Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid

Electro-thermo nonlinear vibration and instability of embedded double-walled Boron Nitride nanotubes (DWBNNTs) conveying viscose fluid is studied in this article based on nonlocal piezoelasticity theory and Euler–Bernoulli beam (EBB) model. Boron Nitride nanotube (BNNT) is surrounded by elastic medium which is simulated as Pasternak foundation. The van der Waals (vdW) forces between the inner and the outer DWBNNTs are taken into account based on the Lennard–Jones model. Using von Kármán geometric nonlinearity, Hamilton’s principle and considering charge equation for coupling of electrical and mechanical fields, the nonlinear higher order governing equations are derived. The differential quadrature method (DQM) is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency and critical fluid velocity of fluid-conveying DWBNNTs. Results indicated that the small scale parameter, elastic medium, temperature change and electric potential have significantly effect on the dimensionless natural frequency and critical fluid velocity. Furthermore, the effect of fluid viscosity on the vibration of DWBNNTs may be ignored.