Vibrations of Three-Phase Nanocomposite Thick Cylindrical Shells Reinforced with Cnts and Time-Dependent Viscoelastic Matrix

In this study, the free vibration of multiscale closed cylindrical shells reinforced with carbon nanotubes and glass fibers is investigated. The governing equations are derived based on Reddy’s higher-order shear deformation theory (HSDT) and Hamilton’s principle, and solved using the Navier analytical method suitable for simply supported boundary conditions. Subsequently, the effects of various parameters, including geometric ratios, volume fractions of nanotubes and glass fibers, distribution coefficient, as well as time and relaxation time, on the dimensionless natural frequencies are examined. The results indicate that increasing the percentages of nanotubes and glass fibers enhances the effective elastic modulus and raises the frequencies, whereas the viscoelastic behavior of the polymer matrix causes a gradual decrease in the natural frequencies over time. Furthermore, it is found that the circumferential mode shapes have a significant influence on the trend of frequency variations. A comparative study with results available in reliable references confirms the high accuracy and reliability of the present model.