Isogeometric free and forced vibration analyses of FG-CNTs plates based on a logarithmic higher order shear deformation theory

Document Type : Research Paper


Department of Mechanical Engineering, Islamic Azad University, Lamerd, 7434155388, Iran



This paper develops the new logarithmic higher order shear deformation theory (LHSDT) incorporating isogeometric method for free and forced vibration analyses of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) plates. In this theory, a logarithmic function is employed to approximate the distribution of shear strains along the plate thickness which satisfies the condition of zero-tractions on the top and bottom surfaces of the plate. It is assumed that the plate is fabricated from a mixture of carbon nanotubes (CNTs) and a polymetric matrix. The CNTs are either uniformly distributed or functionally graded (FG) along the thickness direction of the plate. The modified rule of mixture scheme is applied to estimate effective mechanical properties of FG-CNTRC plates. The governing equations are derived from the Hamilton’s principle. Furthermore, the Newmark approach is utilized to predict the temporal response of FG-CNTRC plates under different transverse dynamical loadings. The applicability and efficiency of the present formulation in predicting vibrational characteristics of FG-CNTRC plates is investigated through an extensive set of numerical examples considering different configurations of the plate. It is revealed that the computed results are in excellent agreement with other solution methods extracted by 3D model as well as other plate theories. Eventually, a detailed parametric study is conducted to explore the influence of related parameters on the natural frequencies and temporal response of FG-CNTRC plates.