Free vibration analysis of functionally graded carbon nanotubes reinforced composite skew folded plates using the isogeometric approach

In this research, an approach based on the isogeometric method is developed to study the free vibration behavior of functionally graded carbon nanotubes reinforced composite skew folded plates. In this method, non-uniform rational B-splines basis functions are used for approximation of the geometry as well as the displacement field. The plates are reinforced by single-walled carbon nanotubes which are assumed to be graded through the thickness direction with different distribution patterns. The effective mechanical properties of composite skew folded plates are captured by the modified rule of mixtures approach. Modeling of the skew folded plate is accomplished by two non-uniform rational B-splines patches which is one of the strengths of the research. The equations of motion of each patch are derived based on classical plate theory and then are discretized using non-uniform rational B-splines basis functions. The final form of the discretized equations is generated after the transformation of the element matrices of each patch and then applying the continuity conditions along the boundary of the patches with the aid of the bending strip method. Afterward, several numerical examples are provided to prove the accuracy and reliability of the proposed formulation. The results exhibit that the present approach can precisely predict the natural frequencies of skew folded plates with a low computational cost. Eventually, a set of new results are presented for different geometrical and material parameters of the skew folded plate.