Bifurcations of Nonlinear Longitudinal-Flexural Oscillations of Cantilevered Single Walled Carbon Nanotube Conveying Fluid

Accounting nonlinear elasticity, the nonlinear self-sustained vibrations of the single walled carbon nanotube (SWCNT) convening fluid is derived using the Euler-Bernoulli beam model. The nonlinear self-sustained vibrations of SWCNT are described by two nonlinear partial differential equations (PDE) with respect to longitudinal and transversal displacements. The Galerkin technique is applied to derive the nonlinear ordinary differential equations, which describe the longitudinal-flexural self-sustained oscillations. The infinite sequence of the period-doubling bifurcations of the longitudinal-flexural self-sustained vibrations is analyzed numerically.