Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels

In this study, free vibration characteristics of composite plates reinforced with single walled carbon nanotubes is investigated. Distribution of the carbon nanotubes through the thickness of the panel may be uniform or functionally graded. Properties of the composite media are obtained according to a refined rule of mixtures approach which contains the efficiency parameters. First order shear deformation shell theory and Donnell-type kinematic assumptions are used. To establish the eigenvalue problem of the system, the energy based Ritz method with Chebyshev polynomials as the basis functions is implemented. The resulting eigenvalue problem is solved to obtain the natural frequencies of the system as well as the associated mode shapes. After performing comparison studies for the simpler cases, numerical results are given for vibration characteristics of carbon nanotube reinforced cylindrical panels. Numerical results reveal that, frequencies of the panel are dependent to both, volume fraction of carbon nanotubes and their distribution pattern across the thickness. Increasing the volume fraction of carbon nanotubes increases the frequencies of the panel.