Numerical modeling of dynamic and parametric instabilities of single-walled carbon nanotubes conveying pulsating and viscous fluid

The dynamic and parametric instabilities of single-walled carbon nanotubes (CNTs) conveying pulsating and viscous fluid embedded in an elastic medium are modeled and numerically investigated. The partial differential equation of motion based on the nonlocal elasticity theory, Euler Bernoulli beam's model and fluid-tube interaction is given. Based on the differential quadrature method, complex eigenmodes and associated eigenfrequencies are investigated with respect to the flow velocity as well as to the other considered physical parameters. Multimodal formulation based on real and complex eigenmodes are presented in the frequency and time domains. Models are elaborated for dynamic instabilities such as divergence and flutter as well as for parametric instability behaviors. The influences of the nonlocal parameter, the fluid pulsation and viscosity, the viscoelastic CNT parameter and the thermal effects on the dynamic behaviors of the CNT-fluid system are analyzed. Instability boundaries and interaction between the dynamic and parametric instabilities are investigated.