Vibration characteristic of moderately thick functionally graded carbon nanotube reinforced composite skew plates

Abstract

A set of first known vibration frequencies and mode shapes for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) skew plates is presented. Moderately thick skew plates are considered while the first-order shear deformation theory (FSDT) is employed to incorporate the effect of transverse shear deformation. Using the IMLS approximation for the field variables, the discretized eigenvalue equation of the problem is derived via the Ritz procedure. Hence the vibration solutions can be obtained through solving the eigenvalue problem. The FG-CNTRC skew plates are studied with the consideration of different distributions of uniaxial aligned single-wall carbon nanotubes (SWCNTs). Material properties of the FG-CNTRCs are assumed to be graded through the thickness direction according to a linear distribution of the volume fraction of carbon nanotubes. Convergence studies are performed to establish the stability and accuracy of the IMLS-Ritz method. Since no existing results can be found for such FG-CNTRC skew plates, comparison studies can only be made with the isotropic case. Close agreement is found from these comparison studies. The influence of carbon nanotube volume fraction, plate thickness-to-width ratio, plate aspect ratio, and boundary condition on the vibration characteristics of the FG-CNTRC skew plates is examined. It is expected that these first known vibration results should serve as benchmarks for future studies.