Nonlinear forced vibration analysis of FG-CNTRC sandwich beams with viscoelastic core under various boundary conditions
Hadj Youzera, Sid Ahmed Meftah, Abdelouahed Tounsi, Mohamed Abdelaziz Salem, Khaled Mohamed Khedher, Murat Yaylacı
Abstract
In this study, the nonlinear forced vibration response of sandwich beams with functionally graded face sheets reinforced with carbon nanotubes (FG-CNTRC) and a viscoelastic core is investigated. In the thickness direction, a functionally graded pattern can be followed or a uniform distribution of CNTs can be used throughout the face sheets. By using the higher order zig-zag theory, shear and normal deformations in the core layer are incorporated into the analytical formulation. Geometric nonlinearity is addressed using von Kármán’s strain-displacement relations. Based on Hamilton’s principle, the equations of motion and boundary conditions are developed. The final nonlinear frequency-amplitude equation contains complex parameters due to the damped core modulus. These parameters arise from the geometrically nonlinear coupling associated with the viscoelastic core layer. The technique of harmonic balance is considered. The damping and frequency response curves are analyzed for beams with different boundary conditions. Different support scenarios are analyzed. An extensive parametric analysis is conducted to investigate the impact of carbon nanotubes on the nonlinear vibration of sandwich beams. Results show that peak amplitude increases with higher core-to-skin thickness ratios and nanotube volume fractions, with the FGX-CNTRC beam exhibiting the highest peak amplitude.