Size-dependent linear and nonlinear vibration of functionally graded CNT reinforced imperfect microplates submerged in fluid medium

Abstract

The linear and nonlinear vibrations of functionally graded carbon nanotubes reinforced microplate (FGCNTRM) submerged in fluid medium have been studied analytically. The primary novelty of this research is to take into consideration the effects of using carbon nanotubes (CNT) and geometric imperfection on the vibrational behavior of microplates submerged in the fluid. Equations of motion are obtained by first-order shear deformation theory of plates and considering the size effects and large deformations. Effective mechanical properties have been determined using the rule of mixtures for four various types of CNT distributions. The nonlinear equations of motion are discretized using the Galerkin method, and the equation response is acquired applying the method of multiple time scales. After verifying the results, the effect of microplate geometric characteristics, small size parameter, fluid height, geometrical imperfection amplitude, weight fraction, and distribution of CNT on linear and nonlinear frequencies as well as amplitude-frequency curves have been studied. The results demonstrate that an increase in fluid height leads to a decrease in the natural frequency. Also, geometric imperfection causes the stiffening behavior of the softening spring and substantially bends the response curve to the right. This bending can induce jump instabilities as the frequency slowly varies.