Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method

Abstract

This paper presents a nonlocal sinusoidal shear deformation beam theory (SDBT) for the nonlinear vibration of single walled carbon nanotubes (CNTs). The present model is capable of capturing both small scale effect and transverse shear deformation effects of CNTs, and does not require shear correction factors. The surrounding elastic medium is simulated based on Pasternak foundation. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the CNTs are derived using Hamilton's principle. Differential quadrature method (DQM) for the natural frequency is presented for different boundary conditions, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory (TBT). The effects of nonlocal parameter, boundary condition, aspect ratio on the frequency of CNTs are considered. The comparison firmly establishes that the present beam theory can accurately predict the vibration responses of CNTs.