We investigate a model of a nonuniform bidirectional functionally graded (BDFG)
nanotube, based on refined beam theory in the framework of nonlocal strain gradient
theory. Material properties change smoothly in the radial and axial direction of the
nanotube, based on the power-law distribution. We obtain equations of motion by
using Hamilton’s principle, and eigenvalues through Galerkin’s method. We also
investigate the impact of temperature. The dynamic response of the nonuniform
BDFG nanotube, not considered in the past, will be a topic of consideration. The
main consideration is how the geometrical coefficient has an effect on the natural
frequency, i.e., how increasing the slope of the nanotube has impact on the
natural frequency. We also consider the critical temperature load, as well as
the influence of the nonlocal and strain gradient parameter on the natural
frequency. Finally, we observe the effect of the power-law indices on the natural
frequency.
Keywords
nanotube, vibration, nonuniform, bidirectional functionally
graded materials, temperature effect