Semi-analytical solutions to buckling and free vibration analysis of carbon nanotube-reinforced composite thin plates

The multi-term Kantorovich-Galerkin method is proposed to investigate buckling and free vibration behavior of thin carbon nanotube-reinforced composite (CNTRC) plates with the classical plate theory. The properties of CNTRC are determined with the extended rule of mixture. The transverse displacement is expressed in a sum of products of characteristic beam functions in one direction and unknown functions in the other. By applying the Galerkin technique, the governing partial differential equation is reduced to the ordinary differential equations which are then solved through the state-space approach. Non-dimensional buckling loads and frequencies of CNTRC plates with different boundary conditions are obtained, and the effects of number of approximation terms, CNT distribution, CNT volume fraction, aspect ratio, and thickness-to-width ratio are examined. It is shown that the exact solutions can be found using the present method for the CNTRC plates with two opposite sides both simply-supported, as well as the semi-analytical solutions for the ones with two opposite sides both clamped and one clamped the other simply supported.