Thermal Buckling and Vibrational Analysis of Carbon Nanotube Reinforced Rectangular Composite Plates Based on Third-Order Shear Deformation Theory

In this paper, thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) are investigated within the framework of third-order shear deformation theory (TSDT). CNT distribution along the thickness direction of the plate is uniformly or functionally graded. The equivalent properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations of motion are derived using the Hamilton principle. Obtained governing differential equations are analyzed by utilizing Fourier series expansion along the longitudinal and latitudinal direction for simply supported edges boundary conditions whereas for other edges boundary conditions we used the differential quadrature method (DQM) to solve numerically. Validation of the present formulation is assessed by comparing the results with those reported in the open literature. The effect of CNT volume fraction, the different patterns of CNT distribution, temperature difference, aspect ratio, and thickness-to-length ratio on buckling and vibration behavior of carbon nanotube-reinforced composite (CNTRC) plate is studied. The numerical illustration reveals that in the FG-X pattern of CNT distribution natural frequency and thermal buckling load is more significant compared with the other patterns of CNT distribution.

Automated summary

This paper investigates the thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) using the third-order shear deformation theory (TSDT). The CNTs are distributed uniformly or functionally graded along the thickness direction of the plate. The properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations are derived using the Hamilton principle and solved using Fourier series expansion and the differential quadrature method. The study examines the effects of CNT volume fraction, distribution patterns, temperature difference, aspect ratio, and thickness-to-length ratio on the buckling and vibration behavior of the carbon nanotube-reinforced composite plate. The numerical results show that the FG-X pattern of CNT distribution has a significant impact on natural frequency and thermal buckling load.