Abstract
This paper studies free vibration and bending behavior of singlewalled carbon nanotubes (SWCNTs) embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, non-local theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radiusto-length ratio.
Highlights
In the last two decades, carbon nano-tubes (CNTs) have attracted the attention of many research groups due to its exceptional mechanical, chemical and electrical properties
An accurate solution procedure based on the three-dimensional theory of elasticity for the bending and free vibration analysis of embedded singlewalled carbon nanotubes (SWCNTs) is presented
It is assumed that SWCNT is surrounded by elastic medium with both radial and shear stiffness
Summary
In the last two decades, carbon nano-tubes (CNTs) have attracted the attention of many research groups due to its exceptional mechanical, chemical and electrical properties. Ansari and his co-workers (Ansari, Hemmatnezhad, et al (2011), Ansari and Sahmani (2011)) used various beam models to study the vibration and buckling of single-walled carbon nano-tubes (SWCNTs) Both experimental and atomistic simulations have shown that nanostructures have size-dependent behavior so that well-known classical theories cannot capture this behavior of nanostructures. Many researchers incorporated nonlocal theory into beam model to study vibration, bending and buckling of CNTs. Wang et al (2006) utilized Timoshenko beam theory to analyzed buckling of nano tubes based on nonlocal elasticity. Yan et al (2010) investigated the small scale effect on the buckling behavior of triple-walled carbon nanotubes (TWCNTs) with nonlocal theory They modeled TWCNTs as three elastic shells and considered axial load in thermal environment. Ansari, et al (2011) studied free vibration response of double-walled carbon nanotubes based on Rayleigh–Ritz technique They incorporated nonlocal elasticity theory into the classical Donnell shell theory. The statespace technique is applied to the equations in radial direction and obtain the stress and displacement fields
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
