Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates

• Published in: Computational materials science Vol. 50; no. 3; pp. 1022 - 1029
• Main Authors: Shen, Hui-Shen, Zhang, Chen-Li
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 2011; Elsevier
• Subjects: Bending; Carbon nanotube; Condensed matter: structure, mechanical and thermal properties; Elastic foundation; Exact sciences and technology; Foundations; Mathematical models; Mechanical and acoustical properties of condensed matter; Mechanical properties of nanoscale materials; Nanostructure; Nonlinear bending; Nonlinear vibration; Nonlinearity; Nonlocal beam model; Physics; Postbuckling; Single wall carbon nanotubes; Small scale; Carbon nanotube; Nonlinear bending; Elastic foundation; Nonlocal beam model; Nonlinear vibration; Postbuckling; Free vibration; Scale effect; Carbon nanotubes; Beam(mechanics); Singlewalled nanotube; Non linear elasticity; Temperature effects; Bending; Miniaturization; Non linear effect; Buckling
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2010.10.042

► The small scale parameter e 0 a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of SWCNTs resting on an elastic foundation. In contrast, it increases and reduces the nonlinear to linear frequency ratios slightly for the nanobeam with immovable and movable end conditions, respectively. ► The effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of SWCNTs resting on an elastic foundation. Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for single-wall carbon nanotubes (SWCNTs) resting on a two-parameter elastic foundation in thermal environments. The SWCNT is modeled as a nonlocal nanobeam which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of both SWCNTs and the substrate are assumed to be temperature-dependent. The governing equation that includes beam–foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e 0 a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of SWCNTs resting on an elastic foundation. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of SWCNTs resting on an elastic foundation.