Nonlinear Dynamic Behavior of Hyperbolic Paraboloidal Shells Reinforced by Carbon Nanotubes with Various Distributions

The analytical solution of the nonlinear dynamic behavior of CNT-based hyperbolic paraboloidal shallow shells (HYPARSSs) with various distribution shapes is presented. A theoretical model was created for HYPARSSs reinforced with CNTs using the von Kármán -type nonlinearity. Then the nonlinear basic equations are reduced to ordinary nonlinear differential equations using Galerkin methods and the correlation for frequency-amplitude relationship is obtained using the Grigolyuk method. In addition, the nonlinear frequency/linear frequency (NL/L) ratio is determined as a function of amplitude. Comparisons with reliable results in the literature were made to test the accuracy of the formulas. Finally, a systematic investigate is performed to control the influences of CNTs in the matrix, CNT distribution types and nonlinearity on the vibration frequency-amplitude relationship.