VIBRATION ANALYSIS OF ELASTICALLY RESTRAINED DOUBLE-WALLED CARBON NANOTUBES ON ELASTIC FOUNDATION SUBJECTED TO AXIAL LOAD USING NONLOCAL SHEAR DEFORMABLE BEAM THEORIES

摘要: Abstract In the context of nonlocal continuum theory, seeking an analytical solution to equations motion stocky double-walled carbon nanotubes (DWCNTs) with arbitrary boundary conditions is a very problematic task. Thereby, proposing efficient numerical techniques for frequency analysis and optimal design such nanostructures great advantageous. Herein, free transverse vibration elastically supported DWCNT embedded in elastic matrix under initial axial force interest. To this end, equivalent structures (ECSs) associated innermost outermost tubes are taken into account. The interaction its surrounding modeled using lateral rotary continuous springs. Through consideration interlayer van der Waals forces via spring system, two appropriately interacted. Using Hamilton's principle, dimensionless DWCNTs established Rayleigh, Timoshenko, higher-order beam theories. unknown fields each model discretized spatial domain reproducing kernel particle method. After tedious calculations, set eigenvalue pertinent extracted numerically solved. convergence checks proposed models predicting flexural frequencies carried out. obtained results also compared those other works reasonably good agreement achieved. various studies, influences slenderness ratio, ratio mean radius thickness ECSs, small-scale parameter, force, rotational stiffness on carefully examined different conditions. capabilities capturing discussed as well.