Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories

Based on nonlocal piezoelasticity theory, dynamic stability of double-walled boron nitride nanotubes (DWBNNTs) conveying viscose fluid is studied by incorporating Euler-Bernoulli beam theory, Timoshenko beam theory, and cylindrical shell theory. The surface stress effects are considered based on Gurtin-Murdoch continuum theory. The DWBNNT is embedded in visco-Pasternak medium and the nonlinear van der Waals forces between the inner and outer surface of the DWBNNT is taken into account. Using von Karman geometric nonlinearity, the governing equations are derived based on Hamilton's principle. In order to obtain the dynamic instability region of DWBNNT, incremental harmonic balance method is applied. The detailed parametric study is conducted, focusing on the combined effects of the nonlocality, surface stress, fluid velocity, and surrounding medium on the dynamic instability region of DWBNNT. Furthermore, dynamic instability region of Euler-Bernoulli beam theory, Timoshenko beam theory, and cylindrical shell theory are compared to each other. Numerical results indicate that neglecting the surface stress effects, the difference between dynamic instability region of three theories becomes remarkable.