Free vibration analysis of laminated CNTRC plates using the pb2-ritz method / Dang Xuan Hung, Tran Minh Tu and Tran Dai Hao

This paper presents the free vibration analysis of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates. The CNTRC layer consists of single-walled carbon nanotubes (SWCNTs) as reinforcement and polymer as a matrix. The material properties are determined according to the extended rule of mixture. Four different patterns of SWCNTs distribution across the thickness of individual layers are considered. Based on the first-order shear deformation theory (FSDT), the equations of motion are derived and then solved by employing the pb2-Ritz method. The accuracy of the present approach is verified by comparing the obtained results with those available in the literature and commercial ANSYS software. The significant influences of CNT volume fractions, CNT distribution patterns, plate aspect ratio, plate width-to-thickness ratio, and boundary conditions on the non-dimensional fundamental frequency of symmetric and anti-symmetric laminated FG-CNTR plates has been proven through the numerical examples. Furthermore, the influence of lamination schemes, CNT fiber orientation and the number of layers is also investigated.