This paper is concerned with the free vibration of the fluid-filled multi-walled carbon nanotubes (MWCNTs) with simply supported ends. Based on simplified Donnell’s cylindrical shell model and potential flow theory, the effect of internal fluid on the coupling vibration of the MWCNTs-fluid system is discussed in detail. The results show that the resonant frequencies are decreased due to the effect of the fluid, and the fluid has only a little influence on the associated amplitude ratio in MWCNTs corresponding to the natural resonant frequency (frequency of the innermost tube), while plays a significant role in the associated amplitude ratios corresponding to the intertube resonant frequency. For the natural resonant frequency, the vibration mode is coaxial. However, for the intertube resonant frequency, the system shows complex noncoaxial vibration, which plays a critical role in electronic and transport properties of carbon nanotubes (CNTs).

An analytically nonlocal Euler-Bernoulli beam model for the wave propagation in fluid-filled single-walled carbon nanotube (SWCNT) is established. The governing equations with the nonlocal effects are derived on the variational principle, and used in the wave propagation analysis of the SWCNT beam. Compared with the partially nonlocal Euler-Bernoulli beam models used previously, the analytically nonlocal model presented in the present study predicts well the effects of the stiffness enhancement and the wave damping at the high wavenumber or the strong nonlocal effects area for the fluid-filled SWCNT beam. Though the analytically model is less sensitive than the partially nonlocal model when the moving velocity of the internal fluid is high enough, it simulates more of the high-order nonlocal effecting information than the partially nonlocal model does in many cases.

This paper is concerned with the characteristics of wave propagation in double-walled carbon nanotubes (DWCNTs). The DWCNTs is simulated with a Timoshenko beam model based on the nonlocal continuum elasticity theory, referred to as an analytically nonlocal Timoshenko-beam (ANT) model. The governing equations of the DWCNTs beam consist of a set of four equations that are derived from the variational principle of the beam with high-order boundary conditions at the both ends, in which the effects of the nano-scale nonlocality and the van der Waals interaction between inner and outer tubes are inclusive. The characteristics of the wave propagation in the DWCNTs beam were analyzed with the new ANT model proposed and the comparisons with the partially nonlocal Timoshenko-beam (PNT) models in publication were made in details. The results show that the nonlocal effects of the ANT model proposed in the present study on the wave propagations are more significant because it is in stronger stiffness enhancement to the DWCNTs beam.

A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier-Stokes (N–S) equations by firstly taking fluid-structure interaction (FSI) into account.This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique,in which motions of both the fluid and the solid boundary structures are well described.The flow passage investigated consists of four rectangular plates,of which two are rigid,while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage.Meanwhile,the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates.The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow’s Reynolds numbers of 3000,7000 and 10,000,respectively.Numerical computations show that FSI has significant influence on both the velocity and pressure fields,and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.

A set of nonlinear partial differential equations was used to describe the motions of an internal flowing system,with the consideration of transient fluid structure interaction (FSI).The stabitity characteristics of the system were analyzed on the basis of the nonlinear FSI-equation model.The results show that the stability of the nonlinear FSI system become very complicated because of the influence of strongly couplied interaction between flowing liquid and vibrating pipe.The flowing velocity,pressure,the piping stiffness,and constrained conditions,etc.play a very important role in developing procedure of the system stabilization.In an analysis example given in this paper,for example,when the flowing pressure is comparatively small,the system exhibits flutter instability,and when the flowng pressure is increases to a specified value,a subcritical divergence and a supercritical flutter bifurcation take successively place in the same velocity range.