frequency analysis of functionally graded carbon nanotube-reinforced cylindrical panels by mesh-free galerkin method

In this work, the three-dimensional mesh-free (3d-mfree) method is used for free vibration analysis of functionally graded (fg) cylindrical panels reinforced by carbon nanotubes. the material properties of panels are considered to be changed linearly in the thickness direction, and the effective material properties of the panels are estimated by the rule of mixture. five models of carbon nanotubes distribution, including a uniform distributed model and four fg distributed models, are considered. the weak form governing equations of motion are derived using hamilton’s principle, and the moving least squares (mls) approximation is used to construct the 3d-mfree shape functions in cylindrical coordinates. various boundary conditions are considered, and effects of boundary conditions, carbon nanotube distribution, the volume fraction of carbon nanotubes, and the panel geometry on the natural frequencies are studied. the results are compared with other results available in the literature, and a close agreement is observed.