Stability analysis of a two-segment constructed nanotube embedded in an elastic matrix

In this paper, the dynamic stiffness method is used to study the stability of a two-segment constructed nanotube embedded in an elastic matrix. The influences of the length ratio, elastic modulus ratio, mass ratio, and elastic coefficient on the stability of the nanotube are investigated. It can be concluded that a change in the elastic coefficient, length ratio, and elastic modulus ratio has no effect on the form of instability of the two-segment constructed nanotube, but a change in the mass ratio has a significant influence on the form of instability of the nanotube. The elastic coefficient of the elastic matrix mainly affects the natural frequency and the critical velocity of the nanotube of the first mode. The change in the length ratio and elastic modulus ratio mainly affects the natural frequency and the critical velocity of the second mode. The mass change in the two materials mainly affects the natural frequency of the nanotube and has no effect on the critical velocity.