Abstract
Present study considers the longitudinal dynamic analysis of carbon nanotubes which has been modeled as an axially functionally graded Rayleigh-Bishop rod with the help of nonlocal stress gradient elasticity theory. Governing equation of motion and boundary conditions for the axial dynamics of nanorod have been obtained with variational formulation. Ritz method has been used in the solution of the problem. Effects of lateral inertia and transverse deformation of carbon nanotubes, material composition properties and grading power-law index on the axial dynamics response have been investigated. Mode shapes of functionally graded Rayleigh-Bishop nanorod have been depicted in various cases. Boundary conditions and power-law index have important effect on dynamics of axially graded Rayleigh-Bishop nanorod. Present results could be useful at designing of nano-electromechanical devices.
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