boron nitride nanotubes are studied in the present paper via the nonlocal strain gradient piezoelectric theory in conjunction with the first-order shear deformation shell assumption in thermal environments. It is supposed that the two adjacent boron nitride nanotubes are coupled with each other in the context of linear deformation by van der Waals interaction according to Lennard–Jones potential function. To achieve a more accurate modeling for low-scale structures, both hardening and softening effects of materials are considered in the nonlocal strain gradient approach. Themotion equations and associated boundary conditions are derived by means of Hamilton’s variational principle, then solved utilizing differential quadrature method. Numerical studies are done to reveal the effect of different boundary conditions, size scale parameters, aspect ratio, inter-tube distance, and temperature change on the variations of dimensionless eigenfrequency and critical flow velocity.