Analytical Modeling for Transverse linear and Nonlinear Vibrations of Glass Fiber/Epoxy Composites Reinforced with Carbon Nano Particles

In this research, the transverse vibrations of the fiber glass composite plate reinforced with carbon nano particles have been investigated. For this purpose, the equations of motion of the composite plate have been written based on the third-order shear deformation theory and Glerkin method, and the linear natural frequency of the plate has been extracted. To obtain the nonlinear natural frequency, the method of multiple scales has been used. Then the sheet has been reinforced using two types of nanoparticles and the effect of these nanoparticles and their mass percentage on the linear natural frequency has been investigated. Finally, the effect of the geometrical parameters including the thickness and the ratio of the length to the width of the sheet has been studied. By reinforcing the composite plate with carbon nanoparticles and by increasing the ratio of the length to the width of the plate, the natural frequency of the plate increases, but the increase in the mass percentage of carbon nanoparticles and the increase in the thickness of the plate leads to a decrease in the natural frequency.