The nonlocal strain gradient theory, when combined with the first-order shear deformation theory, provides many capabilities in size-dependent structures. The aim of the present study is evaluation of the free vibration behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes in hygrothermal environments considering slip boundary condition based on Knudsen number. These two adjacent nanotubes are coupled in the context of linear deformation through van der Waals interaction according to Lennard–Jones potential function. Actually, the contribution of the present work, compared with those previously reported, is investigating the simultaneous effect of hygrothermal loading and slip boundary condition on the dynamic behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes. As an additional step to achieve a more accurate model of low-scale structures, both hardening and softening effects of materials are taken as important variables in the nonlocal strain gradient approach. To derive the motion equations and associated boundary conditions, Hamilton’s variational principle is used. The equations are then solved with the aid of differential quadrature method. Numerical studies are also performed to depict the effects of a number of parameters such as boundary conditions, size scale, aspect ratio, inter-tube distance, and temperature alteration on the variations of dimensionless eigenfrequency and critical flow velocity.

当与一阶剪切变形理论结合使用时，非局部应变梯度理论在尺寸依赖的结构中提供了许多功能。本研究的目的是在湿滑环境中考虑滑移边界条件，基于Knudsen数评估两个垂直排列的流体输送单壁氮化硼纳米管在振动条件下的自由振动行为。根据Lennard-Jones势函数，这两个相邻的纳米管在线性变形的环境中通过范德华相互作用进行耦合。实际上，与以前的报道相比，本工作的贡献是研究湿热负荷和滑移边界条件对两个垂直排列的流体输送单壁氮化硼纳米管动态行为的同时影响。作为获得更精确的低尺度结构模型的附加步骤，在非局部应变梯度方法中，材料的硬化和软化效果均被视为重要变量。为了导出运动方程式和相关的边界条件，使用了汉密尔顿的变分原理。然后借助微分求积法求解方程。还进行了数值研究，以描述诸如边界条件，尺寸比例，纵横比，管间距离和温度变化等许多参数对无量纲本征频率和临界流速变化的影响。为了导出运动方程式和相关的边界条件，使用了汉密尔顿的变分原理。然后借助微分求积法求解方程。还进行了数值研究，以描述诸如边界条件，尺寸比例，纵横比，管间距离和温度变化等许多参数对无量纲本征频率和临界流速变化的影响。为了导出运动方程式和相关的边界条件，使用了汉密尔顿的变分原理。然后借助微分求积法求解方程。还进行了数值研究，以描述诸如边界条件，尺寸比例，纵横比，管间距离和温度变化等许多参数对无量纲本征频率和临界流速变化的影响。