Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory

Abstract

The effects of flow velocity on the vibration frequency and mode shape of the fluid-conveying single-walled carbon nanotube are analyzed using nonlocal elastic theory. Results show that the frequency and mode shape are significantly influenced by the nonlocal parameter e 0 a / L. Increasing the nonlocal parameter decreases the real component of frequency and the decrease is more obvious for a lower flow velocity and a higher-order mode. In addition, a higher mode shape is observed with increasing the value of e 0 a / L. When a critical flow velocity is reached, the combination of first and second modes takes place. The mode shape for the combination is large relative to mode 3 due to the coupled frequency effect, especially including negative imaginary frequency. Furthermore, the mode shape of the combination increases as the nonlocal effect increases.

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.…”

Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

“…One feature of all these theories is that they include one or several internal characteristic lengths and the particles influence one another by long range inter-atomic interactions. However, Eringen's differential form of gradient elasticity has received considerable attention to study the static and dynamic characteristics of micro/nano-structures [18][19][20] for its accurate prediction of vibrational behaviors. The nonlocal elasticity theory assumes the stress at a point is a function of the strains at all other points in the body.…”

Free vibrations analysis of fluid conveying nanobeam based on nonlocal elasticity theory

“…Bu çalışmadan sonra, birçok araştırmacı nano yapıların analizinde Eringen'in yerel olmayan modelini kullanmıştır. Akış hızının, akışkan taşıyan TDKNT titreşim frekansı ve mod yapısı üzerindeki etkileri yerel olmayan elastisite teorisi kullanılarak analiz edilmiştir [8]. Bu çalışmanın sonuçları, yerel olmayan parametre ( 0 / )'nin frekans ve mod yapılarında önemli ölçüde etkili olduğunu göstermektedir.…”