Free vibration of functionally graded carbon nanotube-reinforced composite damping structure based on the higher-order shear deformation theory

Multi-phase functionally graded carbon nanotube-reinforced composite damping structure (FG-CNTRCDS) excels other composite structures in that it inherits the excellent performance of the functionally graded carbon nanotube-reinforced composite, and exhibits an improved damping performance due to the added viscoelastic damping films. Despite its superior properties, investigations on dynamic properties of the FG-CNTRCDS under clamped boundary conditions are still lacking. Aiming at filling this gap and paving the way to accurately design and analyze the FG-CNTRCDS, a dynamic analytical model, which is based on the higher-order shear deformation theory to formulate governing equations for predicting free vibration of FG-CNTRCDS, has been established. The analytical solution that satisfies clamped boundary conditions is obtained using the Rayleigh-Ritz method. The existing analytical results from the literature have been used to verify the correctness of the theoretical model. In addition, effects of various structural parameters (such as volume fraction and core-to-skin thickness ratio) on dynamic performance have been investigated. Here, the dynamic performance refers to the first-order natural frequency and the first-order loss factor.