Vibration of Axially Strained Triple-Wall Carbon Nanotubes

A comprehensive study is conducted on the vibration of axially strained triple-wall carbon nanotubes (TWCNTs). The Flugge shell theory is used, which largely improves the accuracy and enhances the scope of the research. It is found that the tensile or compressive axial strain can strengthen or weaken the structural rigidity of a TWCNT and thus, substantially up- or down-shift its fundamental frequency. The strongest effect occurs for the lowest frequency associated with bending mode with a circular cross-section and radial modes with two to three circumferential waves depending on the radius and axial wavelength of TWCNTs. In addition, torsional, longitudinal or intertube radial modes largely controlled by the material constants or the interlayer van der Waals interaction coefficient are insensitive to the initial axial strain.