nonlinear dynamic behavior of hyperbolic paraboloidal shells ‎reinforced by carbon nanotubes with various distributions

The analytical solution of the nonlinear dynamic behavior of cntbased 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 frequencyamplitude 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 frequencyamplitude relationship.