Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Abstract

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes (CNTs) are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems. Therefore, the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscous fluid and supported on a nonlinear elastic foundation. The proposed model is based on nonlocal Euler–Bernoulli beam theory. The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation, respectively. A detailed parametric study is reported into how the nonlocal parameter, foundation coefficients, fluid viscosity, and amplitude and frequency of the external force influence the nonlinear dynamics of the system. Subharmonic, quasi-periodic, and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories, frequency-response curves, bifurcation diagrams, phase portraits, power spectra, and Poincaré maps. Also, the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.