Vibrations of porous functionally graded CNT reinforced viscoelastic beams connected via a viscoelastic layer

Abstract

This work analyses the vibrational response of porous viscoelastic functionally graded (FG) carbon nanotube (CNT) reinforced double beams. The beams are simply supported, connected through a viscoelastic layer, where four functionally graded patterns of CNT in the thickness directions (uniformly distributed (UD), FG-V, FG-O, and FG-X) are considered. The porosity models considered are UD, PO-V and PO-X. After formulating the coupled equations of motion via an energy-based method, and incorporating the effects of the viscoelastic beams and viscoelastic layers, the equations are solved using an assumed series expansion technique. The equations and solution methodology are verified utilising simplified models from existing literature and also through development of a finite element method (FEM) based simplified model; very good agreement has been achieved. Effects of the stiffness and viscous coefficients of the viscoelastic layer, the structural viscosity parameter of the porous CNT reinforced double beams, the porosity coefficient, and porosity models are examined. Overall, the results indicate that the stiffness and viscous coefficients of the viscoelastic layer have increasing effects on the real and imaginary components of second series fundamental transverse natural frequency of the double beam system, respectively. An increase in the structural viscosity parameter of the porous CNT reinforced double beams leads to an increase in the imaginary components of the fundamental frequencies of both the series. Moreover, a range of different effects on the real and imaginary components of the natural frequencies were noted while varying the porosity coefficient and models. The FG-X CNT porous reinforced viscoelastic double beams with a viscoelastic layer have the highest natural frequencies of all the cases. The study demonstrates the importance of the porosity, viscoelastic layer and viscoelastic material properties on the dynamics of the system.