Analytical solution for free vibration analysis of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation

This paper presents the free vibration analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams resting on elastic foundation, using first order shear deformation beam theory (FSDT). The governing equations and the related boundary conditions are derived using the principal of the minimum total potential energy. The Navier-type solution is used for simply supported boundary conditions, and exact formulas are proposed for the fundamental frequencies. The material properties of functionally graded carbon nanotube-reinforced composites are assumed to be graded through the thickness direction according to linear distributions of the volume fraction of carbon nanotubes. 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