Dynamical parametric instability of carbon nanotubes under axial harmonic excitation by nonlocal continuum theory

• Parametric instability of double-walled nanotube is studied.
• Critical equation is derived and instability condition is presented.
• Parametric instability becomes more obvious with matrix stiffness decreasing.

Structures under parametric load can be induced to the parametric instability in which the excitation frequency is located the instability region. In the present work, the parametric instability of double-walled carbon nanotubes is studied. The axial harmonic excitation is considered and the nonlocal continuum theory is applied. The critical equation is derived as the Mathieu form by the Galerkin's theory and the instability condition is presented with the Bolotin's method. Numerical calculations are performed and it can be seen that the van der Waals interaction can enhance the stability of double-walled nanotubes under the parametric excitation. The parametric instability becomes more obvious with the matrix stiffness decreasing and small scale coefficient increasing. The parametric instability is going to be more significant for higher mode numbers. For the nanosystem with the soft matrix and higher mode number, the small scale coefficient and the ratio of the length to the diameter have obvious influences on the starting point of the instability region.

From the results, the influences of the van der Waals interaction on the parametric instabilities and the instability regions can be shown.Figure optionsDownload as PowerPoint slide