Vibration analysis of cantilever FG-CNTRC trapezoidal plates

In this paper, a numerical solution is presented for free vibration analysis of cantilever functionally graded carbon nanotube-reinforced trapezoidal plates. The plate is modeled based on the first-order shear deformation theory, effective mechanical properties are estimated according to extended rule of mixture, and the set of governing equations and boundary conditions are derived using Hamilton’s principle. Generalized differential quadrature method is employed, and natural frequencies and corresponding mode shapes are derived numerically. Convergence and accuracy of the solution are confirmed, and effect of various parameters on the natural frequencies is investigated including geometrical characteristics, volume fraction and distribution of carbon nanotubes. Because of similarity of the studied model with the wing, tail and fin of aircrafts and missiles, results of this paper can be useful in design and analysis of aeronautic vehicles in the near future. It is worth mentioning that results of this paper may serve as benchmarks for future studies.