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In this research, a three dimensional analytical method is presented for predicting the dynamic properties of polymer nanocomposites. In the present method elastic-viscoelastic correspondence principle is applied on the simplified method of cell, and loss modulus, storage modulus, loss factor and Hysteresis loop are obtained using energy method as well as force balance method. The considered nanocomposite possesses Polypropylene as a matrix reinforced by vapor grown carbon fibers. The rrepresentative volume element consists of three isotropic phases including fiber, interphase and matrix with linear viscoelastic behavior based on Zener model. Furthermore the nanocomposite constituents dynamic properties are extracted in frequency domain by employing Fourier transform method and Schapery model First to assure the validation of the model, the results are compared with experimental results. Parametric studies such as the effects of number of subcells, fibers volume fraction (FVF) and aspect ratio, matrix/fiber link strength factor and interphase loss factor on the nanocomposite dynamic properties are investigated.. Obtained results reveal that the presented method has acceptable speed and accuracy. Moreover fiber aspect ratio and FVF increasing leads to decrease the nanocomposite hysteresis loop area, subsequently its damping capacity reduces. Interphase also contains considerable effects on the nanocomposite dynamic properties, so its modeling has a great importance.

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In this paper, a new model for estimation of the electrical conductivity of polymer carbon nanotube (CNT) nanocomposites based on the conventional power-law model and Halpin-Tsai formulation has been proposed. Halpin-Tsai model was originally presented to calculate the tensile modulus of composites, which can be modified for estimation of the electrical conductivity by replacing the electrical parameters. The nature of “b” exponent in power-law model is defined according to CNT dimensions, CNT electrical conductivity and the interphase thickness and also the impacts of these parameters on the “b” and the electrical conductivity of nanocomposite are taken into consideration. The developed model interprets that the electrical conductivity of polymer-CNT nanocomposite increases as the concentration, length and electrical conductivity of CNT and the interphase thickness increase. Furthermore, reduction in CNT diameter and waviness results in growth of nanocomposite electrical conductivity. In order to validate the developed model, nanocomposite samples with different volume fractions were produced by solid-state technique of the melt-blending method. The results of calculations and experimental procedure show good agreement.