A smoothed finite element formulation using zig-zag theory for hybrid damping vibration control of laminated functionally graded carbon nanotube reinforced composite plates

The paper presents an efficient numerical approach to deal with the hybrid damping vibration control of laminated functionally graded carbon-nanotube reinforced composite plates (FG-CNTRC) structures. In order to evaluate the damped response, a smoothed finite element model has been derived to simulate the laminated FG-CNTRC plate integrated with active constrained layer damping (ACLD) treatment patches consisting of 1-3 piezoelectric composite (1-3 PZC) layer and a viscoelastic layer. The constrained layer of the ACLD patch is modeled as viscoelastic materials by using the complex modulus. In order to enhance the efficiency of the numerical approach, the proposed framework integrates the zig-zag theory into the cell-based smoothed discrete shear gap method (CS-DSG3) to help increase the accuracy and reduce the computational cost. The accuracy and reliability of the present study are validated by comparing its numerical results to those of other available numerical methods. Moreover, the effect of CNT distribution, nanotube volume fraction, and CNT orientation on the damping behavior of FG-CNTRC plates are investigated. Additionally, the influence of symmetrical and asymmetrical damping treatment configuration for controlling the vibration is also examined in detail.