Nonlinear vibration and stability analysis of a clamped-clamped nonlocal strain gradient fluid-conveying nanosensor subjected to a longitudinal magnetic field

Abstract In this study, the nonlinear vibration and stability analysis of fluid-conveying carbon nanotubes (CNTs) sensor subjected to a longitudinal magnetic field are studied. Firstly, in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli theory, the higher-order fluid–structure interaction (FSI) governing equation is first derived by employing the Hamilton principle. The higher order boundary conditions are then obtained using the weighted residual method. The differential transformation method (DTM) is next used to solve the six-order linear differential equation of motion, and the Galerkin method and variational iteration method are used to solve the six-order nonlinear problem. After that, dimensionless natural frequencies and the critical flow velocity—associated with divergence of nanosensor system are investigated with the rotary inertia terms, the nonlocal and strain gradient parameter, higher order boundary conditions as well as the longitudinal magnetic field. In addition, the nonlocal frequency shift percent (NFSP) and strain gradient frequency shift percent (SFSP) are further analyzed which are useful to design the fluid-conveying CNTs sensor. Finally, the influence of various fluids on critical flow velocities in nanosensors is investigated. The results provided in this work are expected to explain the experimentally-observed size-dependent phenomena in nanomechanics and to effectively design the fluid-conveying CNTs nanosensors.