Nonlinear vibration of fluid conveying cantilever nanotube resting on visco-pasternak foundation using non-local strain gradient theory

Frequency analysis and forced vibration response of fluid conveying viscoelastic nanotubes that resting on nonlinear visco-pasternak foundation under magnetic field using size-dependent non-local strain gradient theory are considered in this study. It is supposed that the nanotube is modelled as cantilever type beam and subjected to a harmonic load. The material property of the nanotube is modelled by Kelvin-Voigt viscoelastic constitutive relation and slip boundary conditions of nanotube conveying fluid are taken into account. Extended Galerkin method is used to obtain the nonlinear differential equation of the motion and the multiple time-scales method is utilised to investigate the primary vibration resonance of the nanotube. Firstly, the frequency analysis is performed on the linear system and the effects of foundation coefficients on the natural frequency are investigated at several flow velocities. Moreover, the resonance properties of the system are solved in closed form and analysed from the frequency-response curves, and then the effects of the non-local parameter, length scale parameter and magnetic field are fully investigated. In this case, non-local parameter, length scale parameter and foundation coefficients are highly influential on the frequency response of the considered system.