Sound Wave Propagation in Viscous Liquid-Filled Non-Rigid Carbon Nanotube with Finite Length

   In this paper, numerical results obtained and explained from an exact formula in relation to sound pressure load due to the presence of liquid inside the finite-length non-rigid carbon nanotubes (CNTs), which is coupled with the dynamic equations of motion for the CNT. To demonstrate the accuracy of this work, the obtained formula has been compared to what has been used by other researchers. For this purpose, the solution of the modified complex Helmholtz equation was derived by considering the non-rigidity of the CNT and the wave reflections at the open ends of the CNT for three different liquids with or without considering the relaxation time. The results showed that neglecting the non-rigidity of CNT would cause a decrease on the pressure fluctuations and the pressure associated with the viscosity force of the liquid in the liquid-filled CNT, at both axi-symmetric, and asymmetric cases. Also, it is showed that the viscous liquid in a CNT is a dispersive medium for sound wave propagation and ignoring the energy loss in the liquid in the high frequency analysis and ignoring the non-rigidity of the CNT would cause errors in the prediction of the sound pressure load exerted on the finite-length liquid-filled CNT.