A comprehensive study of sound pressure in a finite-length fluid-filled multi-walled carbon nanotube

The aim of this paper is to analyze vibrational behavior and the sound wave propagation in the finite-length fluid-filled multi-walled carbon nanotubes (MWCNTs) and to determine the exact sound pressure load effect on it, and compare it to what has been used by the other researchers. For this purpose, the solution of the modified complex Helmholtz equation is derived by considering the non-rigidity of the CNT and the wave reflections at the open ends of the MWCNT. These investigations are very important for potential application of CNT-filled polymeric foam that is used as sound absorber. In this paper, in formulating the sound pressure load exerted on the innermost tube of the finite-length fluid-filled MWCNT, the following points have been studied for the first time: (i) the energy loss in the fluid, which cannot be ignored in the high frequency analysis; (ii) the non-rigidity of the MWCNT through considering finite acoustical impedance for its walls; (iii) the wave reflections at the open ends of the finite-length MWCNT to calculate the sound pressure load term which is coupled with the dynamic equations of motion for the finite-length fluid-filled MWCNT. The results show that ignoring the mentioned points would cause errors in the prediction of the sound pressure load exerted on the finite-length fluid-filled MWCNT.