The Effect of Volume Fraction of Single-Walled Carbon Nanotubes on Natural Frequencies of Polymer Composite Cone-Shaped Shell Made from Poly(Methyl Methacrylate)

Abstract

In this paper, the effect of volume fraction of single-walled carbon nanotubes on natural frequencies of polymer composite cone-shaped shells made from Poly(Methyl Methacrylate) (PMMA) is studied. In order to determine the characterization of materials reinforced with nanoparticles, the molecular dynamics and mixture rule has been used. The motion equations of composite shell based on the classical thin shells theory using Hamilton’s principle are obtained. Then, using the Ritz method, approximate analytical solution of the natural frequency is presented. Results indicate that the nanotubes have a noticeable effect on the natural frequencies.