In this article, the effects of carbon nanotubes distributions on natural frequencies are studied for a functionally graded nanocomposite thick hollow cylinder reinforced by single-walled carbon nanotubes using a hybrid mesh-free method. The FG nanocomposite cylinder is excited by a shock loading, which is applied on the inner surface of cylinder. The first natural frequency is obtained for various nonlinear grading patterns and distributions of the aligned carbon nanotubes. The effects of various nonlinear grading patterns on natural frequency values are obtained and discussed in detail. The presented hybrid mesh-free method is based on generalized finite difference (GFD) method for spatial coordinates and Newmark finite difference (NFD) for time domain. To obtain the dynamic behavior and also first natural frequency, time histories of displacements are transferred to frequency domain by fast Fourier transformation (FFT) technique. Numerical results demonstrate the efficiency of the proposed method in frequency domain analysis for functionally graded nanocomposites reinforced by carbon nanotube (FGNRCN).

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