Pressure dependence of the instability of multiwalled carbon nanotubes conveying fluids

Abstract

Based on an elastic beam model, the instability of multiwalled carbon nanotubes (MWCNTs) induced by the moving fluid inside is investigated. At critical flow velocities, the MWCNTs become unstable and undergo pitchfork bifurcation and subsequently Hopf bifurcation. These critical velocities are found to increase very quickly with respect to decreasing inner radius and are inversely proportional to the length-toouter-radius ratio. The effect of the van der Waals (vdW) interaction between tubes is investigated and it is found that the vdW interaction can enhance the stability of MWCNTs in general, but the vdW interaction reduces the stability capacity of MWCNTs with very small inner radius.

Size-dependent vibration characteristics of fluid-conveying microtubes

“…Microbeams/nanobeams have become one of the major structures used widely in micro-electronic-mechanical systems (MEMS) and nanotechnology, such as those employed in sensors, actuators, fluid storage, fluid transport and drug delivery [see, e.g., Moser and Gijs (2007), De Boer et al (2004), Yoon et al (2005), Reddy et al (2007), He et al (2008), Lee and Chang (2008), Kuang et al (2009)]. In such applications, the thickness of the beam-type structures is typically on the order of microns or even nanometers (Park and Gao, 2006).…”

Longitudinal-Flexural Self-Sustained Vibrations of Nanotube Conveying Fluid

“…The characteristic exponents are determined from the following eigenvalue problem: * * FINITE DEGREES OF FREEDOM NONLINEAR DYNAMICAL SYSTEM In order to study the self-sustained vibrations of the system (14) the finite degrees of freedom model is derived. Then the flexural displacements are expanded in the form (15) and the longitudinal displacements take the form:…”

“…The model of vibrations of triple-walled carbon nanotubes (CNT) conveying fluid is obtained on the basis of the Euler-Bernoulli beam model in the paper [14]. The model of the vibrations of the multi walled carbon nanotubes conveying fluid is derived in the paper [15]. The Timoshenko beam model is used to describe the multi-walled carbon nanotubes conveying fluid by Khosravian, Rafii-Tabar [16].…”

Microfluid-induced vibration and stability of structures modeled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory

“…It ought to be mentioned that, in the past years, the theoretical models for vibration properties of nanoscale pipes/ tubes containing internal fluid flow have also attracted many researchers (see, e.g., Yoon et al 2005;Natsuki et al 2007;Reddy et al 2007;Chang and Lee 2009;He et al 2008;Wang and Ni 2009;Wang et al 2008;Lee and Chang 2008;Wang 2009; and several other references cited therein). In these studies, the effects of internal fluid flow velocity on the natural frequencies and instability of nanotubes/nanopipes has been analyzed, displaying some fundamental vibration properties of such nanostructures.…”

“…In these studies, the effects of internal fluid flow velocity on the natural frequencies and instability of nanotubes/nanopipes has been analyzed, displaying some fundamental vibration properties of such nanostructures. The available theoretical models developed for vibration analysis of fluid-containing nanopipes may be grouped into two: the classical continuum beam/shell theoretical models (see, e.g., Yoon et al 2005;Natsuki et al 2007;Reddy et al 2007;Chang and Lee 2009;He et al 2008;Wang and Ni 2009;Wang et al 2008) and the nonlocal theoretical models (see, e.g., Lee and Chang 2008;Wang 2009). The classical continuum theoretical models, as the name implies, presume that the materials of the nanopipes and the internal fluid are essentially continuous; physically, the continuum models are not able to exactly describe the properties of nanoscale structures, since the material nanostructure becomes increasingly important and its effect can no longer be ignored.…”