An investigation of the nonlinear forced vibrations of carbon nanotube reinforced microplates in contact with static liquid and under mechanical force

This paper discusses the nonlinear dynamic behavior of nanocomposite microplates reinforced with carbon nanotubes in contact with static fluids. Equations of motion are derived using the first-order shear deformation theory of plates and considering the size effects and large deformations. Effective mechanical properties are determined by applying the law of mixtures. By use of the Galerkin method, the nonlinear equations governing motion are discretized and the numerical solution is obtained. The results have been verified and the effect of micro-plate geometrical characteristics, small size parameter, fluid height and weight fraction of the carbon nanotubes studied on natural linear and nonlinear frequencies and the dynamic response has been evaluated. The results indicate that the natural frequency of the system decreases with increasing fluid height. The reinforcement of microplates by carbon nanotubes also results in a softening of the stiffening behavior of the spring and a substantial bending of the response curve. Depending on the excitation frequency, this bending may result in jump instability. By examining the time response, phase, and Poincaré map of the system, periodic, quasi-periodic, and chaotic vibration behavior can be observed.