Electro-Mechanical Nonlinear Vibration of Pasternak Coupled DWBNNTs Based on Nonlocal Piezoelasticity Theory by Euler-Bernoulli Beam Theory

Electro-mechanical nonlinear vibration of coupled double-walled Boron Nitride nanotubes (DWBNNTs) 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 in terms of other efficient parameters. The obtained results indicate that the small scale parameter, elastic medium and electric potential have significant effect on the dimensionless natural frequency.