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In this article, the effect of Multi‐walled carbon nanotubes (MWCNTs) on the electrical conductivity and mechanical properties of polycarbonate (PC) toughened with cross‐linked ethylene‐propylene copolymer (EPC) was investigated. The solubility parameters of the PC and EPC were calculated using Hoy methods to clarify the miscibility of the polymer blends. It could be concluded that in the cooled state, the blends form a heterogeneous structure with two separate phases. The tensile, flexural, impact toughness properties of the PC/EPC blend and PC/EPC/MWCNT nanocomposites were carried out to illuminate the optimum concentration of polymer blends and MWCNTs. The 335% increment for the impact strength results appeared with combination of 10% EPC in the PC matrix. The flexural modulus and strength of PC/EPC blend increased by 75.1% and 59.1%, respectively. The Nielsen model was performed to fit the best curve of theoretical simulation to experimental results for elastomeric dispersed in the plastic matrix. Halpin‐Tsai model was applied to estimate the stiffness of nanocomposites blends with different volume fraction and aspect ratio of MWCNTs in the PC/EPC blends. Finally, in the presence of MWCNTs, all nanocomposite samples were semi‐conducting and the percolation threshold of the PC/EPC (10%) blends was between 0.5% and 1.0% MWCNTs. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 44661.

In order to obtain the equations of motion of vibratory systems, we will need a mathematical description of the forces and moments involved, as function of displacement or velocity, solution of vibration models to predict system behavior requires solution of differential equations, the differential equations based on linear model of the forces and moments are much easier to solve than the ones based on nonlinear models, but sometimes a nonlinear model is unavoidable, this is the case when a system is designed with nonlinear spring and nonlinear damping. Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained; homotopy perturbation method (HPM) is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic; the enhanced HPM is used to solve the nonlinear shock absorber and spring equations.