The aim of this paper is to fabricate a sound absorber flexible semi-open cell polymeric foam based on polyether urethane (PEU) with carboxylic functionalized multi-walled carbon nanotubes (COOH-MWCNTs) as an energy decaying filler at low loadings up to 0.20 wt. %. This paper provides the relationship between the mentioned foam microstructure via field emission scanning electron microscopy and different acoustical and non-acoustical properties of PEU/COOH-MWCNT composites. Addition of just 0.05 wt. % COOH-MWCNTs enhanced the sound absorption coefficient of the mentioned nanocomposite foam over the entire frequency range. Raman spectra revealed the better dispersion of COOH-MWCNTs in the PEU matrix leading to more stress transfer between them to cause a significant dissipation of energy.

In this paper, a detailed theoretical study on the dispersion of waves in carbon nanotubes (CNTs) is presented. For this purpose, CNTs are considered as nonlocal elastic thin cylindrical shells. The Eringen’s nonlocal elasticity theory is used for modeling the microstructure of CNT such that the proximity of the mathematical model to the actual atomic structure of CNT is retained. The results are compared with the results that are obtained based on the second-order strain-gradient elasticity (SG) theory. It has been shown that the SG theory is the first approximation of nonlocal continuum elasticity (NC) theory, which is used in the present paper. Also, it has been shown that the bending rigidity has important effect in the dispersion of waves in CNTs.

In this paper, an exact formula is obtained for the inner diameter of double-walled carbon nanotube (DWCNT) as a function of its higher radial breathing mode (RBM) frequency, using the symbolic package of maple software. Its outer diameter is obtained from the inner diameter formula by considering the constant interlayer spacing between two tubes of DWCNT. For this purpose, DWCNT is considered as double concentric elastic thin cylindrical shells, which are coupled through the van der Waals (vdW) forces between two tubes. Lennard-Jones potential is used to calculate the vdW forces between tubes. The advantage of this analytical approach is that in the double concentric elastic shell model all degrees of freedom in the vibrational analysis of DWCNTs are considered. To demonstrate the accuracy of this work, the relationship between RBM frequency of a single-walled carbon nanotube and its radius is deduced from the DWCNT formula that is well consistent with other publications. To illustrate the application of this approach, the diameters of DWCNTs are obtained from their known RBM frequencies which show an excellent agreement with the available experimental results. Also, the influence of changing the geometrical and mechanical parameters of a DWCNT on its RBM frequencies has been investigated.